Definition and Properties of Alternative Bus Service Reliability Measures at the Stop Level

The Transit Capacity and Quality of Service Manual (TCQSM) provides transit agencies with tools for measuring system performance at different levels of operation. Bus service reliability, one of the key performance measures, has become a major concern of both transit operators and users because it significantly affects user experience and service quality perceptions. The objective of this paper is to assess the existing reliability measures proposed by TCQSM and develop new ones at the bus stop level. The latter are not suggested as replacements for the existing measures; rather, they are complementary. Using empirical data from archived Bus Dispatch System (BDS) data in Portland, Oregon, a number of key characteristics of distributions of delay (schedule deviation) and headway deviation are identified. In addition, the proposed reliability measures at the stop level are capable of differentiating between the costs of being early versus late. The results of this study can be implemented in transit operations for use in improving schedules and operations strategies. Also, transit agencies can use the proposed reliability measures to evaluate and prioritize stops for operational improvement purposes. Journal of Public Transportation, Vol. 16, No. 1, 2013 98 Introduction Monitoring of the performance measures of public transportation systems has improved since advanced surveillance, monitoring, and management systems have been deployed by transit agencies worldwide. In recent years, service reliability, a key performance measure, has become an important topic for researchers, transit agencies, and policy makers because it significantly affects user experience and service level perceptions. Reliability affects the waiting time of passengers at a stop for a bus to arrive. Reliability also affects total trip time of a passenger. Abkowitz et al. (1978) suggested that reliability is one of the most important factors influencing passenger mode choice. Bowman and Turnquist (1981) found that service unreliability increases operating costs. Reliability is influenced by a number of factors. As listed in the TCQSM (2004), these factors include: • traffic conditions • road construction • vehicle and maintenance quality • vehicle and staff availability • transit preferential treatments • schedule achievability • evenness of passenger demand • differences in operator driving skills, route familiarity, and adherence to schedule • wheelchair lift and ramp usage (generally dwell time) • route length and number of stops • operations control strategies • weather • incidents Despite all these, the transportation profession lacked a uniform set of transitcapacity and quality-of-service definitions, principles, practices, and procedures for planning, designing, and operating vehicles and facilities until the publication of the Transit Capacity and Quality of Service Manual (TCQSM 1999), First Edition. Also the Highway Capacity Manual 2000 (HCM 2000) provides a broad range of Level-of-Service (LOS) measures for all the modes, including auto, transit, bicycle, and pedestrian modes. Chapter 27 of the HCM 2000 provides four transit LOS measures: service frequency, hours of service, passenger load, and service reliabilDefinition and Properties of Alternative Bus Service Reliability Measures at the Stop Level 99 ity. Most recently, the Highway Capacity Manual 2010 (HCM 2010) defines transit service reliability as the “unplanned passenger waiting time at the stop.” Also, chapter 17 of the HCM 2010 suggests that excess wait time reflects transit vehicle reliability. In 2004, Transportation Research Board’s Transit Cooperative Research Program (TCRP) released the second edition of the TCQSM (2004), which contains information about various types of public transportation and provides a framework for measuring transit availability and quality of service from the passenger point of view. The TCQSM introduces a new approach to measure performance of transit service using a two-dimensional LOS framework covering two service quality dimensions (availability and comfort/convenience) for three levels (stops, route segments, and the whole system). Camus et al. (2005) discussed advantages and limitations of the TCQSM method for LOS estimation. The TCQSM reliability measures 1) do not consider the amount of delay but only the number of trips that are late, 2) do not adequately address the effect of early departures on users, and 3) introduce a fixed tolerance around the schedule to estimate the on-time performance. From different perspectives, it may be of interest to investigate reliability from the standpoint of changes and adaptations necessary in case of system disturbances (such as unavailability of service between certain stations, etc.). This is considered in some publications (see, e.g., Kepaptsoglou and Karlaftis, 2009) but usually is not a topic in transit reliability. Moreover, issues considered in behavioral sciences may also be investigated in public mass transit. For instance, according to Duarte et al. (2010), public transport service impacts the quality of travel experience and the well-being of travelers, as well as their travel behavior leading to the influences of transportation happiness or satisfaction on transport mode choice. The objective of this paper is to assess the existing reliability measures proposed by the TCQSM and develop alternative complementary reliability measures that account for the interactions among the above-listed factors and capture more characteristics of transit service unreliability. This paper uses the TCQSM definition of reliability: “Reliability includes both on-time performance and the evenness of headways between transit vehicles” (TCQSM 2004). Using empirical data from archived Bus Dispatch System (BDS) data in Portland, Oregon, several key characteristics of distributions of delay and headway deviation are identified, and alternative measures at the stop level are proposed. Toward this end, the results of this study can be fed into the transit operations field for use in improving schedules and operations