Traffic Density Thresholds for Rail Transit: A Retrospective
publictransit.us Special Report No. 2
 
Leroy W. Demery, Jr. • J. Wallace Higgins • Michael D. Setty • February 15, 2005
 
 
Copyright 2003–2007, Publictransit.us & J. Wallace Higgins
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Abstract
A 1982 report by Pushkarev et al., published by the New York Regional Plan Association, established a minimum traffic density threshold for low-cost light rail transit. Based on economic analysis of operating expense and potential savings in labor, energy and land, Pushkarev et al. concluded that light rail transit could be justified in corridors having a traffic density of 4,000 weekday passenger-miles per mile of route. Independent studies from other developed economies including Japan and Germany, and a historic analysis from the U.S., are found to corroborate this result.
The 1982 report by Pushkarev et al. recommended that U.S. total rail transit route length be doubled over 25 years. The program was not adopted but total rail route length, in operation or under construction, reached the recommended extent by 2004. Pushkarev et al. also estimated potential rail ridership in a number of cities. These forecasts were conservative, as revealed by results in cities that built new rail lines. Pushkarev et al. consistently underestimated weekday traffic density. In most cases, weekday peak-hour passenger volumes equal or exceed the implied minimum levels. These observations fail to support the assertion by Pickrell (1985) that Pushkarev et al. assumed unrealistically high levels of peak period travel.
Critiques of Pushkarev et al. (1982) by Pickrell (1985) and Kain (1988) have major conceptual flaws and technical errors. Such problematic analysis fails to support the findings and conclusions of Pickrell and Kain.
Additional research is indicated to update the findings of Pushkarev et al. using data from LRT facilities opened after 1982, and to establish threshold criteria for enhanced bus and bus rapid transit facilities. The authors believe that the number of U.S. corridors where traffic density justifies enhanced bus service probably numbers in the hundreds, compared to several dozen corridors where traffic density may justify new rail lines not yet built.
 
1. Introduction
Nearly twenty-five years ago, a report authored by Boris Pushkarev, Jeffrey Zupan and Robert Cumella (1982) called for a national rail transit expansion program, estimated to cost $22 billion (1980$s; roughly $50 billion in 2003$s) for construction over 25 years.
The initial report was prepared by the Regional Plan Association, New York, under contract from the Urban Mass Tranportation Administration (U.S. Department of Transportation) and was published late in 1980. Criteria for evaluation among modes included space per passenger, service frequency, labor savings over bus operation, energy savings over other modes, and land savings over freeway construction.
Pushkarev et al. (1982) presented their rail threshold criteria in terms of weekday passenger traffic density – “weekday passenger-miles per line-mile,” or passenger-miles per mile of route per weekday. Pushkarev et al. used this approach because weekday passenger miles could be estimated directly from “origin and destination pairs” by “forecast and analysis zone.” Peak period passenger volume is a function of the above and varies by mode and other factors; as such, peak volume as a measure is inherently less stable than weekday passenger miles (Pushkarev 2004). Weekday traffic density was a fundamentally different measure than those used by previous U.S. studies, and study results were much different.
Pushkarev et al. (1982) found that a weekday traffic density of 4,000 pass-mi per mile of route was sufficient to justify a “very low-capital light rail line.” This finding is remarkably consistent with European and Japanese studies – and with detailed analysis accepted by a U.S. court more than fifty years ago.
However, the findings of Pushkarev et al. (1982) differed substantially from previous U.S. analysis. Many U.S. transportation (i.e. “highway”) professionals, economists and academics responded with skepticism and criticism. In addition, Carter Administration and Reagan Administration officials were not pleased by the recommendation for such a large increase in the mass transit capital program. Donald H. (”Don”) Pickrell authored a 1985 response to Pushkarev et al. (1982) for the Transportation Systems Center, U.S. Department of Transportation. This, together with a 1988 paper by John F. Kain, acquired the cachet of “definitive refutation.”
Despite the apparent widespread concurrence with Kain’s 1988 findings, from 1980 to 2004, the combined route length of U.S. heavy rail transit (HRT) and light rail transit (LRT) lines nearly doubled, bringing total route length to more than 1,400 miles (2,300 km). Additional route length opened after 1980 totals more than 650 miles (1,050 km). This include segments planned for opening in calendar year 2004, and are exclusive of lines reconstructed or rehabilitated. The sum of current U.S. HRT and LRT route length, together with the 145 miles (234 km) currently under construction, is about 1,560 miles (2,520 km). Remarkably, this total is only slightly greater than the total route length recommended by Pushkarev et al. (1982). This fact suggested that a retrospective analysis of the threshold estimates, forecasts and recommendations of Pushkarev et al. might be informative and useful.
This paper outlines the findings of Pushkarev et al. (1982) and provides comparisons with overseas research. The paper also considers the responses by Pickrell (1985) and Kain (1988). It finds major errors in Kain, and conceptual flaws in both. Such problematic analysis fails to support the findings and conclusion of these authors.
 
2.  The Rail Transit Threshold Analysis by Pushkarev et al.
The economic analysis performed by Pushkarev et al. (1982) used travel volume as the primary indicator, specifically the measure “weekday passenger miles per mile of route.” This, they explained, is “both an indicator of transportation related benefits and is reasonably predictable” (Pushkarev et al. 1982, 59). They suggested five “volume-related criteria for the deployment of fixed guideways.” These are:
  1.     Possibility of attaining adequate passenger space and service frequency;
  2.     Possibility of attaining labor savings compared to bus operations;
  3.     Possibility of saving energy compared to modes previously used;
  4.     Possibility of attaining land savings compared to modes previously used;
  5.     Level of investment per unit of service provided (Pushkarev et al. 1982, 59).
The analysis by Pushkarev et al. establishes the threshold traffic density for low-cost light rail transit (LRT) at 4,000 weekday pass-mi per mile of route. Pushkarev et al. (1982) also established threshold criteria for heavy rail transit (HRT), and tentative criteria for automated guideway transit used as “downtown people movers.”
(The present authors use the terms “weekday traffic density” and “passenger-miles per mile of route per weekday” interchangeably. Readers are reminded that conversion to metric units – passenger-kilometers per kilometer of route – does not change the number itself.)
At this density level, “minor labor savings compared to local buses can be realized, but there are no energy savings, and peak period use of land is just about as efficient as that of an arterial street” (Pushkarev et al. 1982, 165).
In other words, Pushkarev et al. (1982) established a weekday traffic density of 4,000 as the nominal break-even point between low-cost LRT and bus. Given a weekday traffic density greater than 4,000, low-cost LRT provides overall cost savings.
The analytical framework used by Pushkarev et al. (1982) remains useful, although details related to certain “input” values are subject to revision. Much more data are available today than 25 years ago regarding energy efficiency, labor requirements and labor productivity for U.S. LRT, to give just three examples.
Another crucial issue revolves around consumer tolerance for peak-period crowding aboard transit vehicles. Outside of the busiest corridors in the most crowded and congested urban centers, it is now clear that U.S. (and Canadian) consumers will not tolerate the loading standards used typically for early planning studies until the mid-1990s. The preponderance of empirical data also indicates that rail transit attracts greater peak-period utilization than buses per unit of “nominal” capacity. This finding is supported by a large quantity of data from cities throughout the U.S. and Canada:
The data also corroborates a 1989 paper by Tennyson:
The following exercise is based on a weekday traffic density of 5,000, supported as the threshold for low-cost LRT by the studies described below.
Traffic density cannot be related to crude boarding counts without reference to
  1. Average travel distance (ATD) per boarding and
  2. Route length.
The relationship among these parameters may be expressed as follows:
Density = (average weekday boardings  * ATD) / route length
Assuming a hypothetical LRT line with a route length of 10 miles and ATD of 5 miles, a traffic density of 5,000 pass-miles per mile of route implies:
5,000 = (x * 5) / 10
x = 10,000 boardings per weekday
For a given traffic density, an inverse relationship exists between ATD and boardings per weekday. In other words, a larger ATD implies a smaller number of weekday boardings.
A low-cost light rail line might be justified economically with fewer than 10,000 boardings per day. Assume a 15-mile route length, a 10-mile ATD (similar to what has been observed in Salt Lake City) and a weekday traffic density of 5,000:
5,000 = (x * 10) / 15
x = 7,500 boardings per weekday
A low-cost LRT line serving two corridors, similar to the initial Sacramento system, would carry a lower ATD and would therefore require a higher number of weekday boardings in order to attain the threshold. Assume a 15-mile route length, a 4.5-mile ATD and a weekday traffic density of 5,000:
5,000 = (x * 4.5) / 15
x = 17,000 boardings per weekday
The relationship between weekday boardings and average travel distance, all else equal, is illustrated in Figure 1 below.
 
 
The fact that 7,500 passengers per weekday, ATD ten miles, represents exactly the same “workload” as 30,000 passengers, per weekday, ATD 2.5 miles, has major implications for transit planning and policymaking. In particular, analysis of ridership forecast accuracy must consider ATD-related issues.
The authors note that the threshold criteria outlined in this paper appear to be nominally independent of route length, at least for short intercity distances. Therefore, a line extending 50 miles between terminals would be justified economically with an average weekday traffic density of 5,000 (assuming that traffic is distributed along the line rather than concentrated into a few short segments). A carefully planned single-track line might be justified with a somewhat lower weekday traffic density. If such a line managed to attract a significant number of long-distance trips, it could be justified with a relatively small number of boardings per weekday. Assume a 50-mile route length, a 35-mile ATD and a weekday traffic density of 5,000:
5,000 = (x * 35) / 50
x = 7,000
Results such as those above arise from economic analysis designed to provide rational comparisons without the distorting effects of subsidies.
It is essential to note that Pushkarev et al. (1982) explicitly avoided the benefit-cost analytical framework:
Attempting to develop any value such as the “full cost” of a mode, or its “total benefit” can easily obscure, rather than illuminate analysis because of the multiplicity of hidden assumptions that have to be made. Instead, the evaluation approach chosen here is first of all discrete, dealing with a few selected objectives one at a time. Second, the approach seeks to stay away from monetary measures as long as possible, focusing instead on physical quantities, such as space, time, labor, energy and land. One can always attach to these quantities any desirable set of prices, if one wishes. Third, the approach concentrates on the easily measurable transportation relation objectives  (Pushkarev et al. 1982, 82).
The focus on physical quantities is the common analytical framework shared by the studies considered below. The authors attribute the remarkable concurrence of results to this framework, which recognizes that real costs are determined by the laws of physics.
 
