Metro Service Delay Recovery

Transcription

1 Metro Service Delay Recovery Comparison of Strategies and Constraints Across Systems Jan-Dirk Schmöcker, Shoshana Cooper, and William Adeney This study was conducted to identify the strategies used by operators to provide a high level of service. The research distinguishes between punctuality and regularity of service and proposes that metro passengers primarily value regularity. The focus of this research is not on incident prevention, but on strategies that can be implemented after an incident to restore service swiftly and to minimize delay. The research identifies the recovery strategies used by six metros and summarizes advantages and disadvantages of these strategies. The influence of the type of delay on the choice of strategy is described. Similarly, the impact of constraints such as line length, service frequency, and passenger crowding on the effectiveness of each strategy is also discussed. It was found that it was generally sufficient to distinguish minor incidents, slow-moving delays, and major incidents. A case study shows that those metros with higher inbuilt flexibility can return more easily to normal service. This finding will have implications for metro management. The research has been carried out by the Railway Technology Strategy Centre at Imperial College London in collaboration with the Community of Metros benchmarking group. The performances and service qualities of six metros (three European, two American, and one Asian) have been analyzed and compared. The study consists of a quantitative analysis of the performance of two lines from each metro, together with a more qualitative assessment of the strategies used to optimize performance, through structured interviews with key operational and managerial staff. Reliability has often been identified as the main performance criterion for customer satisfaction on metros [e.g., Rehnström (1) or Lombart and Favre (2)]. These studies compare different aspects of service quality and both provide evidence of the importance of the issue to the customer. Adeney et al. look at metro performance from the point of view of the metro operator (3). This presentation, from the Community of Metros (CoMET) annual conference in 2001, shows strong evidence that an improved service should be desired by operators because improved reliability is associated with increased productivity through (a) increased ridership within economic and environmental constraints, and (b) reduced expenditures on reactive maintenance. Another study providing strong support for the assumption that improved reliability has many positive consequences in terms of social welfare and financial benefit to the operator was undertaken by the University of Westminster (4). In fact, research regarding the importance of reliable public transport services reaches much further J.-D. Schmöcker and W. Adeney, Centre for Transport Studies, Department of Civil and Environmental Engineering, South Kensington Campus, Imperial College London, London SW7 2AZ, United Kingdom. S. Cooper, Division of Operations Planning, MTA New York City Transit, 2 Broadway, Room B17.86, New York, NY Transportation Research Record: Journal of the Transportation Research Board, No. 1930, Transportation Research Board of the National Academies, Washington, D.C., 2005, pp back. Chapman (5) already refers to studies undertaken in the 1960s and concludes that there should be no need to justify an enquiry into the reliability of buses. The matter of reliability is important to both passenger and operator, as many studies have shown. Generally, the service reliability can be improved in two ways: first, through avoiding incidents leading to service disruptions, and second, through a better recovery to a normal service once a disruption has occurred. This paper examines the latter point with the objective of identifying strategies that allow the service to recover quickly. The paper explains different strategies and shows the factors or constraints influencing the choice of strategies. The evaluation of the success (or failure) of a specific strategy is difficult, because data are not available about what would have happened if a different strategy would have been chosen. Research at the Massachusetts Institute of Technology evaluates different service recovery strategies with a simulation approach (6, 7 ). Researchers show that real time control to quickly apply strategies such as turning a train short before it reaches the terminal or not stopping at the next station can significantly reduce the overall delay to passengers. Their research shows which strategies are optimal for a given set of constraints but does not analyze how changing the constraints will influence the choice of strategy and how this will influence the recovery process, which is the focus of this research. The next section shows that recovering the service means restoring service regularity and not necessarily punctuality; therefore, measuring service regularity is a better measure of performance than measuring punctuality. The following section then explains the methodology that was used to determine the constraints that different metros face and to understand which strategies are used by these metros. The paper provides an explanation of 10 identified strategies and explains which constraints influence the choice of strategy. Finally, examples are given on how these constraints influence the service recovery after a delay and conclusions are drawn. IMPROVING SERVICE THROUGH