strategies. Also transit agencies can use the proposed reliability measures to evaluate and prioritize stops for operational improvement purposes. Journal of Public Transportation, Vol. 16, No. 1, 2013 100 The remainder of this paper is organized as follows. The second section provides a brief background on transit reliability. In the third section, existing reliability measures in the TCQSM are reviewed. In the fourth section, derivations of the proposed reliability measures are presented. The fifth section presents some empirical analysis results, and the last section concludes the paper. Background Various studies build upon the body of research on bus service reliability by employing detailed statistical analysis to measure service reliability using archived Automatic Vehicle Location (AVL) data. AVL technology has been widely implemented in the transit industry in the past decade. Bertini and El-Geneidy (2003) demonstrated robust ways that data collected by a BDS can be converted into potentially valuable transit performance measures. The Metropolitan Transportation District of Oregon (TriMet) provides transit service in the three-county Portland metropolitan area. TriMet operates 62 million annual bus trips, serving a population of 1.2 million in a 592-square-mile area with 700 vehicles on 98 routes. TriMet’s BDS reports detailed operating information in real time, every 90 seconds. In addition, the BDS archives very detailed stop-level data from the bus during all trips (Bertini and El-Geneidy 2003). This includes actual stop time, dwell time, and number of boarding and alighting passengers at every stop. Each geocoded stop has a predefined 30-m (98-ft) stop circle around the stop. The BDS records the arrival time when the bus enters the stop circle and records the departure time when the bus departs the same circle (Bertini and ElGeneidy 2004) (see Figure 1). Using the archived BDS data, a number of measures can be simply calculated. The scheduled headway at a particular stop can be computed as the scheduled stop time for trip i at a stop minus the scheduled stop time for trip i-1 at the same stop: Scheduled Headway = stop timei ‒ stop timei-1 (1) Similarly, actual headway, delay (or schedule deviation), and headway deviation can be computed as follows: Actual Headway = leave timei ‒ leave timei-1 (2) Delay (schedule deviation) = leave timei ‒ stop timei (3) Headway Deviation = Actual Headway ‒ Scheduled Headway (4) Definition and Properties of Alternative Bus Service Reliability Measures at the Stop Level 101 Source: Bertini and El-Geneidy 2003 Figure 1. TriMet BDS system: (a) time distribution, (b) stop circle description Lin et al. (2008) used AVL data from Chicago Transit Authority (CTA) bus routes to develop a quality control framework involving Data Envelopment Analysis (DEA). The framework aggregates different service reliability measures into a comprehensive reliability measure. El-Geneidy et al. (2010) used AVL data from Metro Transit in Minnesota to analyze bus service reliability of a few routes at the segment and route levels in Minneapolis. A review of AVL system implementations in the U.S. can be found in El-Geneidy et al. (2010) and Furth et al. (2003). Several studies have evaluated existing reliability measures and proposed new metrics at different levels (Camus et al. 2005; Xin et al. 2005; Tumlin et al. 2005; Furth and Muller 2006; Fu et al. 2007; Ap. Sorratini et al. 2008; Chen et al. 2009). Camus et al. (2005) discussed advantages and limitations of the TCQSM method for LOS estimation and proposed a new reliability measure named “weighted delay index.” Xin et al. (2005) used the TCQSM measures to study several routes and found that Journal of Public Transportation, Vol. 16, No. 1, 2013 102 TCQSM measures are sensitive to planning/design variables and can be simply calculated by transit agencies using available data. Tumlin et al. (2005) developed a method to evaluate transit performance in the context of different transportation environments. Furth and Muller (2006) found that traditional transit service measures underestimate the total costs of service unreliability because waiting time and service reliability are analyzed separately. Fu et al. (2007) developed a Transit Service Indicator (TSI) that estimates the quality of service results from the interaction of supply and demand. TSI uses multiple performance measures, including hours of service and service frequency. Ap. Sorratini et al. (2008) investigated measures to assess reliability, such as headway, excess waiting time, service regularity, and recovery time of an urban network, using a dynamic micro-simulation model (DRACULA). Most recently, Van Oort et al. (2012) studied ways to improve reliability by adjusting schedule timetables using holding points. To measure reliability, they used punctuality (deviation from the scheduled arrival time) and probability of departing on time. Reliability measures are important because they can be used to identify bus bunching. Unreliable routes are more likely to experience bunching. “Bus bunching takes place when headways between buses are irregular leading to longer waiting times for riders, overcrowding in some buses, low numbers of passengers in the remaining buses, and an overall decrease on the level of service and capacity” (Feng and Figliozzi 2011). For additional information on bus bunching see, e.g., Bellei and Gkoumas (2010). None of the above-mentioned studies have used empirical cumulative distribution of delay or headway deviation obtained from detailed AVL data. Chen et al. (2009) proposed three reliability measures using data from the Beijing transit system: a Punctuality Index based on routes (PIR), a Deviation Index based on stops (DIS), and an Evenness Index based on stops (EIS). The EIS and DIS measures proposed by Chen et al. (2009) require a coefficient of variation of headway, individual headway deviation at each stop, and boardings at each stop. However, unlike the proposed measures in this paper, they do not fully take advantage of the characteristics provided by a cumulative distribution. Existing Reliability Measures Bus service reliability has been defined in