3.  Rail Transit Threshold Summary
The remarkable corroboration of results among Pushkarev et al. (1982) and other studies is summarized below. Rigorous analysis based on current U.S. conditions is beyond the scope of this paper, but the authors have added comments as appropriate.
A.  Pushkarev, Zupan and Cumella (1982; original report published 1980).
 
Threshold traffic density levels for LRT.
LR-1: A very low-capital light rail line near grade with 4,000 weekday passenger-miles or 5 million annual place-miles per line-mile, allows a construction expenditure of $5 million a mile at 1977 prices, offers minor labor savings compared to local buses but offers no energy savings and no savings in land compared to a local arterial street. Its major justification would have to be in terms of travel speed and convenience.”
[5 million annual place-miles per line-mile is approximately 36,000 vehicle-miles per line-mile; $5 million in 1977$s had about the same purchasing power as $15 million in 2003$s.]
LR-2: A light rail line with considerable grade-separation but no tunnels with 7,200 weekday passenger-miles or 9 million annual place-miles per line-mile, allows a construction expenditure of $9 million a mile at 1977 prices, begins to offer labor savings compared to buses operating at the same speed, uses land during the peak period more efficiently than a local arterial, and begins to offer energy savings.”  
[9 million annual place-miles per line-mile is approximately 64,000 vehicle-miles per line-mile; $9 million in 1977$s had about the same purchasing power as $27 million in 2003$s.]
LR-3: A light rail line with 1/5 of the route in tunnel with 13,600 weekday passenger-miles or 16 million annual place-miles per line-mile, allows a construction expenditure of $17 million a mile at 1977 prices, begins to offer labor savings compared to buses operating at the same speed, energy savings compared to modes previously used, and uses land during the peak period more efficiently than a freeway lane.”
[16 million annual place-miles per line-mile is approximately 114,000 vehicle-miles per line-mile; $17 million in 1977$s had about the same purchasing power as $52 million in 2003$s.]
(Pushkarev et al. 1982, 256-7.)
Threshold traffic density levels for HRT (“rapid transit”).
RT-1: Rapid transit above ground with 15,000 daily passenger-miles or 18 million annual place-miles per line-mile is in scale with prevailing minimum service frequency, allows a construction expenditure of about $18 million a mile in 1977 prices at the median investment level, saves land compared to freeways, saves labor compared to local buses, and can attain modest savings in energy.
[18 million annual place-miles per line-mile is approximately 127,000 vehicle-miles per line-mile; $18 million in 1977$s had about the same purchasing power as $55 million in 2003$s.]
RT-2: Rapid transit up to one-third in tunnel with 24,000 daily passenger-miles or 29 million annual place-miles per line-mile offers more than minimum service frequency, allows a construction expenditure of about $30 million a mile in 1977 prices at the median investment level, saves land compared to freeways, can save labor compared to express buses on freeways, and can attain savings in energy.
[24 million annual place-miles per line-mile is approximately 169,000 vehicle-miles per line-mile; $29 million in 1977$s had about the same purchasing power as $88 million in 2003$s.]
RT-3: Rapid transit fully in tunnel with 29,000 daily passenger-miles or 35 million annual place-miles per line-mile offers good service frequency, allows a construction expenditure of $52 million a mile in 1977 prices with the relaxed 75th percentile investment level (assuming some non-transportation benefits of tunnels), can save labor compared to express buses on busways and can begin to attain energy savings under some conditions.
[35 million annual place-miles per line-mile is approximately 246,000 vehicle-miles per line-mile; $52 million in 1977$s had about the same purchasing power as $158 million in 2003$s.]
(Pushkarev et al. 1982, 250-1.)
Tentative threshold traffic density levels for downtown people movers.
DPM-1: A low-capital peoplemover guideway with about 5,000 weekday passenger-miles, or 6 million annual place-miles per line-mile, allows a construction expenditure of roughly $6 million a mile in 1977 prices using the “median” investment level; its passenger volume is comparable to that of existing systems such as Morgantown and Airtrans; it can begin to attain labor savings compared to downtown buses operating at 6 mph (9.6 km/h) if it is about 3 miles (4.8 km) long or longer; it can begin to use land during peak periods more efficiently than a local arterial; it will not save any energy directly in a downtown setting.”
[DPM-1 implies guideways of a scale used by technologies such as the “German Cabintaxi system and the ‘Project 21’ two-in-one guideway.” No examples were in operation in the U.S. at 1980 (Pushkarev et al. 1982, 264)].
[Pushkarev et al. did not specify DPM vehicle size. $6 million in 1977$s had about the same purchasing power as  $18 million in 2003$s.]
DPM-2: A peoplemover guideway for the currently prevalent rubber-tired vehicles with about 12,000 weekday passenger-miles, or 14 million annual place-miles per line-mile, allows a construction expenditure of roughly $15 million a mile in 1977 prices using the “median” investment level; it begins to attain labor savings compared to downtown buses operating at the same speed if it is about 3 miles (4.8 km) long or longer, or compared to downtown buses at 6 mph (9.6 km/h) if it is shorter; it used land during peak periods more efficiently than a local arterial; it will not save any energy directly in a downtown setting. The cost per mile could easily be some 60 percent greater. The passenger volume shown for the middle criterion is therefore indicated as a range between 12,000 and 20,000 weekday passenger-miles per mile of line.”
DPM-3: A peoplemover guideway described under DPM 2 generally above ground in a downtown setting will begin to offer direct energy savings at volumes in excess of 46,000 weekday passenger-miles or 55 million annual place-miles per line-mile, if no snow melting is required. If the guideway is in tunnel the energy saving threshold rises to 67,000 weekday passenger-miles or 80 million annual place-miles per line-mile; it rises above that level, if the guideway is in the open air and requires snow melting.
(Pushkarev et al. 1982, 265-6.)
Pushkarev et al. (1982) did not address commuter rail explicitly.
Annualized capital cost per passenger-mile, implied by the threshold criteria derived by Pushkarev et al (1982), are illustrated in Figure 2 below. These were derived using the following factors:
--Annual passenger-miles per route-mile = 280 weekday equivalents per year * weekday traffic density (Pushkarev et al. 1982, 166).
--Annualized capital cost, in 1977$s, calculated based on seven percent discount rate and 30-year project life (i.e. criteria used currently for Federal alternatives-analysis purposes). Calculated using "Engineering Economics Calculator."
Readers are reminded once again that annualized costs per passenger-mile presented in Figure 2 are in 1977$s.
 
 
Authors’ comments:
  1. Price escalation in the construction industry from the late 1970s outstripped the general economy-wide inflation rate. Conversions from 1977 dollars, provided above, should therefore be interpreted with care.
  2. The authors believe that relatively higher consumer tolerance for peak-period crowding aboard railcars, revealed by a broad cross-section of data from various U.S. and Canadian cities, is a major issue in the mode choice question. It is therefore worth noting that the definition of “passenger-place” used by Pushkarev et al. (1982) – 5.4 sq. ft. = 0.5 m2 of gross floor space per passenger – implies unrealistically high peak-period crowding.
In the U.S. and Canadian environment, where most consumers have alternatives and are not forced to travel under crush-loading conditions, available data suggest strongly that the threshold of tolerance for crowding aboard rail vehicles lies between 4.0 and 5.0 passengers per meter of vehicle length (pass/m). That for buses is consistently less, slightly below 3.0 pass/m (Demery and Higgins 2003).
The HRT standard of 142 places per vehicle with a gross floor area of 71m2, assuming a 75-foot (23-meter) vehicle length, implies 6.2 pass/m, 25-55 percent greater than the threshold suggested by empirical data.
The LRT standard of 140 places per vehicle with a gross floor area of 70m2, assuming a 92-foot (28-meter) vehicle length, implies 5.0 pass/m, at the upper threshold suggested by empirical data. For 40-foot (12-meter) buses, 63 passengers per vehicle implies 5.2 pass/m, almost 80 percent greater than the threshold suggested by empirical data. For 60-foot (18-meter) articulated buses, 91 pass/veh implies 5.0 pass/m, more than 70 percent greater than the threshold suggested by empirical data. (As noted above, Pushkarev et al. (1982) did not specify DPM vehicle size.)
An important inference is that relatively higher services levels than outlined by Pushkarev et al. (1982) are associated with various traffic levels. The greater willingness of consumers to tolerate peak-period crowding aboard railcars places bus modes at a relative disadvantage. Higher levels of nominal capacity are associated with given consumption (ridership) levels if buses are operated rather than railcars.
Other issues that would need to be addressed during updating or replication of Pushkarev et al. (1982) include:
  1. Relative costs of line and vehicle construction, including labor, energy and materials.
  2. Relative energy consumption, particularly for buses operated with stops spaced 0.5 – 1.5 mile (0.8–2,5 km) apart with a “cruise speed” between stops equivalent to LRT (e.g. 55-65 mph or 90–105 km/h).
  3. Labor (staffing) requirements based on results achieved by U.S. LRT opened from 1982.
  4. Labor productivity for LRT and bus modes, based on results actually achieved from 1982.
B.  Japan – Japanese National Railways Branch Line Closure (1980).
Pushkarev and his colleagues investigated criteria for construction of new rail lines at the same time when Japan struggled with a contrasting issue: closure of uneconomic branch lines.
The Railway Construction Law of 1922 outlined local branches and connections throughout the country, but did not establish priorities. Branch line expansion, halted with the onset of World War II, was resumed in 1951. Motor transport was proliferating but branch line expansion attracted strong political support. The Japanese National Railways management, well aware that new rural lines would be unprofitable, allocated its construction budget among a large number of proposed new lines. This amounted to purposeful postponement of construction. In response, Diet (Parliament) members led by future Prime Minister Kakuei Tanaka secured a change in policy. Responsibility for building new railway lines was handed in 1964 to the new Japan Railway Construction Public Corporation. Thereafter, JRCC built lines with state funds and leased them without charge to JNR. The latter, however, still had to bear branch line operating losses.
JNR began incurring losses from 1964, when branch line losses first exceeded trunk line profits. In 1968, an advisory committee recommended replacement of 83 branch lines totaling 2,600 km (1,600 mi) with bus services. The committee found that, of the existing 20,800 km (12,900 mi) network, 64 percent was suited to rail transport but the remainder, 7,400 km (4,600 mi), was more suitable for road transport. The initial closure proposals generated strong opposition, and JNR stopped the program in 1972 after shedding 11 lines totaling just 120 km (70 miles).
JNR’s financial position worsened steadily through the 1970s, due in part to losses incurred by new JRCC-built branch lines. The government of Prime Minister Masayoshi Ohira suspended further branch line construction at the end of the decade. The “Special Measures to Promote JNR Rehabilitation” law of 1980 ended state support for branch line construction, and permitted JNR to close existing lines carrying a traffic density less than 4,000 pass-km per km of route per day (Aoki et al. 2000, 168; Suga 1998, 3).
Criteria for branch-line closure were refined subsequently, and by 1990 JNR and its successors had closed or spun off 83 lines totaling 3,200 km (2,000 mi).
Authors’ Comments
Working at the same time as Pushkarev et al. (1982), for the opposite purpose, Japanese investigators established the “threshold” traffic density for passenger rail at about the same level. By Japanese convention, “daily” traffic statistics are equal to annual statistics divided by 365. Adjusting upward to account for 300 weekday equivalents per year, the “implied” threshold weekday traffic density becomes 5,000 pass-km per km of route (= the same number of pass-mi per mi of route).
The threshold traffic density for retention of an existing rail line would logically appear to be lower than the threshold density for new construction, because retention does not require new investment.  The subsequent history of the 38 lines of these 83 that were transferred to other operators, however, consistently did include investment that allowed these lines to be operated more efficiently.  Among the changes were centralized signaling and control systems, which eliminated the need for station staff where trains cross, and lightweight railcars designed for one-man operation and on-board fare collection. Only a very small number of the lines closed or spun off had any remaining freight traffic after 1980. Freight traffic was therefore not a factor in most branch line closure decisions.
Pushkarev et al. (1982) were not aware of the Japanese studies described above (Pushkarev 2004). The authors have found no evidence that the Japanese investigators were aware of the work by Pushkarev et al.
C.  Japan – Application Criteria for Urban Transit Modes (ca. 1980).
Development of monorail and automated guideway transit (AGT) technology in Japan during the 1960s and 1970s led to establishment of criteria for application. The “domain of efficiency” for each mode was established based on technical and economic factors. These criteria are well defined but defy straightforward conversion into terms familiar to U.S. planners. As explained above, traffic density cannot be related to crude boarding counts without reference to ATD and route length. Figure 3 below, a reproduction of “Figure 1” from Nehashi (1998), is presented to illustrate criteria based on traffic density.
 
Figure 3.  Urban Transport Traffic Density Criteria - Japan
(Nehashi 1998, 5, Figure 1).
 
Readers should note that the horizontal and vertical scales on the diagram above are non-linear. In addition, “Transport density” refers explicitly to passenger-km per km of route per direction per day. In the following discussion, density values in the above figure have been multiplied by two for consistency of comparison with other studies. Readers are again reminded that 1.) “daily” traffic density refers to the annual statistic divided by 365 per Japanese convention, and 2.) conversion from miles to kilometers or vice versa does not change the value of a traffic-density statistic.
Nehashi (1998) was interested primarily in the threshold criteria for provision of public transport and the domain of application for “New urban transit systems” (the L-shaped dashed line and the grey shaded area in the chart, respectively). Summarizing the implications of Figure 3:
Individual transport (e.g. walking, bicycles, private automobiles) is considered adequate for all trips shorter than 1 km (0.6 mi). Prospective passengers are likely to walk rather than wait for a transit service if the journey time by foot is less than 10 minutes.  Moving sidewalks might be provided in locations where traffic volume is great enough.
For example, no public transportation would be provided where the ATD was 2 km (1.2 mi) and the daily traffic density was less than 2,500. A daily traffic density of 2,500 and an ATD of one mile imply 2,500 boarding passengers per day.
Individual transport is also considered adequate for all trips along corridors where the daily traffic density is less than 4,000. For journeys requiring more than ten minutes by foot, prospective passengers are likely to drive or ride bicycles rather than wait for infrequent transit services. However, some corridors having a daily traffic density less than 4,000 may have sufficient traffic to support transit services operated only during peak periods.  
Buses are economical for daily traffic densities up to 8,000 given a low ATD, or up to 6,000 given a somewhat greater ATD. Bus operation provides no economies of scale (a fact emphasized in Japanese-produced literature, whether in Japanese or English). Therefore, bus operation becomes uneconomical at higher traffic densities. Buses in mixed traffic are relatively unattractive for longer journeys owing to low commercial speed.
(The standard Japanese transit bus is about 35 feet long, eight feet wide and seats 28 passengers. The "maximum load" established under transport laws is 74 passengers, or 6.9 passengers per meter of vehicle length. Articulated buses are not used for urban transport services in Japan.)
Urban Railways: The minimum daily traffic density required to justify urban railway construction (this, in Japan, implies full grade separation) is 20,000 given a relatively low ATD. A relatively higher ATD implies a relatively longer route length, and this is associated with a lower threshold traffic density owing to economies of scale. As explained by Pushkarev et al. (1982, 93-94):
Long rail transit lines inherently tend to have higher output in place-miles per worker than short ones. This is so because their vehicle requirements – and as a result, many labor requirements as well – are set by the peak hour capacity needed at the maximum load point on the downtown edge. Once that requirement is satisfied, running trains for a somewhat longer distance out from downtown and clocking additional place-miles may require only modest added labor.
One critical fact often overlooked in the U.S. is that longer ATD requires a higher number of vehicle-miles to serve a given number of “passengers” or “boardings per route-mile.” If these are not provided, then average vehicle occupancy will increase (more passenger-miles per vehicle-mile), and by implication peak-hour crowding will also increase.
New Urban Transit Systems: The gray-shaded area in the figure above includes traffic density and ATD ranges too great for economical bus operation but too small to justify full-scale urban railways. Technologies include monorail, automated guideway transit (AGT) and aerial cable cars. “HSSTs” refers to the Japanese magnetic levitation technology (“High Speed Surface Transport) developed originally to connect airports with city centers.  “LRTs” refers to upgraded or new street tramway systems using low-floor cars and carrying high volumes of short-distance travel.
It is possible to imagine a fixed-guideway facility that cannot accommodate a sufficiently high traffic density to justify its cost. The best example in the Japanese context is personal rapid transit (PRT), owing to safety standards that preclude close-headway operation.
Highway Bus: This term refers in Japan to express bus services using toll expressways. These are economical for long-distance suburban and intercity travel given daily traffic densities in the range of 4,000 – 6,000.
Shinkansen: In Japan, Shinkansen (“new trunk line”) refers unambiguously to dedicated high speed rail lines. The authors believe that “Shinkansen” in the figure above refers to services on existing high-speed lines to serve long-distance suburban and short-distance intercity travel. These become economical given a daily traffic density greater than 6,000.
Authors’ Comments
Working at about the same time as Pushkarev et al. (1982), with reference to Japanese economic conditions, researchers established the threshold criteria for rail transit at very roughly the same level. However, several additional facts must be kept in mind.
The term “light rail transit” as understood in the U.S., Canada and Europe cannot be applied meaningfully in Japan. LRT implies compatibility with operation on surface streets. There are very few Japanese examples of suburb-to-downtown electric railways that use surface streets for business center (CBD, “central business district”) access. The typical recent U.S. pattern of LRT operation on lightly-used or disused freight rail alignments is also not found in Japan, where a disused rail corridor extending from a major city is almost a contradiction in terms.
“Low-cost LRT,” as outlined by Pushkarev et al. (1982) for the U.S. (“LR-1”), is not a realistic possibility in Japan. As a corollary, the field of application for “New Transit Systems” is greater in Japan than in the U.S., where many cities have rail corridors suitable for use by LRT or commuter rail services.
The high “urban rail” threshold in the diagram above reflects the high costs of constructing urban railways where no available alignment exists. This daily traffic density threshold, converted to weekday traffic density based on 300 weekday equivalents per year, becomes a weekday traffic-density threshold of 24,000, somewhat less than that established by Pushkarev et al. (1982) for full-scale subway lines.
The sharply lower rail threshold given a relatively higher ATD reflects two major factors. First, Japanese cities are relatively compact by comparison with their U.S. counterparts. A line 20 – 30 km (12 – 19 mi) in length is likely to extend into areas where the cost of construction is less than in urban centers, owing to less intensive development. Thus, the overall cost per km of route may be less. Second, longer ATD requires operation of more vehicle-km per boarding passenger. This, in turn, may lead to reduced unit operating costs owing to economies of scale, lowering the traffic-density threshold for rail.
With reference to the U.S., a large daily boarding count is required to justify a short-distance fixed-guideway facility. ATD tends to be low relative to the route length (e.g. 20-30 percent of route length) for CBD circulators and similar facilities. In consequence, traffic density is relatively low and operating cost per passenger-mile relatively high.
(It is, however, possible to operate such a line at a profit if passengers are willing to pay a high per-mile fare for a short trip. The most relevant U.S. example is the Seattle Monorail, which charges $1.50 for a trip of one mile, and recovers all operating expenses from fares. Another factor of importance is that ATD is identical to route length in this case.)
In the U.S., some fixed-guideway facilities carry a relatively long ATD (e.g. 60-70 percent of radial route length). This arises because of high commercial (passenger) speed relative to other modes, station locations away from the CBD that are not well located for short-distance travel, and fare structures that discriminate against short-distance passengers. Traffic density may be relatively high, and operating cost relatively low, even given a modest weekday boarding count. Such facilities therefore do not require a large weekday passenger count (boardings per route-mi) to justify construction. This fact reflects operational efficiency and is independent of revenue issues. (In Japan, distance-based or zone or "stage" fares are long established and universally accepted.)
The diagram above implies that the minimum daily traffic density for rail transport is 4,000 given an ATD greater than 10 km (6 mi). This corresponds to a weekday traffic density of 5,000, not much different than the threshold established by Pushkarev et al. (1982).
D.  Berlin (1991).
A report published in 1991 by the Berliner Senat (the Berlin Senate, or municipal council) stated that LRT becomes more economical to operate than buses when travel demand reaches 5,000 pass-km per km of route per day (Ludwig 1991). It should be noted that motorbuses cost more to operate in Europe than in the U.S. owing to higher fuel prices – three times higher, according to Rode (1999). However, roughly 60 percent of transit operating costs are “staff related” (Apel 1990). This statistic appears to reflect European experience; the American Public Transportation Association estimates that labor expense accounts for 80 percent of U.S. transit operating costs, both for bus and fixed-guideway modes (American Public Transportation Association). Significant upward revision of the threshold to fit “U.S. conditions” might not be justified.
E.  Germany (1993).
Engineering subsidiaries of four large (West) German public transport authorities organized the engineering, operations and maintenance consulting firm of Light Rail Transit Consultants GmbH (LRTC) in 1985 (Company Profile of LRTC). An LRTC handbook published in 1993 presents fields of application and design profiles for four categories of “light rail” systems (Gerndt et al. 1993). These are presented in Table 1 below.
 
Table 1.  Urban Transport Traffic Density Criteria - Germany
   
Similar to Tramway
Similar to Metro
   
Category 1
Category 2
Category 3
Category 4
Criterion for choice of category
MinimumWeekday transport performance pass-km/line-km
4,000
10,000
20,000
>30,000
City and Travel Demand Classification
 
Size
Small city
Medium city
Large city/ conurbation
Large city/ conurbation
Service Area pop.
200,000- 500,000
500,000-1,000,000
1 million-2 million
2 million- 5 million
Population density in traffic corridor
2,000/km2- (5,000/mi2)
3,000/km2- (8,000/mi2)
5,000/km2- (13,000/mi2)
8,000/km2- (21,000/mi2)
Public transport demand of a 15 km (9 mi) long corridor
30,000/weekday
60,000/weekday
100,000/weekday
>160,000/weekday
Additional demand from feeder traffic
5,000/weekday
15,000/weekday
25,000/weekday
>40,000/weekday
Implied average travel distance (rail)
2.0 km
(1.2 mi)
2.5 km
(1.6 mi)
3.0 km
(1.9 mi)
>2.8 km
(1.7 mi)
Guideway
Alignment
(Right of way)
At grade
20% shared
80% separate
5% tunnel & elevated
10% shared
85% separate
20% tunnel & elevated
80% separate
> 50% tunnel & elevated
<50% separated ROW
Stations
Average Station
Spacing
0.5 km
(0.3 mi)
0.6 km
(0.4 mi)
0.75 km
(0.5 mi)
1.0 km
(0.6 mi)
Platform length
40 m
(130 ft)
60 m
(200 ft)
90 m
(300 ft)
100 m
(330 ft)
Vehicles
Cabs/car
Single / double-ended
Double-
ended
Double-ended
Double ended
Vehicle width
<2.4 m
(<7’ 10”)
2.4 m/2.65m
(7’ 10”/8’ 8”)
<2.65 m
(8’ 8”)
<2.65 m
(8’ 8”)
Capacity 6-axle car (6 standing persons/m2)
160
200 to 220
260
300
Max. peak vehicle occupancy, U.S. & Canada (4 - 5 persons / m of vehicle length
80 to 100
120 to 150
120 to 150
100 to 125
Table 1.  Urban Transport Traffic Density Criteria - Germany   CONTINUED
   
Similar to Tramway
Similar to Metro
   
Category 1
Category 2
Category 3
Category 4
Criterion for choice of category
MinimumWeekday transport performance pass-km/line-km
4,000
10,000
20,000
>30,000
Operation
 
Maxim cars/train
2
2
3
4
Minimum headway
90 seconds
90 seconds
90 seconds
90 seconds
Maximum trains/hour
40
40
40
40
Nominal max. capacity
13,000 places/hour/direction
18,000 places/hour/direction
31,000 places/hour/direction
48,000 places/hour/direction
Likely maximum peak period volume, U.S. and Canada conditions
6,000-8,000 pass/hour/direction
10,000-12,000 pass/hour/direction
14,000-18,000 pass/hour/direction
16,000-20,000 pass/hour/direction
Train protection
None. Manual operation
Some sections train protection
Most sections train protection
Train protection throughout
 
Wayside control of street traffic lights
Mostly
Throughout
Priority
Integrated w/ train protection
 
Average operating speed
20 km/hr
(12 mph)
25 km/hr
(16 mph)
30 km/hr
(19 mph)
40 km/hr
(25 mph)
(Table 1 adapted from Stadtbahn in Deutschland / Light Rail in Germany 2000, 71. One-way weekday traffic density converted to two-way for consistency of comparison with other studies. “Implied average travel distance (rail)” added by authors; calculated based on “Public transport demand of a 15 km (9 mi) long corridor.” “Maximum peak vehicle occupancy, U.S. /Canada (4 - 5 persons/ m of vehicle length),” and “Likely maximum peak-period volume, U.S. and Canada” added by authors, based on Demery and Higgins (2003).)
Authors’ Comment
The LRT and HRT criteria above, which pertain to German economic conditions and operating environments, are equivalent to those derived by Pushkarev et al. (1982) with respect to low-cost LRT. Criteria for facilities requiring significantly greater investment per route-km, owing to grade separation and tunnels, are significantly higher than those derived by Pushkarev et al. As noted above, the rate of price escalation in the construction industry has outstripped the general economy-wide inflation rate from the 1970s, a circumstance not confined to the U.S. More recent analysis has established higher traffic-density thresholds for facilities requiring greater investment.
The table above also has important implications for U.S. transit planning. It is now clear that American consumers with access to alternative transportation will not tolerate peak-period crowding aboard transit vehicles at levels implied by the German loading standards. Therefore, in order to transport a given peak-period passenger volume, a U.S. transit service would have to provide a higher level of nominal capacity than its European counterpart. This could, in turn, put bus alternatives at a relative disadvantage with reference to operating cost. Unlike rail, buses provide no economies of scale. The marginal cost of increased peak-period capacity may be quite small, unless the vehicle fleet size is too small for existing traffic levels, or peak-period train lengths and service frequencies are at their maxima.
It is also important to note the low ATD characteristic of German urban transport. This reflects, among other factors, the relatively compact character of German cities and the presence of well-developed suburban rail (“S-Bahn”) networks that carry much longer-distance travel. As noted above, longer ATD requires a higher service level, all else being equal. Again, the implications for U.S. transit planning are significant. The combination of relatively high ATD and low consumer tolerance for peak-period crowding suggests that U.S. transit facilities must provide significantly more service per unit of consumption than those elsewhere. This, as explained above, tends to place bus alternatives at a relative disadvantage in terms of operating cost.
F.  Pittsburgh (1949).
Nearly six decades ago, and more than 30 years prior to the work of Pushkarev et al. (1982), the rail traffic threshold issue arose during litigation associated with the bankruptcy of Pittsburgh Railways Company (PRCo).
In 1948, the City of Pittsburgh sought a court order mandating a study for replacement of all streetcar lines with buses. PRCo trustees objected but the court ordered an independent study. This recommended replacement of 19 streetcar routes, about 25 percent of the network, with buses (Lougee 1949).  The trustees again objected, and proved that conversion of only one line could be justified on economic grounds. The trustees then proved that losses from the reduction in operating flexibility (e.g. for emergencies) would more than offset any financial gain from bus substitution. Remarkably, the trustees secured court approval for the investment required to retain rail service on this line (Tennyson 2004).
The court finding for rail was justified on the basis of data, statistics and analysis related to PRCo operations. The minimum utilization to justify rail retention implies about 2,700 passenger-miles per mile of track per weekday. In 1948, the company operated 528 miles of track (Lougee 1949). Not all routes were double track, therefore, total route length was somewhat greater than 264 mi (= 528 / 2). Using 300 miles as the approximate route length, the implied threshold works out as follows:
2,700 * (528 / 300) = 4,752
The statistic above becomes 5,000 pass-mi per mi of route when rounded to a single significant digit.
Authors’ Comment
The threshold for economic justification of streetcar operation, established by Pittsburgh Railways Company trustees and accepted by the Federal District Court overseeing the company’s bankruptcy proceedings, implies a traffic density threshold of about 5,000 passenger-miles per mile of route per weekday. This tends to corroborate the threshold for low-cost LRT established by Pushkarev et al. (1982).
 
4.  Recommendations of Pushkarev et al
Pushkarev et al. (1982) recommended a nationwide rail transit expansion program, with heavy rail route length increased by 50 percent and light rail route mileage increased by 150 percent.
“Altogether, potential additional rapid transit [i.e. heavy rail] mileage in the United States conforming to the criteria presented here might total about 350 miles (563 miles) in 40 corridors, which represents about a 50-percent expansion of the extant 647-mile (1,041-km) rapid transit system.
“More conjecturally, potential additional light rail mileage confirming to the criteria might total about 320 miles (515 km), which represents more than a doubling of the extant 215 mile (356 km) light rail and streetcar system” (Pushkarev et al. 1982, xxv).
[“Extant” mileage includes lines then (1980) under construction but not yet opened.]
Pushkarev et al. (1982) described this program as:
“a task of finite magnitude that would take about 25 years to accomplish at the current [1980] pace. Its cost of $17.2 billion in 1977 prices . . . is split about equally between ‘future’ rail cities and those with systems in existence or under construction.
“This refers strictly to new lines and excludes elevated removal, station reconstruction, and line rehabilitation on existing systems to bring them up to the quality of the new lines, especially in Chicago, New York and Philadelphia”  (Pushkarev et al. 1982, xxv).
This was not a recommendation to build rail transit in every U.S. city and town:
“the criteria used indicate that the 10 cities with rapid transit [i.e. heavy rail] extant or under construction could only be joined by 4 cities, but that the 7 cities which only have light rail extant or committed could be joined by at least 10 more, for a total of about 30 urban areas with some form of rail.”
[Counts of cities with rail transit include those where such facilities were then (1980) under construction but not yet opened.]
Comparisons between the number of U.S. rail transit cities and route lengths at 1980 and 2004 are presented in Table 2 below.
 
Table 2. U.S. Rail Cities and Route Length
1980
2004
Numerical Change
Percent Change
HRT Cities
8
12
+4
 
HRT
562.0 mi
810.9 mi
+248.9 mi
+44
Route Length
(906.5 km)
(1,307.9 km)
(+401.5 km)
 
LRT Cities
7
24
+17
 
LRT
197.4 mi
608.3 mi
+410.9 mi
+208
Route Length
(318.4 km)
(981.1 km)
(+662.7 km)
 
Urban Rail Cities
11
30
+19
 
Urban Rail
759.4 mi
1,419.2 mi
+659.8 mi
+87
Route Length
(1,224.8 km)
(2,289.0 km)
(+1,064.2 km)
 
Sources for Table 2:
American Public Transportation Association
Light Rail Central
National Transit Database
Pushkarev et al. (1982).
Taplin (Light Rail Transit Association)
UrbanRail.Net
 
Total U.S. urban rail transit route length at 1980 and at 2004 are compared in Figure 4.
 
Notes for Figure 4:
Route length of “HRT-Closed from 1980” and “LRT -Closed from 1980” subtracted from “HRT-1980” and “LRT-1980” in the 2004 column. The actual route lengths built from 1980 is equal to the “numerical change” in each category (Table 1), plus line closures.
Comparisons between the number of U.S. rail transit cities and route lengths at early 2004 (0perating and under construction) and those recommended by Pushkarev et al. (1982) are presented in Table 3 below.
 
Table 3.  U.S. Rail Transit Cities and Route Length - Existing (2004) and Recommended (Pushkarev et al (1982)
Operating or Under Construction (2004)
Recommended by Pushkarev et al (1982)
Numerical Difference
Percent
 Difference
HRT Cities
12
14
-2
 
HRT Route Length
810.9 mi
1,000 mi
-189.1 mi
-19
 
(1,307.9 km)
(1,600 km)
(-305.0 km)
 
LRT Cities
27
17
+10
 
LRT Route Length
751.2 mi
535 mi
+216.2 mi
+40
 
(1,307.9 km)
(863 km)
(348.7 km)
 
Urban Rail Cities
33
30
+3
 
Urban Rail Route Length
1,562.1 mi
1,535 mi
+27.1 mi
 
 
(2,519.5 mi)
(2,424 km)
(+43.7 km)
 
Source Notes for Table 3:
APTA Heritage Trolley and Streetcar Site:
Light Rail Central
National Transit Database
North American Vintage Trolley Systems:
Pushkarev et al. (1982).
Taplin (Light Rail Transit Association)
UrbanRail.Net
 
5.  Forecasts for Specific Cities and Corridors
Pushkarev et al. (1982) did not recommend a specific blueprint for U.S. rail expansion. Instead, they developed criteria related to travel volume – that is, to traffic density – and demonstrated how these might be applied to site-specific analysis. Among their expressed intents was to determine where site-specific analysis might most profitably be focused (Pushkarev et al. 1982, iii). Toward this end, they estimated potential demand based on population density, population distribution, automobile ownership, existing transit use, and nonresidential floor space in the business center (CBD, or “central business district”). Based on these estimates, they determined potential rail traffic densities in a number of cities and corridors.
Pushkarev et al. (1982, 280-283, Exhibit 4.9 and 4.10) did not present a single traffic density forecast for each of the various cities, nor a range of forecasts under a constant set of assumptions. Instead, they considered various combinations of radial line length, nonresidential CBD floor space, “transit orientation” (high or low), auto speed (slow or fast) and access. The range of weekday traffic densities forecast by Pushkarev et al. in 30 cases is presented in Table 4, together with actual weekday traffic densities observed on 18 new urban rail transit systems opened from the mid-1970s.
 
Table 4. U.S. Urban Rail Transit Weekday Traffic Density - Forecast (Pushkarev et al 1982)  and Actual (2002)
Weekday Traffic Density
(passenger-miles per mile of route)
LIGHT RAIL
Forecast
Actual
Baltimore
 
6,000
Buffalo
6,000 – 9,000
8,000
Cincinnati
5,000 – 8,000
 
Columbus
4,000 – 7,000
 
Dallas
10,000 – 22,000
11,000
Dayton
2,000 –3,000
 
Denver
4,000 – 7,000
11,000
Detroit
14,000 – 23,000
 
Honolulu
8,000 – 19,000
 
Houston
11,000 – 22,000
 
Indianapolis
4,000 – 8,000
 
Jersey City
 
5,000
Kansas City
4,000 – 8,000
 
Los Angeles (Blue Line)
20,000
28,000
Louisville
4,000 – 6,000
 
Milwaukee
10,000 – 14,000
 
Minneapolis–St Paul
8,000 – 11,000
 
New Orleans
3,000 – 6,000
4,000
Phoenix
2,000 – 3,000
 
Pittsburgh
10,000 – 13,000
6,000
Portland
4,000 – 7,000
13,000
Providence
1,000 – 3,000
 
Sacramento
 
8,000
St. Louis
9,000 – 17,000
11,000
Salt Lake City
 
10,000
San Antonio
2,000 – 3,000
 
San Diego
5,000 – 9,000
9,000
San Jose
 
3,000
Seattle
19,000 - 22,000
 
Tampa - St. Petersburg
1,000 – 2,000
 
HEAVY RAIL
Forecast
Actual
Atlanta
11,000 – 13,000
31,000
Baltimore
11,000 – 12,000
15,000
Los Angeles
20,000 – 30,000
36,000
Miami
14,000 – 16,000
17,000
Washington, DC
26,000 – 30,000
48,000
Source Notes for Table 4:
“Forecast” weekday traffic density statistics from Pushkarev et al. (1982, 280-283, Exhibit 4.9 and 4.10); range is bounded by lowest and highest values, rounded to a single significant digit.
“Actual” weekday traffic density statistics calculated from National Transit Database (FTA) and American Public Transportation Association data, rounded to the nearest thousand. See Appendix IV for U.S. urban rail transit passenger traffic statistics for 2002.
Baltimore “forecast” is that for a “15-mile route,” i.e. one extending 15 miles from the CBD.
“Los Angeles Blue Line” forecast statistic is that presented by Pushkarev et al. for “Harbor Freeway to Long Beach” corridor.  “Actual” statistic calculated from Los Angeles County Metropolitan Transportation Authority monthly boarding statistics, based on 9-mile average travel distance.
Miami “forecast” is that for a “9-mile route,” i.e. one extending 9 miles from the CBD.
New Orleans “actual” statistic is for streetcar lines.
Comparisons between weekday traffic density forecasts by Pushkarev et al. (1982) and actual weekday traffic density statistics for FY 2002 for 13 cities that opened new rail systems from the mid-1970s are presented in Figure 5.
 
Pushkarev et al. (1982, 270) were well aware of the uncertainty associated with their forecasts:
In view of the long chains of assumptions needed to produce the travel estimates and threshold volumes shown here, the figures presented are conditional, and the exact values should not be taken too literally. What is important is the relative scale of the estimates, and the general ranking of the urban areas with respect to their prospect for fixed guideway transit.
The authors add that in retrospect, the consistent pattern of underestimation of weekday traffic density by Pushkarev et al. (1982) is of similar importance. Observed results exceeded the predicted minimum values in all but one of the 14 cases above, and the predicted maximum values in eight of the cases above. Such results tend to support the observation of Pushkarev et al. (1982, 270) that their traffic density estimates were “very conservative.”
On the other hand, the labor and the energy savings estimates may be liberal, approaching as they do the best existing, rather than average practice. While no other assumption would be proper for planning new systems, to insure against any slippage in labor and energy efficiency the patronage estimates are deliberately left low.
 
6.  Does the Predicted Travel Demand Exist?
The predictions of weekday traffic density by Pushkarev et al. (1982) were based on estimates of weekday passenger volumes (passenger-trips) to and from the business centers (CBDs) of various cities.
It might therefore seem reasonable to determine potential CBD passenger-trip volumes for comparison with the forecasts of Pushkarev et al. (1982). However, such comparisons must be performed with care. A traffic-density statistic (or forecast) cannot be reduced to a weekday passenger volume (unlinked passenger-trips, or boardings) without reference to 1.) route length and 2.) average travel distance (ATD). (Of course, ATD can be no greater than corridor route length, and both must be greater than zero. The weekday passenger volume implied by a given traffic density may vary over a wide range.
Given a 10-mile route length and a 5-mile ATD, a weekday traffic density forecast of 5,000 passenger-miles per mile of route implies 20,000 passenger-trips per weekday. If ATD is increased to 7 miles, the forecast implies 14,000 weekday passenger-trips. If ATD is decreased to 4 miles, the forecast implies 25,000 weekday passenger-trips.
Pushkarev et al (1985, 239) did not calculate peak-hour passenger volumes:
No assumptions are made about the magnitude of the [weekday] peak hour volume which averages 26 percent of the [weekday] one-directional load at the maximum load point on existing systems. Rather, the implication is that whatever the daily peaking factor, service can be fitted to it and to the average trip length calculated here such that one-directional weekday peak hour occupancy at the maximum load point does not exceed 100 percent and average annual occupancy [passenger-miles per place-mile] is held to about 23.3 percent.
Pickrell (1985, 43-44) attempted to compare the traffic-density forecasts of Pushkarev et al. (1982) with potential peak commute travel volumes in “typical” radial corridors for various cities. Unfortunately, he did not address the issues above. Instead, he estimated total three-hour commute travel volumes in “typical” radial corridors for each city, based on 1980 Journey-to-Work statistics published by the U.S. Census Bureau. This suggests comparison among the busiest-hour, busier-direction volumes implied by Pushkarev et al. (1982), rail volumes actually observed, and total peak-hour volumes estimated by Pickrell (1985), presented in Table 5 It is essential to note that Pickrell (1985) estimated total peak hour volumes, carried by all modes, in typical corridors. This suggests comparison between rail volumes actually observed and total corridor volumes estimated by Pickrell. These implied peak-hour rail shares of total corridor volumes are also presented in Table 5.
 
Table 5. U.S. Urban Rail Peak Hour Passenger Volumes - Implied by Pushkarev et al (1982) & Pickerell (1985) vs.
Observed
Rail Volume Implied by Pushkarev et al (1982)
Observed Rail Volume (year)
Volume Implied by Pickrell (1985)
Implied Rail Volume (percent of total corridor travel)
LIGHT RAIL
       
Baltimore
 
920 (2000)
3,000 – 5,000
20-30%
Buffalo
1,000 – 2,000
1,200 (1997)
3,000
40%
Cincinnati
1,000 – 2,000
 
4,000 – 5,000
 
Columbus
1,000
 
3,000 – 5,000
 
Dallas
2,000 – 3,000
1,900 (2000)
3,000 – 4,000
50-60%
Dayton
400 - 700
 
2,000
 
Denver
1,000
2,400 (2002)
3,000 – 4,000
60-80%
Detroit
2,000 – 4,000
 
5,000 – 7,000
 
Honolulu
2,000 – 4,000
 
3,000 – 4,000
 
Houston
2,000 – 4,000
 
4,000 – 6,000
 
Indianapolis
1,000 – 2,000
 
3,000 – 4,000
 
Kansas City
600 – 1,000
 
2,000
 
Los Angeles (Blue Line)
5,000 – 6,000
2,618 (2001)
4,000 – 6,000
40-70%
Louisville
1,000 – 2,000
 
3,000 – 4,000
 
Milwaukee
2,000 – 3,000
 
3,000 – 4,000
 
Minneapolis –St Paul
1,000 – 2,000
2,000 (2005)
3,000 – 5,000
 
New Orleans
1,000
     
Phoenix
400 – 800
 
3,000 – 5,000
 
Pittsburgh
1,000 – 2,000
2,448 (2000)
   
Portland
900 – 1,000
2,375 (1999)
3,000
80%
Providence
400 – 600
 
1,000 – 2,000
 
Sacramento
 
1,600 (2000)
2,000
80%
St. Louis
2,000 – 3,000
2,500 (1996)
3,000 – 5,000
50-80%
Salt Lake City
 
1,400 (2000)
3,000
50%
San Antonio
400 – 600
 
2,000 – 3,000
 
San Diego
1,000 – 2,000
2,015 (2000)
2,000 – 3,000
70%
San Jose
 
1,327 (1997)
   
Seattle
3,000 – 4,000
 
4,000 – 5,000
 
Tampa - St Petersburg
400 - 600
     
HEAVY RAIL
       
Atlanta
2,000 – 4,000
5,093 (1994)
4,000 – 8,000
60%
Baltimore
4,000 – 5,000
3,700 (2000)
3,000 – 5,000
70%
Los Angeles
5,000 – 6,000
3,400 (2001)
4,000 – 6,000
60-80%
Miami
3,000 – 4,000
3,854 (1998)
1,000 – 1,500
n/a
Washington, DC
5,000 – 10,000
9,700 (2000)
   
Source Notes for Table 5:
“Weekday one-way trips” forecast by Pushkarev et al. (1982, 280-283, Exhibit 4.9 and 4.10) converted to hourly volumes based on a peaking factor range of 20-26 percent (i.e. 20-26 percent of one-way, all-day traffic moves during the busiest hour, in the busier direction, at the maximum load point). Range is bounded by lowest and highest values, rounded to a single significant digit.
Baltimore statistic is that implied for a “15-mile route,” i.e. one extending 15 miles from the CBD.
“Los Angeles Blue Line” statistic is that implied for the “Harbor Freeway to Long Beach” corridor.
Miami statistic is that implied for a “9-mile route,” i.e. one extending 9 miles from the CBD.
“Estimated 3-Hour Peak Commute Travel Volume in Typical Radial Corridor” estimated by Pickrell (1985, 44, Table 12) converted to hourly volumes based on a factor range of 30-40 percent (i.e.  30-40 percent of one-way traffic during the busiest three hours moves during the busiest hour, at the maximum load point). Range is bounded by lowest and highest values, rounded to a single significant digit.
“Observed” peak-hour volumes from Demery (2002)
Data are most recent available. St. Louis data estimated as explained in source. Washington data from eight corridors averaged; range is 4,200 – 15,800.
“Implied Peak-Hour Rail Share” statistics rounded to a single significant digit.
As a group, the “Implied Peak-Hour Rail Share” statistics appear implausibly high. This implies in turn that Pickrell (1985) underestimated peak commute travel volumes in the busiest corridors, where traffic levels justify rail transit.Comparisons between weekday peak-hour passenger volumes implied by Pushkarev et al. (1982) and observed peak volumes in 13 cities that opened new rail systems from the mid-1970s are presented in Figure 6.
 
In the majority of cases, observed peak hour passenger volumes approach or exceed at least the “minimum” levels implied by Pushkarev et al. (1982). The major exceptions to this pattern are the LRT Blue Line and the HRT Red Line in Los Angeles – both of which carry remarkably high traffic density. The Blue Line, by far the busiest of any U.S. LRT line outside of Boston and San Francisco, carries more than double the traffic density of any U.S. LRT facility opened after World War II. The Red Line carries the third highest traffic density among U.S. HRT systems opened after WWII; only San Francisco’s BART and Washinton’s Metrorail carry higher passenger traffic densities.
However, despite remarkably high traffic density and weekday passenger volume, the Blue Line cannot provide peak-period capacity commensurate with a travel volume of 5,000 passengers per hour per direction (phd). This fact reflects limitations on maximum train length (three cars) and peak-period service frequency. The Red Line, which could in theory provide such capacity, is not dominated by peak-period, peak-direction travel.  The commuter rail interchange at Union Station provides significant reverse-peak traffic, to a significant degree not anticipated by Pushkarev et al.
 
7.  Kain and Pickrell: Ideology Over Science?
Pushkarev et al. (1982) found that rail transit could be justified, from the standpoint of economic analysis, at lower traffic levels than established by previous U.S. studies. Pushkarev and his colleagues also recommended a nationwide rail transit expansion program, with HRT route length increased by 50 percent and LRT route mileage increased by 150 percent. All this, as noted above, generated skepticism and criticism from road-oriented transportation professionals, economists and academics. One of the authors heard one of the latter remark that Pushkarev et al. (1982) had “lowered the threshold for rail by half.”
Disagreements over transit policy arise from fundamental disagreements over urban form: what residential housing patterns and other urban characteristics are desirable, and how these should be encouraged.
Policy toward transit is inseparable from policy toward cities. Large downtowns can attract the ridership needed to make effective use of fixed guideway investment. There is less reason to invest in rail if there is no effort to encourage the development of downtowns and of compact residential patterns around them. A consensus on making such an effort has been difficult to achieve, and the controversies are reflected in conflicting attitudes toward urban rail (Pushkarev et al. 1982, iii; emphasis added).
Previous U.S. analysis, notably that by John R. Meyer, John F. Kain and Martin Wohl (1965) and similar studies (e.g. Boyd, Asher and Wetzler 1973; Keeler and Small 1975) found that, from the standpoint of economic analysis, rail transit could be justified only in corridors with very high peak traffic volumes. Meyer et al. (1965) set the busiest-hour threshold at 50,000 passengers per hour per direction (phd).
According to then-prevailing viewpoint in the U.S. academic world – which continues to attract strong and influential support – rail transit can be justified only in corridors with very high peak traffic volumes. The dominance of private automobiles is explained as the result of consumer choice. The influences of marketplace distortions, introduced by large public expenditures for highways, policies and subsidies that favor dispersed suburban housing development, and so forth are typically downplayed or ignored. Because the urban transport status quo is regarded as a natural economic outcome, attempts at reform or change draw resistance.
This point of view was stated explicitly, and succinctly, by Meyer et al. (1962, 40):
 
. . . most importantly, it would seem best to define the public transit problem as that of finding ways to meet the transit rider’s different needs . . . with reasonable economy and to reject those approaches . . . that place emphasis on reshaping the city and its growth pattern.” [emphasis added].
As documented above, the findings of Pushkarev et al. (1982) are corroborated by economic analyses from other developed countries – and a historic example from the U.S. The authors did not find any studies that established rail traffic density thresholds significantly different from those established by Pushkarev et al. (1982). Pickrell (1985) and Kain (1988) attempted to do so, but their efforts do not stand up to critical analysis.
The fundamental issue associated with Kain (1988) and Pickrell (1985) is illustrated graphically in Figure 7.
 
It would appear that the LRT traffic-density threshold, as estimated by Kain for the U.S., is two to three times greater than within the context of other developed economies – and the U.S. economy of the immediate post-World War II period. Neither Kain (1988) nor Pickrell (1985) explain the underlying economic factors giving such dramatically different results.
Kain (1988) and Pickrell (1985) were concerned with comparing the results obtained by Pushkarev et al. (1982) with the findings of previous U.S. analysis, in particular, Meyer et al. (1965); the authors found no evidence that Kain or Pickrell were aware of the corroborative studies cited above. Although comprehensive review of previous U.S. analyses is beyond the scope of this paper, an overview of Meyer et al. should bring key analytical issues into focus.
Meyer et al. (1965) produced the first comprehensive economic analysis of U.S. urban transportation. This pioneering study remains of interest but has a number of problems. Meyer et al. could refer to experience with high traffic volumes in only one city, New York, where the historic maximum occurred under wartime conditions that restricted auto use. Much more data are available today, from a much broader cross-section of applications.
Meyer et al. (1965) analyzed capital and operating cost for HRT and express bus modes, in the context of high-density and medium-density metropolitan regions, including residential collection, trunk (“line-haul”) and CBD distribution costs. All capital costs were allocated to peak-hour passengers. The analysis considered peak-hour corridor volumes in the range of 5,000–50,000 passengers per hour per direction (phd), with radial route lengths of 6, 10, or 15 miles (Meyer et al. 1965, 236-237). The analysis also considered “1-way service,” that is, with peak-period service in the “return” or “low-volume” direction operated on a “nonstop express basis” (Meyer et al. 1965, 238-239), and “low-cost line-haul systems” (Meyer et al. 1965, 240-241). Cost per one-way passenger trip was found to be less with express buses as the trunk mode, except in corridors requiring peak-hour capacity of 50,000 phd or greater.
Analytical sophistication belies fundamental problems in Meyer et al. (1965) and subsequent studies. Such problems are not confined to so-called “economic” studies (e.g. Meyer et al., Boyd et al. 1973, Keeler et al. 1975). These studies establish unit costs of peak period service supply, then derive unit costs of peak period service consumption based on various assumptions of service consumption (passenger-trips) per unit of supply (vehicle-miles). Results are extremely sensitive to the assumptions of the analyst (Vuchic 1979, 257).
[Meyer et al. 1965] concluded that busway systems were cheaper than rail systems up to a one-way peak-hour passenger volume of 50,000 per hour (for medium-density situations), while rail transit systems were less expensive at volumes above that. [Miller et al. (1973) conclude] that equal costs occur at volumes of 2,000 to 5,000 per hour, with rail systems being cheaper at passenger volumes above that level. The difference in the conclusions between the two papers approximates 1,000 percent. I confess to some measure of satisfaction that my paper [Deen and James 1969], presented to the Highway Research Board in 1969, found the bus/rail equal cost point at about 12,000 per hour, somewhere between the extremes of the other two papers (Deen 1973, 11).
In addition, results are not associated with any particular quantity of travel. This is a serious analytical flaw and may be elaborated as follows. A “trip,” or passenger-trip, is defined as a “one-way movement” (Meyer and Miller 1984, 21); this movement is, of course, an individual or consumer behavior. The fundamental characteristic of this behavior is movement or displacement between two distinct points: origin and destination. The distance between any two distinct points is unique, and positive (however, in the real world, alternate routes of different lengths may exist). All trips must therefore have a “spatial characteristic” or distance between origin and destination. Because all trip makers have mass, this “spatial characteristic” also represents work, which requires an input of energy. The work or energy input required to transport a given passenger varies directly with the distance traveled. In other words, the amount of energy consumed by a one-mile trip is proportionately less than that consumed by a ten-mile trip.
It should be clear that an average travel distance must exist for any aggregation of trips. However, “volume” is defined as the number of persons (or vehicles) passing a point during a one-hour period (Meyer and Miller 1984, 38). It is therefore not possible to determine ATD from a volume statistic.
Because it is not possible to determine ATD from a volume statistic, it is also not possible to determine traffic density. Peak-hour volume, the threshold criteria used by Meyer et al. (1965) and other studies, is therefore independent of traffic density.
Kain (1988) provides an unwitting demonstration of the point above. He attempts to convert the weekday traffic-density thresholds established by Pushkarev et al. (1982) into peak-hour volumes. This is of course possible, but results are highly sensitive to the assumptions of the analyst.  Kain made the apparent error of failing to convert from average weekday ridership to peak-hour, peak-direction passenger volume. Corrected results are presented in Figure 8 below, and further elaboration is presented in Appendix I. It is unfortunate that the error was not caught by Kain (1988) or his referees before the paper was published.
The fundamental problems with Pickrell (1985) are two-fold:
  1. The analytical framework is not compatible with that used by Pushkarev et al. (1988), and
  2. The results do not pass the “reasonableness test.”
As noted above, the analytical framework used by Pushkarev et al. (1982) explicitly eschews the benefit-cost approach in order to focus on relationships among physical quantities: space, time, labor, energy and land (Pushkarev et al. 1982, 58).
Pickrell (1985), by contrast, uses an explicit benefit-cost framework. This fact quickly becomes apparent when reading through the paper: Benefits from “Labor Cost Savings,” “Savings in Energy Inputs,” “Savings from Reduced Parking Demand,” travel-time savings and capital savings are assessed and aggregated. These benefits are then compared with estimated rail construction costs (Pickrell 1988, 40, Figure 3a and 3b).
The problems with this approach are manifold. Key parameters may be difficult to reduce to monetary terms. Even well defined parameters may have a considerable range of associated monetary values; an important example is the monetary value of travel-time savings. Results of previous benefit-cost analyses varied over a very wide range. The concept fell into disrepute in the U.S. during the 1970s (Deen 1979) but was later incorporated into Federal Transit Administration project evaluation. Smerk (1991, 282) favors benefit-cost analysis but recognizes that results are highly sensitive to the assumptions of the analyst:
The use of cost-benefit analysis is a good idea if carefully carried out . . . the difficulty is that cost-benefit analysis, like the words of the Holy Bible, can be used to prove just about anything.”
Pickrell (1985, 8) begins his critique with under the following heading: “Potential Complications in Estimating Benefits.” But Pushkarev et al. (1982, 58-59) do not attempt to determine benefits; instead, they use travel volume as “an indicator of transportation-related benefits” [emphasis added].
Whether a fixed guideway can in fact attain its enumerated objectives, and to what degree, depends in large measure on its travel volume. . . . At some point, as volume rises, the unit costs of fixed guideway service become lower than those of the pre-existing mix of free-wheeled vehicle modes. . . . At that point, the fixed guideway mode starts fulfilling its objectives (Pushkarev et al. 1982, 59).
Pickrell (1985, 7-8) treats the five volume-related criteria suggested by Pushkarev et al. (1982, 59; above) as benefits – “resource savings.” This is fundamentally different from the approach used by Pushkarev et al., although the distinction is subtle. In brief, Pushkarev et al. compare the non-monetized inputs (e.g. labor, energy) required to produce a given level of output – travel volume. Monetary measures are used only when necessary – to estimate relative levels of investment per unit of service provided. It should be clear that this analytical framework is fundamentally different from the benefit-cost framework.
It is possible to evaluate the results of a given study using a different analytical framework. This is not only possible, but common practice. However, important caveats cannot be ignored. The first is the issue of uncertainty, or tolerance. In relative terms, the tolerance associated with Pushkarev et al. (1982) is less than that associated with the benefit-cost framework. This is the case because benefit-cost analysis requires a larger number of assumptions, many of which can be hidden or not obvious to the reader.
The second issue is that of reasonableness. With reference to the revised HRT threshold, Pickrell (1985, 41) states “This result accords closely with the conclusions of earlier studies regarding the volumes at which rail rapid transit becomes the cost-minimizing mode of line-haul transportation service.”
Figure 8 illustrates some of the issues related to reasonableness of results presented by Pickrell (1985, 42).
 
Note for Figure 8: Thresholds calculated by Pickrell (1985) are those “excluding capital savings,” i.e. from reduced auto and bus use.
The authors found no evidence that Pickrell (1985) was aware of the studies cited above. However, Pickrell’s results are outliers in the context of Pushkarev et al. (1982) and corroborating studies. Figure 9 (below) provides additional illustration of this point.
 
The traffic-density threshold for HRT, entirely in tunnel, as revised by Pickrell is roughly 35 percent higher than that carried by any HRT system in the U.S., Canada or Western Europe. Moreover, the threshold for HRT without tunneling exceeds the annual traffic density carried by more than 60 percent of these systems. Results obtained by Pickrell (1985) are also outliers in the context of actual experience.
As noted above, it is common practice to evaluate or critique the results of a given study using a different methodology. However, such analysis requires much more than presentation of crude results. These, if different from the original study, need to be evaluated within the context of that study. For example, Pickrell (1985) obtained threshold criteria two to six times greater than those obtained by Pushkarev et al (1982), but failed to evaluate these within the analytical framework used by Pushkarev et al. Results that differ significantly from actual experience also need to be explained. For example, Pickrell obtained a threshold criterion for HRT entirely in tunnel that is significantly greater than that carried by any U.S., Canadian or Western European HRT system, but failed to expound on this.
 
8. Conclusions
The threshold traffic density for low-cost LRT, as established by Boris Pushkarev and his colleagues, is corroborated to a remarkable degree by similar analysis from other developed economies, and from the U.S. of the late 1940s. The authors attribute the concurrence of results to the common analytical framework, which focuses on relationships among physical quantities, e.g. space, time, labor, energy and land. Although prices for these inputs may vary among regions and countries, the underlying relationships are likely to be similar.
Peak period capacity, expressed as passengers per hour, is an important planning issue but is essentially independent of traffic density. Traffic density is a determinant of operating and certain capital costs. Higher traffic density requires higher service levels (vehicle-miles), and may require additional capital expenditure (e.g. for a larger vehicle fleet and servicing facilities). Therefore, peak-hour volume cannot be used exclusively as the modal threshold criterion.
The much greater thresholds of Pickrell (1985) and Kain (1988) appear as outliers when compared with the analyses cited here. The Kain thresholds are based on a calculation error, as outlined in Appendix I. The Pickrell thresholds differ dramatically from results obtained using methodology similar to that used by Pushkarev et al. (1985) but are not evaluated within a similar analytical framework. In addition, the Pickrell thresholds cannot be reconciled with actual experience in the U.S., Canada and Western Europe. The authors reject the findings of Kain and Pickrell for these reasons.
Pickrell (1988, 5) describes Pushkarev et al. (1982) as
the first careful estimates of travel volumes necessary to support construction of light rail transit lines.
If this is true, then it is so only within the U.S. context. The methodology used by Pushkarev and his colleagues was not new and was not unknown in other countries. The authors believe that similar studies, other than those cited above, have been conducted outside the U.S.Time has also proven that that the rail traffic density forecasts produced by Pushkarev et al were conservative. With but a single exception, new rail facilities carry higher traffic densities than the “minimum” forecast in the 13 cities where predictions by Pushkarev et al. (1982) can be compared with actual results. The exception is Pittsburgh, where the two-stage LRT program had not been completed at early ,2004 (when the bulk of this paper was written).
It is true, as Pushkarev et al (1982, 270) wrote, that “site-specific conditions are a matter for local alternatives analysis and cannot be given justice in a macro-study at the national scale.”
Local available alignments for light rail may not, in fact, reach the highest density corridor; local travel estimates, local types of construction and local costs will always be different from the average values shown here. The importance of the data presented is that they are prepared in a standardized and consistent manner, enabling comparisons between cities that hold as many variables as possible constant.
However, the fact that such standardized analysis gave rise to consistently conservative forecasts has important site-specific implications. The number of corridors where potential traffic density might justify rail transit may be greater than commonly assumed. This may augur well for smaller cities wanting to pursue LRT development, if available alignments are preserved and costs are contained.
The findings above do not provide sufficient grounds to build a rail transit project in any city.  The fact that a corridor has a sufficient traffic density to justify a given LRT or HRT does not establish that such a facility should be constructed. As a corollary, the fact that an existing fixed guideway facility carries less than the “threshold” traffic density does not establish grounds for closure and replacement by bus. Site-specific issues must be addressed.
Nor do the threshold criteria for various LRT and HRT establish that a given level of capital expenditure should be made. One would not, for example, build a full-scale HRT line just because the anticipated weekday traffic density exceeds 15,000. Site-specific conditions may prove amenable to LRT operation at traffic density levels considerably higher than this threshold.
The fact that total U.S. rail transit route length, operating or under construction, had grown by 2004 to that recommended by Pushkarev et al. is an interesting coincidence, but a coincidence nonetheless. U.S. rail development proceeded without reference to the recommended threshold criteria. It is not clear whether rail development would have proceeded to greater or lesser extent, or in the same locations, had these criteria been adopted. That said, the methods and criteria used by Pushkarev et al. – and in developed economies overseas – provides a framework for the orderly allocation of financial resources to urban transit development. These methods could obviously work well in the U.S.
Additional research is indicated to update the findings of Pushkarev et al. using data from LRT facilities opened after 1982. Additional research is also indicated to establish threshold criteria for enhanced bus and bus rapid transit facilities. The authors believe that the number of U.S. corridors where traffic density justifies enhanced bus modes is much larger than the number of corridors where traffic density justifies rail modes.
The following observations of Louis J. Gambaccini provide an appropriate exposition on the findings described in this paper:
Fixed guideway transit is not a universal solution nor should it be applied in all urban areas. Fixed guideway is a potential strategy, as is the bus, the ferryboat, the car pool or the van pool. In many possible applications, fixed guideway is a superior strategy. But whatever strategy is finally selected, each should be evaluated not in the narrow context of transportation alone, nor solely in the framework of accounting. It should be measured in the broader context of its contribution to the overall long-term aspirations of the urban society it is supposed to serve (Pushkarev et al. 1988).
 
Acknowlegments
The authors express sincere gratitude to E. L. Tennyson, P.E., former Transit Commissioner, City of Philadelphia and former Deputy Secretary of Transportation, Commonwealth of Pennsylvania, for information and insights provided during preparation of this paper, and to Boris S. Pushkarev, Jeffrey M. Zupan, and Robert S. Cumella, whose work inspired ours. We also offer sincere appreciation for the feedback and information supplied by the following persons during preparation of this paper: Maurice M. Carter, Darrell Clarke, Roger Christensen, Allen Drake, Frank S. Miklos, Charles J. Lietwiler, E. L. Tennyson, P.E., Van Wilkins and Julian Wolinsky.
 
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Appendix 1: Analysis of Errors Found in Kain (1988)
Traffic density, expressed in terms of passenger-miles (or km) per mile (or km) or route per weekday, may be converted to peak-hour volume as follows:
A.) Peak hour volume = ((weekday traffic density * route length) / ATD)* PTS
“PTS,” or peak traffic share, refers to the share of two-way, all-day traffic that is transported during the busiest hour, past the maximum load point, in the busier direction.
Whatever values the analyst may assume for route length, ATD and PTS must be consistent with the following relationship, derived from equation A.) above:
B.) Peak hour volume / PTS =  (weekday traffic density * route length) / ATD
The relationship described by equation B.) may be elaborated as follows:
B1.) Average weekday ridership = peak-hour volume / PTS
B2.) Average weekday ridership = (weekday traffic density * route length) / ATD
Kain (1988) postulates:
a ten mile system, a peak period (4 peak hours) ridership of 80 percent of total daily ridership, and a uniform distribution of boardings (Kain 1988, 204).
A “uniform distribution of boardings” implies a five-mile ATD, a reasonable assumption for a ten-mile suburb-to-downtown corridor. The implied PTS of 20 percent is very high; the “benchmark” for U.S. and Canadian cities, supported by a broad cross-section of data, is 13 percent (Demery 1994). Kain (1988) then states that 8,000 phd is the equivalent of 4,000 passenger-miles per mile of route per weekday.
Testing this result using equation B.) above:
8,000 / 20 percent =  (4,000 * 10) / 5
40,000 = 8,000
But “40,000 = 8,000” presents a contradiction. Kain’s conversion cannot be correct.
The corrected result, using the parameter values postulated by Kain (1988) is 1,600 phd, derived as follows:
((4,000 * 10) / 5) * 20 percent = 1,600 phd
Given a four-mile average travel distance and a 10-percent peak traffic share, parameter values more typical of recent U.S. LRT facilities than those postulated by Kain (1988), a weekday traffic density of 4,000 implies a peak-hour volume of 1,000 phd:
((4,000 * 10) / 4) * 10 percent = 1,000 phd.
Corrected peak-hour volume equivalents of the threshold criteria established by Pushkarev et al. (1982), based on the parameter values postulated by Kain (1988, 205, Table 1), are illustrated in Figure I-1.
 
 
Kain (1988, 205, Table 1) defines the following parameters:
PM/LM = “passenger miles per line mile.”
MP/PH = “peak hour passengers in the peak direction assuming an average trip length of 5 mi., i.e. equally distributed boardings.”
The apparent error associated with the conversions from “PM/LM” to “MP/PH” by Kain (1988, 205, Table 1) is failure to reduce average weekday ridership to peak-hour volume using the PTS factor. The statistics presented under the heading “Pushkarev-Zupan MP/PH” are equal to the average weekday ridership implied by the various weekday traffic density criteria, a ten-mile route length and a five-mile ATD.