REGULARITY Because of the importance to customers of public transportation, it must be the objective of every public transport operator to provide high service reliability and to reduce the travel time uncertainty. Ideally, this will be achieved through an increase in punctuality. This is commonly measured as the percentage of trains that arrive at the scheduled time. Often it is measured as the percentage of trains that arrive at the scheduled time ± a threshold. Information boards indicating service punctuality are displayed in many train stations across Europe and often measure train arrivals ±5 min of the scheduled time. From the passengers perspective, however, an improvement in regularity is often already sufficient. Regularity will be of special interest if a service operates to a headway (and not timetable), because it measures the deviation from the proposed headway. If a timetable is pub- 30

2 Schmöcker, Cooper, and Adeney 31 lished, passengers will arrive accordingly, whereas if the service operates with a headway service, it is realistic to assume an even distribution of passenger arrivals (Figure 1). Consequently, in the case of a timetabled service, passengers will have a clear perception as to whether a train is late or not. However, for the headway service, the delay measure will be inexact because passengers will only expect a train at regular time intervals and could have just missed one. For a service with a short headway Nuzzolo (8) suggests a threshold of 12 to 15 min regularity is a more important measure than punctuality. In general, the measure of regularity becomes less important as the frequency of the service is reduced. For low-frequency services, punctuality is more important. In addition, frequent services are more likely to suffer more from irregularity than less-frequent services. For example, if a uniform passenger arrival distribution is assumed, the train immediately following a large service interval will have to carry significantly more of the average demand. This is likely to lead to longer dwell times and even more delays to and irregularity of the service. Lombart and Favre point out that in the event of a disruption to a service, it is even more important to the passengers that trains depart regularly, because deviations in regularity can produce situations in which the entire train cycle on a line becomes unstable (2). In extreme cases, trains might even have to be taken out of service or additional trains put into service. The risk of instability increases as the scheduled headway shortens. Lombart and Favre also state that the regularity can be evaluated with Equation 1: 1 f = Z where f = average deviation from proposed service (s), Z = number of measured intervals between trains, h plan = planned headway between services (s), and h real = real headway between services (s). Similar to the coefficient of variation, Lombart and Favre propose the definition of an irregularity coefficient b. This coefficient weights deviations higher if they occur on services with a short planned headway. b = f h plan Z i = 1 hreal_ hplan_ ( 1) i i 100 ( 2) where b = irregularity coefficient and h plan = average planned headway between services (s). Pr (passengers arriving on platform) A B Train departures FIGURE 1 Likely passenger arrival profile at platform for (A) service operating with headway and (B) service operating with published timetable. Because most metro services operate with a high frequency and without a published timetable, metro passengers are interested primarily in regularity and not punctuality. It can further be said that regularity is, in many cases, a precondition for punctuality (with small thresholds). However, whereas regularity is already sufficient for passengers, this is often not the case for the operator. It is mainly because of staff and network constraints that the operator will focus on punctuality rather than regularity. This can be problematic for passengers if service strategies improve the punctuality of some trains but reduce the regularity. This may occur because punctuality is not a precondition for regularity. For example, if every train is exactly 10 min late, the service has a perfect regularity of f = 0 but a punctuality of 0% (because every train arrives outside the punctuality threshold). THE RECOVERY PROBLEM A delay recovery strategy can be defined as the series of decisions made by the operations management to maximize the service performance following the delays that occur after an incident. By definition, an incident of duration t delays the affected train x by t. Without any action taken from the operational management, the following train x + 1 will pass the location of the incident delayed by at least t (h o h min ) with h o being the operated headway and h min the minimum possible headway in the system. This minimum possible headway is in most cases defined by the signaling system. Train x + 2 will be delayed by at least t 2(h o h min ), and so on. Therefore, for an initial delay t, at least n trains will be delayed at the point of incident, with n being determined through the smallest n that fulfils t n( ho hmin ) 0 ( 3) The difference between operated and minimum possible headway determines the possibility of service recovery in Equation 3. In most cases, n will be larger than the minimum n because the metro operator may not decide to run all trains with h min. (Because of safety rules or control system features, headways larger than h o might be required, which then amplifies the recovery problem.) Running the delayed trains with headways h min will lead to headways larger than h o further upstream and therefore an irregular service overall. The additional passenger demand created through the incident is also likely to increase the dwell times of subsequent trains. It is therefore very likely that cumulative (or knock-on ) effects of a delay are carried on to a large number of trains. Although this will certainly affect their punctuality, it will not necessarily affect the regularity of the service. The conflict for the operator is therefore often between the reduction of the delays for on-board passengers (through short-term maximization of punctuality) and the reduction of delays for passengers waiting to board (through maximization of regularity). Depending on the level of crowding, not prioritizing regularity might have the added disadvantage that even slight irregularities may lead to significantly longer dwell times for trains arriving with headways larger than h o, thus leading to further delays. The result will be the same as the commonly known bus-bunching effect on roads. If the difference between h o and h min is minimal, the service might recover through use of the inbuilt recovery time at the terminals. The terminal times are always longer than the time required for the turnaround procedure. Therefore, these recovery times can often be used to reduce both the cumulative delay and the number of affected trains. Rahbee, for example, shows that small increments in dwell times or

3 32 Transportation Research Record 1930 terminal times can lead to a 10% reduction in waiting time at certain stations because the timetable becomes more robust (9). METHODOLOGY: COMET CASE STUDY This research has been carried out by the Railway Technology Strategy Center (RTSC) in collaboration with CoMET. CoMET was established in 1994 as a group of the world s largest urban railways to share practices and provide a forum for the discussion of relevant issues (10). It currently comprises 10 metros: Berlin, Hong Kong MTR, London, New York, Madrid, Mexico City, Moscow, Paris, Sao Paulo, and Tokyo. This study has analyzed the performance of six metros (three European, two American, and one Asian) to compare their service performance and the strategies used to achieve it. (For confidentiality reasons the names of the metros cannot be revealed. For more information please contact the authors.) The case study comprised three stages. First, the six participating metros were asked to submit data on line characteristics, operational details, passenger numbers, and details of some common incidents for two of their lines. Ideally, each metro would have selected two dissimilar lines in terms of signaling and line complexity, Because it is believed that automatic train operation (ATO) and line complexity (whether it is a simple end-to-end line or a line with various branches) might significantly influence the service regularity. Second, the metros were asked to submit headway data for a few selected incidents. It was hoped that these data would be available for a number of measurement points along each line. This would allow analysis of the service recovery over both time and distance. Data were not available from all the metros and this unavailability of data in itself showed the focus of the performance measurement of some of the metros. In particular, headway data showing the service regularity are rarely collected or retained by the metros. Finally, structured interviews were carried out with management and operating staff of the metros through visits or by telephone. It was mainly through these interviews that a comparison of the strategies used for service recovery and of the problems that the metros encounter in providing a regular and/or punctual service after incidents was achieved. LINE CHARACTERISTICS Table 1 shows some of the basic characteristics of the lines for which data were submitted. The first two letters show whether the metro is in Europe (Eu), Asia (As), or America (Am). The suffixed letter iden- tifies the line (A or B). Note that the third European metro only submitted data for one line. A white background indicates an average value, light gray indicates that the value is at some variance, and a darker background indicates that the line varies significantly from the majority of the other lines. In the final project report the analysis is described in more detail (11). The results of this study concur with Rahbee in identifying some of these characteristics as those that most influence the service regularity (9). Performance data are analyzed on line and network level. The number of incidents per year and million train kilometers for each line are shown in Figure 2. The figure only shows incidents with an initial delay larger than 5 min. The threshold for incident reporting varies between 2 and 5 min for the different metros. It would also be interesting to compare the number of incidents smaller than 5 min and the results shown in this paper provide some evidence that it is often the short incidents that lead to an irregular service. The figure shows the significantly better performance of the Asian and the second American metro. It further confirms that looking at single lines instead of network averages is valuable. Especially the lines from the first American metro and the lines chosen from Eu2 perform very differently compared with the network average. For Eu2 the differences can be explained partly by the worse performance of a group of complex lines and partly through the better signaling and control technology on Eu2-B. Discussions with Am1 revealed that Line A only appears to perform significantly worse. The line is much shorter than an average line in the Am1 network, which leads to many incidents being reported on this line that are not reported on other longer lines. At Am1 and many other metro systems, only one incident can be reported between two measurement points. However, Am1 only has two measurement points on each line, the two termini, whereas other metros often have multiple measurement points. Note that a higher density of measurement points leads to a lower probability of more than one incident occurring between two measurement points. Therefore, the general conclusion is that the distance between the measurement points influences the performance data, and analyses of the number of incidents should always consider this finding. The line characteristics and the number of incidents that occur on each metro have to be considered in the context of identifying an appropriate delay recovery strategy as well as understanding the constraints that influence the delay recovery. The following section shows that short lines provide more opportunities for recovery from delays than longer ones. For a line that inherently suffers from more incidents, operators might also choose to deal with incidents differently than they would on lines with a high level of performance. TABLE 1 Overview and Some Characteristics of Lines in This Study Line Am1-A Am1-B Am2-A Am2-B As1-A As1-B Eu1-A Eu1-B Eu2-A Eu2-B Eu3-A ATO/manual M M A A A A M M M A A (S)imple/(C)omplex C C S S S S C S C S S Screendoors: yes/no/partly N N N N N P N N N N N Line length (km) Avg. dist. btw. stations (km) Pass. per weekday (1,000) Peak hour headways (s) NOTE: Clear background indicates average values; light gray background indicates small variance; and dark gray background indicates significant variance.

4 Schmöcker, Cooper, and Adeney 33 Incidents per Million Train Kilometers Incidents on lines Networkwide average Am1-A Am1-B Am2-A Am2-B As1-A As1-B Eu2-A Eu2-B Eu3-A FIGURE 2 Annual incidents with initial delay 5 min. Figure 3 shows the difference between operated headways and minimum possible headways for the lines considered in this study. It can be seen that there is no recovery potential for Eu2 and Eu3. This means that all delays will be transferred without reduction to the following trains, and n in Equation 3 becomes infinite. The only recovery possibilities will be the terminal times or through some of the strategies described later. Eu1 will have minimal problems recovering from small delays. The big gap between operated headway and minimum headway offers sufficient flexibility. CONSTRAINTS AFFECTING SERVICE RECOVERY POSSIBILITIES Reserve headway capacity is only one of the factors influencing the ability to recover from delays, although one of the most important ones. Through the interviews with the metro operators, four groups of constraints were established: Network constraints: crossovers, sidings, depot location, length of line, station design, terminal configuration. More sidings and additional platforms at terminals clearly give the operator more flexibility in recovering back to a regular service following a service disruption. For example, sidings could be used to store trains and bring them back into service when needed. Am2-A showed the greatest flexibility with 15 turnaround possibilities (average of 1.3 km). The terminal configuration further made sure that outgoing trains are not delayed by late incoming trains. Eu2-A clearly offered the least flex- ibility among all lines with turnaround possibilities only every 7.8 km (average). Technological and operational constraints: signaling and control systems, operated headways, inbuilt recovery times, communications, control room design, ability to communicate strategies to customers. Good communication between control room staff and drivers is essential for service recovery. The operational staff also need to be provided immediately with information about train location, causes, and expected duration of the delays. The case study showed that the lines with ATO (see Table 1) generally offer better recovery possibilities because their control room equipment (both control and communications) is more modern. Staff constraints: skill and experience of controllers, driver behavior, labor rules. Train drivers have a maximum driving time before they are required by law to take a break. This leads to the constraint that trains have to be at the crew changeover point at a certain time. Consequently, more lenient labor rules lead to a greater flexibility in recovering from delays. Interviews with service management further revealed that the quality of the service greatly depends on the skill of the operations controller. The service regularity is often worse when less experienced staff are in control. Restrictions on driving time are stricter in Europe, which leads to lower flexibility. Passenger constraints: demand profile of line, customer action, quality of service required. As explained previously, it is significantly more difficult to recover from delays on networks with a high passenger demand. Customers on the European and one of the American metros further obstruct the automatic door closing more often Minimum headway Operated headway during peak Headway [sec] FIGURE 3 Am1-A Am1-B Am2-A Am2-B As1-A As1-B Eu1-A Eu1-B Eu2-A Eu2-B Eu3-A Minimum headway due to signaling and operated headway during peak hours.

5 34 Transportation Research Record 1930 than passengers on the Asian or the second American metro. This can be both a source of delay and a hindrance to delay recovery at the same time. Passengers in Asia are, in general, more disciplined than European passengers, which leads to less door holding and more constant dwell times on the Asian metro. The study looked at these constraints for each line and ranked them from 1 (very low flexibility) to 5 (very high flexibility) for each of the above four criteria. Table 2 shows the resulting total score. The scores provide general guidelines because these are differing opinions as to whether each of the four categories should be simply summed up (as done in Table 2) or whether some categories should be given more weight. A detailed discussion on the ranking can be found in the RTSC project report (11). RECOVERY STRATEGIES The interviews with the six metros identified the following 10 strategies to recover from delays, which are applied when the recovery time at the terminal is not sufficient to bring service back to normal. Each strategy has some advantages and disadvantages. 1. Stacking (do nothing). Let all following trains run as close as possible to the affected train. 2. Stacking (de-train). Remove passengers from the affected train, let all following trains run as close as possible to the affected train. Advantage: Minimizes delay for onboard passengers. In case of stacking (de-train) the empty train can fill the service gap by skipping stations. Disadvantage: Creates very uneven headways: queuing trains behind the affected one(s); gap before affected train train bunching. 3. Freezing. Hold all trains on the lines. instant freezing (stop all trains immediately, regardless of their current position) and soft freezing (let trains run into next station) can be distinguished. Advantage: Keeps headways even, potentially easier to recover to a regular service than stacking. Disadvantage: Increases the delay for onboard passengers. 4. Holding some trains. Hold all trains in the vicinity of the affected one. As this is a mixture between stacking and freezing, it also has some of the same advantages and disadvantages. It should be noted that other metros not interviewed in this study introduced automatic recovery systems, which balance headways between services, for example, through holding of trains for a few seconds before arriving at a station. This requires a well-calibrated objective function when and for how long to hold trains. 5. Removing trains. Take trains out of service (not the affected one). Advantage: Free up trains at depot/sidings to be inserted back into service when service gap reaches depot. It also frees up drivers to replace delayed drivers who need a relief. Disadvantage: Reduces service immediately. 6. Adding a gap train. Add train from sidings to close gaps in the service. Advantage: Fills the service gap. Disadvantage: Requires spare staff and spare trains. 7. Turning short. Turn selected trains into return direction prior to scheduled terminus. Advantage: Fills the service in the return direction. It also allows drivers to reduce their travel time and get back on schedule. Disadvantage: It reduces the service at the end of the lines and it is difficult to insert this train into a frequent service and might therefore delay trains in the opposite direction. 8. Station skipping. Let a train not stop at one station where it is scheduled to stop. This strategy is only possible if good in-train and on-platform communication with the passengers exists. Advantage: Allows train to catch up and reduce the service gap. Disadvantage: Passengers on the train who wanted to alight have to travel back one stop. It will further increase the delays for the passengers waiting at the skipped station. 9. Diverting. Let trains bypass the affected train(s) on other routes. This strategy is not possible on many networks. Good communication with the customers is essential. Advantage: Service between both termini is continued. Disadvantage: Service on the line diverted to might be impacted as well. 10. Shuttle service. Split line into two or more sections and run a separate service between the new termini (plus possibly a bus shuttle service if a larger section of the line needs to be closed). Advantage: Service continues even though there is a blockage. A shuttle service can further be used to free up drivers and trains until the blockage is resolved. Disadvantage: No through route for passengers. In most cases a shuttle service also means a reduced service frequency. Operational staff of the metros confirmed that the strategies are used depending on the constraints mentioned in the previous section as well as the time of day, location of incident, and type of delay. This is discussed in more detail in the following two sections. Finally, it should be noted that these strategies are only those that influence the waiting and in-vehicle time for the passengers directly. Other strategies are used for resequencing of trains and/or staff. CHOICE OF STRATEGY DEPENDING ON TYPE OF DELAY Discussions with metros led to categorizing three basic types of incidents: Minor incidents: relatively short incidents; Slow-moving delays/bottlenecks: incidents that cause trains to travel with reduced speed over a section of the line (reduction of capacity); and Blockage and major incidents: incidents that are likely to close sections of the track for some time. TABLE 2 Aggregate Flexibility Score for Lines (of 20) Am1-A Am1-B Am2-A Am2-B As1-A As1-B Eu1-A Eu1-B Eu2-A Eu2-B Eu3-A Total score

6 Schmöcker, Cooper, and Adeney 35 Minor incidents are often caused by passengers (e.g., obstruction of doors), whereas major incidents are often caused by problems with the rolling stock or fixed infrastructure. From the operator s point of view, the main difference between these two is that when notified of an incident and its cause, the line manager expects a minor incident to be cleared quickly, thus requiring a different recovery strategy to be selected compared with a major incident. Typical causes of slowmoving delays are track circuit or signal failures. It is important for the operator to know by how much the capacity is reduced due to an incident. Passenger crowding can also be defined as a bottleneck because the longer dwell times effectively mean a capacity reduction. Other passenger-related incidents (e.g., a sick passenger needing to alight or a police investigation) might be treated by the operator as a minor or major incident depending on further information. Table 3 lists the most popular strategies among the lines considered in this study. The data stem from the interviews with operational staff and reflect what strategies are commonly used by the control room staff, but exceptions might well be possible. None of the metros wants to remove trains from service, but it may be unavoidable during an enduring slow-moving delay. Similarly, for extended blockages it may be necessary to run a shuttle service or to divert trains onto other routes. Metros differ in their immediate reactions to bottlenecks and blockages. For example, Eu3 refrains longer from removing trains and first tries to solve the problem through stacking or holding a number of trains. This may be a superior strategy if it turns out that the bottleneck is resolved quicker than expected. For minor incidents, some of the metros apply the stacking (do nothing) strategy, whereas other metros immediately freeze some or all trains. Figure 3 shows that, for example, Eu1 can afford to do nothing because of the long headways. For any kind of delay, the Asian metro immediately stops the train in front and behind the affected one. Eu2-B starts turning trains short immediately, even if the delays are only minor. This is because the line is extremely long and any delay will make it difficult to get the drivers back to the depot in time for their required meal relief. This is also a good example of how the choice of strategy depends on the constraints, as will be discussed further. Station skipping is only done by Am1 when the distance between the stations is relatively short (see Table 1). Applying the strategy on other metros might cause a higher inconvenience for the passengers. However, when other metros were asked why it is not applied (e.g., Eu1 or Eu3), answers showed that the possibility was some- TABLE 3 Percentage of Transit Lines Applying Strategies Minor Slow Moving Incident Delay Blockage Stacking (do-nothing) 55% 36% 0% Stacking (de-train) 0% 9% 91% Freezing 64% 18% 55% Hold number of trains 82% 45% 55% Remove trains 18% 100% 9% Add gap trains 0% 18% 0% Turning short 36% 55% 82% Station skipping 18% 0% 0% Diverting 0% 18% 18% Shuttle service 0% 0% 100% times not fully considered. This is true of some of the other strategies as well. CHOICE OF STRATEGY DEPENDING ON CONSTRAINTS For this type of analysis one would ideally construct a multinominal logit model with strategy being the dependent variable and constraints as the set of independent variables. However, with observations from only 11 transit lines, this approach is not practical. As a simple alternative, the following analysis was carried out. Let the strategy matrix S ij have binary values. Where s ij = 1 means that metro i uses strategy j and 0 means it does not use this strategy. A second constraint matrix C ik is defined, where each element c ik describes constraint k of metro i. C ik can have rows consisting of binary values, indices, or continuous variables. An example for a column k where c ik has binary value is Central Control, for a column k consisting of indices is number of spare drivers per shift and for k being a continuous variable is operated headway in peak hour. Matrix X = C T S then shows strategies versus constraints, where X has the size k*j. To account for popular strategies, X is divided by the number of metros using strategy j. xkj x kj = S i ij The interpretation of X is the following. If k is a binary constraint, a value of x kj near 1 (0) means that most metros that have (not) constraint k (do not) use strategy j. If k is an index or continuous value, x kj shows the average value of this constraint for those metros using strategy j. Note that this approach does not consider correlation between the independent variables but gives some indicative results. Table 4 provides the analysis for some of the constraints and minor incidents. The table indicates, for example, that it is those metros that use all their signaling capacity that are most likely to remove trains. Signaling capacity used is here defined as the operated headway during peak hour divided by the shortest possible headway due to signaling constraints. This is also what one would expect because these lines would otherwise have no possibility to free up track space and accelerate delayed trains. The table further shows that those lines that operate with ATO and those that operate with cab secure radio are more likely to use hold number of trains and turning short, which are more complicated, in the sense that they probably require more communication to the drivers. This suggests that upgraded technology will also give operators more options to recover from delays. Constructing the tables also for slow-moving delays and blockage gives similar results because it shows that those metros with fewer constraints have more options to recover from delays. It is, however, important to note that this approach does not consider correlation between the independent variables. The authors therefore suggest that these results are only indicative and further analysis should be carried out once more observations become available. EXAMPLES OF CONSTRAINTS AND SERVICE REGULARITY According to the constraints identified above, one would expect a more regular service and a better service recovery from the Asian metro and the metros with higher flexibility scores in Table 2. The following example data confirm this assumption. ( 4)

7 36 Transportation Research Record 1930 TABLE 4 Minor Incidents Average Constraint Value for Metros Using This Constraint Stacking; Hold Number Remove Turning Station Strategy Do-Nothing Freezing of Trains Trains Short Skipping Line length (km) Avg. station spacing (station/km) Line complexity (1:yes, 0:no) Signaling capacity used (%) Turnarounds/line length (1/km) ATO (1:yes, 0:no) Cab secure radio (1:yes, 0:no) Level of service control centralization (2:network control room (CR), 1:line CRs, 0:line section CRs) Unions and level of regulation (1:complex, 5:simple) Figure 4 shows the service regularity of Am1-A (flexibility score 12) over 1 day at three different measurement points. One minor incident occurred during this day. The irregularity coefficient b is calculated with Equations 1 and 2. The deterioration of the regularity further downstream can be seen, which is an indication that bunching effects occur and that the recovery process is slow. The figure shows that b Station A < b Station B < b Station C and that there are more large headways at Station B, which is downstream from Station A, and even more large headways at Station C, which is even further downstream. (The scheduled headway is 5 min but at Station A 43% of the headways are larger than 6 min, at Station B 47% are larger, and at Station C, this increases even more to 50%.) Note, that there are fewer short headways at B or C which could be due to trains being regularly turned around before reaching the terminus or because the data are only a random sample of headways with different numbers of observations. In contrast to this is the recovery process and regularity performance of As1-A (flexibility score 16 ). Detailed headway data were available for the service before and after a 4-min incident occurred during the morning peak, at a 10-min travel time downstream from the South Terminal near Station 1. A door defect meant that all passengers had to alight and the empty train was then taken out of service. For a quicker recovery one of the southbound trains was turned short a few stations before reaching the South Terminal. The headways are relatively quickly damped (service mainly recovered within 30 min). Examples from Eu2 and Am1 showed recovery times of more than 2 h for incidents with a similar initial delay and which also occurred during the morning peak hour. Comparing three characteristics of any recovery process in more detail shows that the Asian metro has advantages in terms of: (a) time needed for service recovery, (b) extremely long headways caused by the incident, and (c) damping down of irregularity downstream. Figure 5 shows the headways during the first 2 h only after a minor incident occurred on As1-A. These are the 2 h of worst regularity performance, which emphasizes the difference compared with Figure 4 (complete day performance of Am1-A on a day with a minor incident). Figure 5 shows that (a) the time needed for recovery is short (few headways deviating to a large degree from the scheduled headway), (b) there is only one extremely long headway occurring at Station 1, and (c) at the downstream terminal, the headways are more regular than at the incident location (b Station 1 > b North terminal). Therefore, this can be seen as an example for good service recovery. The general difference in service regularity between Am1 and the Asian Metro can also be seen through the three to four times higher irregularity coefficients b on the American line. Data from 31 min Station C Station B Station A % Trains Later than Threshold 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Scheduled Headway Station C Station B Station A (b=120) (b=113) (b=95) Headway Threshold (sec) FIGURE 4 Regularity of Am1-A northbound service (over 1 day).

8 Schmöcker, Cooper, and Adeney 37 North Terminal (NT) Station 1 (S1) South Terminal (SN) % Trains Later Than Threshold 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Scheduled Headway (average) Station 1 N Terminal (b=21.6) (b=16.8) Headway Threshold (sec) FIGURE 5 Regularity of As1-A northbound service (after a minor incident). European metros are more similar to Figure 4 than Figure 5, which are in line with the ranking of constraints in Table 2. CONCLUSIONS This paper started by outlining why service reliability is important for customers and operators, and how the priorities of the two differ. It was then argued that for high-frequency metro railway services passengers waiting on the platform require a headway rather than a timetabled service because this minimizes their travel time uncertainty. The implication for the mass transit rail operator is that the customer prefers a regular over a punctual service. However, passengers already on a train would like to see the travel time of their train minimized and metro operators also prefer a timetabled service mainly because of train operator and rolling stock constraints. This conflict between regularity and punctuality maximization is the main reason why metros use a number of service recovery strategies (in particular, a mixture between stacking and holding). The study identified 10 delay recovery strategies used by metro railways, and then went on to identify the key constraints that influence the likelihood of success of each delay recovery strategy. Data analysis from 11 lines suggests a relationship between constraints and choice of strategy. It is pointed out that those metros operating with more modern signaling and control technologies (for example, ATO or cab secure radio) also have a wider choice of recovery strategies. The examples of service recovery illustrated in this paper suggest that metros with fewer constraints are more likely to recover more quickly from delays. One implication for metro management is therefore to consider whether some of the existing constraints could be removed. Network and technological constraints such as crossovers and signaling systems might only be changeable in the long term, and also staffing levels and passenger behaviors take longer to alter. However, in the short term, metro operators can learn from the strategies and management techniques used by other metros and optimize within their existing constraints. ACKNOWLEDGMENTS The authors thank the participating metros for their support and their help with the data collection. They also thank Robin Hirsch (RTSC), Larry Gould (NYCT), and several anonymous reviewers for helpful comments. REFERENCES 1. Rehnström, G. Increasing the Service Quality of Metropolitan Railways. Report 3. 49th International UITP Congress, Stockholm, Sweden, Lombart, A., and M. Favre. Global Quality of Metros. Report 2. 51st International UITP Congress, Paris, Adeney, W. E., R. J. Anderson, D. J. Graham, and R. C. D. Hirsch. CoMET Key Performance Indicator (KPI) Research and Development. Presented at CoMET Annual Meeting, Hong Kong, October Bates, J., P. Jones, and J. Polak. The Importance of Punctuality and Reliability: A Review of Evidence and Recommendations for Future Work. Report, BR Business Consultancy, University of Westminster, Transport Studies Group, Chapman, R. A. Bus Reliability: Definition and Measurement. Research Report 18. Transport Operations Research Group, University of Newcastle upon Tyne, Shen, S., and N. H. M. Wilson. An Optimal Integrated Real-Time Disruption Control Model for Rail Transit Systems. Lecture Notes in Economic and Mathematical Systems, Vol. 505, 2001, pp Eberlein, X. J., N. H. M. Wilson, and D. Bernstein. Modeling Real- Time Control Strategies in Public Transit Operations. Lecture Notes in Economic and Mathematical Systems, Vol. 471, 1996, pp Nuzzolo, A. Transit Path Choice and Assignment Model Approaches. In Advanced Modeling for Transit Operations and Service (W. H. K. Lam and M. G. H. Bell, eds.), Pergamon, New York, Rahbee, A. Rail Transit Operations Analysis: Framework and Applications. M.Sc. thesis. Massachusetts Institute of Technology, Cambridge, Mass., Hirsch, R. C. d A, and W. E. Adeney. Making a Real Difference to Performance: Global Benchmarking in Railways. Proc., Performance Measurement Theory and Practice, Churchill College, University of Cambridge, U.K., July 14 17, Railway Technology Strategy Center. CoMET Benchmarking 2003: Train Service Reliability, Regularity and Punctuality Case Study. Final Project Report. RTSC, Imperial College London, The Rail Transit Systems Committee sponsored publication of this paper.