a variety of ways, from the perspective of both users and transit agencies. Characterizing the user-perceived service reliability is quite complicated due to the heterogeneity of user preferences, views, and values of time. That is, transit agencies use several different reliability measures. The most widely used of these are on-time performance and headway adherence. Definition and Properties of Alternative Bus Service Reliability Measures at the Stop Level 103 Some agencies also use missed trips and distance traveled between mechanical breakdowns. When buses run at frequent intervals, usually less than 10 minutes, headway adherence becomes more important from the perspective of a passenger. Poor headway adherence causes bus bunching, overcrowding on the lead bus, and longer waiting times. For a passenger arriving shortly before a scheduled bus departure, an early departure is equivalent to a bus being delayed a full headway. The current reliability LOS proposed by the TCQSM considers on-time performance to be an arrival no more than five minutes after the scheduled time. Early departures are considered on-time only in locations where no passengers would typically board. Most transit agencies consider a bus to be late when it is more than five minutes behind the schedule. Early departures are considered to be as bad as being late. Some agencies allow buses to depart up to one minute ahead of the scheduled time. Transit agencies use on-time performance as a key measure of schedule adherence for evaluating system reliability. Therefore, it is important to differentiate between buses that are late versus early, because the cost of being late is different from the cost of being early. Also, it is necessary to know how late and how early buses are. The on-time performance measure proposed by the TCQSM does not take these factors into account. For frequent services, headway adherence is used to determine reliability. As in the TCQSM, headway adherence can be calculated as follows: cvh = standard deviation of headway deviations (5) mean scheduled headway where cvh= coefficient of variation of headways (headway adherence). Headway adherence is based on standard deviation only and does not capture the extreme cases of unreliability. Also, similar to the on-time performance measure, it does not differentiate between the cost of being early versus late. Figure 2 shows a color counter time-space diagram of a selected bus route in Portland, Oregon (Route 15 westbound), visualizing hourly calculated headway adherence. The color, ranging from gray to light gray, represents low LOS to high LOS. The white area in the color counter time-space diagram shows that there are no data for those time intervals and the outlined area represents the high frequency service time periods and stop locations. Journal of Public Transportation, Vol. 16, No. 1, 2013 104 Source: Feng and Figliozzi 2011 Figure 2. Color counter time-space diagram of headway adherence Figure 3 illustrates the empirical cumulative distribution of delay at the SE Stark & 82nd stop (solid curve) from the same bus route shown in Figure 2. The dashed curve is the same distribution when altered slightly, representing delay distribution at a hypothetical stop. These two distributions have identical standard deviation (121.5 sec) and, therefore, identical headway adherences. However, they have considerably different width, defined as the 95th percentile of delay minus the 5th percentile of delay. The distribution width of the solid curve is 378 sec, and the distribution width of the dashed curve is 442.5 sec. This implies different unreliability characteristics that cannot be captured by the existing TCQSM metrics and, thus, calls for a supplementary measure. Definition and Properties of Alternative Bus Service Reliability Measures at the Stop Level 105 Figure 3. Empirical cumulative distribution of delay at the SE Stark & 82nd (solid curve) and a hypothetical cumulative distribution curve (dashed curve) Derivation of New Measures for Bus Service Reliability Focusing on service reliability from the perspective of a transit agency, we propose new reliability measures, using distribution of delays and headway deviations. Here, we use the term delay for schedule deviation. It should be noted that, in some cases, reliability measures from the perspective of a transit agency are entirely different from the user-perceived service reliability. Passenger perceptions of service reliability are partly related to service frequency. Routes with higher frequency may be considered reliable by passengers even if they have poor service reliability. A study by TriMet reported in Kimpel (2001) showed that passengers are more likely to express satisfaction with the performance of bus routes that operate at high frequencies, although later analysis demonstrated that these same routes were among the least reliable. This obvious discrepancy exists because passenger waiting times are still relatively short on high frequency routes with inadequate service reliability, compared to better-performing routes that operate less frequently (Kimpel 2001). Therefore, schedule adherence has been the most important existing reliability measure for infrequent services that operate with headways of more than 10 minutes. For routes characterized by high frequency service, headway variability has been the most important existing reliability measure. Journal of Public Transportation, Vol. 16, No. 1, 2013 106 In the remainder of this section, three alternative reliability measures are proposed. For frequent services the distribution of headway deviations and for non-frequent services the distribution of delays are used to capture unreliability characteristics of a bus service. Earliness Index The Earliness Index (EI) is defined as the percentile rank of delay/headway deviation of zero. The percentile rank of a particular delay/headway deviation is the percentage of delay/headway deviations in its frequency distribution that are lower or equal to it. Let X denote the delay (for infrequent services) or headway deviation (for frequent services) and F(x) denote the cumulative distribution function of x as follows: