TAPPING INTO DELAY: ASSESSING RAIL TRANSIT PASSENGER DELAY USING TAP-IN-TAP-OUT FARE-SYSTEM DATA

Transcription

1 0 0 TAPPING INTO DELAY: ASSESSING RAIL TRANSIT PASSENGER DELAY USING TAP-IN-TAP-OUT FARE-SYSTEM DATA Justin Antos Washington Metropolitan Area Transit Authority 00 Fifth Street, NW, Washington, DC 000 Tel: 0--; Fax: 0--0; jantos@wmata.com Michael D. Eichler, Corresponding Author Washington Metropolitan Area Transit Authority 00 Fifth Street, NW, Washington, DC 000 Tel: 0--00; Fax: 0--0; meichler@wmata.com Word count: _,_ words text + tables/figures x 0 words (each) = _,_ words November, 0

2 Antos, Eichler 0 0 ABSTRACT How do we measure customer delay on a rail transit system? Research into quantifying reliability and passenger delay often defines delay as when speeds or travel times fall above or below a fixed threshold. When applied to a rail transit system, however, this technique may not fully capture the impacts to all transit riders. This paper proposes a new way to assess passenger delay, leveraging the power and richness of transaction-level fare system data not always available in other contexts. To truly understand the full spectrum of impact on transit passengers, this method analyzes the entire distribution of passenger travel times, rather than simply tallying individuals with travel times above a threshold. This method comparing the cumulative distribution of travel times - combines concepts from traffic queueing theory and travel time reliability research in both the transit and highway arenas. The proposed method is then applied to fare system data from the Washington Metropolitan Area Transit Authority s Metrorail system to illustrate the delay from different strategies for providing continued service during rail system rehabilitation. Keywords: Transit, Public Transportation, Rail, Delay, Cumulative Distribution, Travel Time, Travel Time Reliability, Excess Journey Time, Economic Impact

3 Antos, Eichler INTRODUCTION The Washington Metropolitan Area Transit Authority s (WMATA) Metrorail system is a heavy rail transit system of lines, stations, and over 00,000 boardings per typical weekday. At peak times Metrorail is very crowded, and levels of demand often strain the system s vertical circulation capacity (escalators, elevators, and faregates) or line-haul capacity (trains). In 0, the Washington Metropolitan Area Transit Authority (Metro) embarked on a multi-year, multi-billion dollar, system-wide rebuilding and renewal of the nearly 0-year-old Metrorail system. This reinvestment is a critical component to maintaining a State of Good Repair. Metro employs two strategies to maintain service while performing this track and station maintenance work: single tracking around work zones, or closing entire stations and rail segments over weekends, replacing rail service with bus bridges. To accommodate the work, Metro reroutes trains and/or closes stations in some areas, during which some customers may experience increased travel time. Metrorail fares vary according to distance traveled, so passengers must tap in to the rail system at their origin station, and then tap out at their destination station. In this process, WMATA also captures every passenger s total travel time between entering and exiting the fare gates, which combines on-vehicle time as well as walk and wait time. This paper proposes a strategy for measuring the travel time cost to customers (total person delay) that is a departure from current methods evaluating excess journey time (EJT) in highways and transit, and instead looks to queueing theory for a way to compare the entire distribution of travel times to quantify delay. By evaluating the time-cost of different strategies for providing alternate service, Metro can understand much better the impacts to customers, and leverage this knowledge when engaging in necessary system renewal. LITERATURE REVIEW Methods to quantify passenger delay arising from incidents, special events, and other events have been studied in the past, particularly in highways but emerging in transit as well Quantifying the costs arising from changes in travel time is certainly nothing new most travel demand forecasting models estimate changes in travel time as a key output. The U.S. Department of Transportation states that the value of travel time is a critical factor in evaluating the benefits of transportation infrastructure investment, and issues guidance on how to monetize travel time savings for a variety of applications (). But this type of quantification is designed to evaluate changes in typical travel times. In the field of highway research, the cost of roadway congestion is extensively studied, perhaps most publicly in the Texas Transportation Institute s Urban Mobility Report (). A distinction is often made between recurring and non-recurring congestion, and between delay caused by weather, incidents, work zones, and more (). Estimating the amount and cost of delay at a systemwide level for roadways is usually calculated as the difference between free flow speed and actual observed (slower) speed.

4 Antos, Eichler In public transportation, research on non-recurrent delay to passengers has often focused on the vehicles in the transit network, and is thus only an indirect proxy for the passengers experience. This is perhaps because transit operators have better data on train and bus movements, and weaker data on passenger movements. Many transit operators, including WMATA (), measure schedule or headway adherence, and report on-time performance of vehicles. Such metrics are useful in the short-term to operating agencies, whose immediate priority is to operate the scheduled service. However, these measures do not always correspond to passengers perceptions. Customers may perceive impact for reasons unrelated to vehicle movement vehicle too full to board, or queues behind turnstiles and staircases. Furth & Muller () extend the concept of headway reliability to the passenger s perspective, for waiting time only. They use data on the location and of transit vehicles to show that the cost to the passenger is not only the average time spent waiting on a platform or a bus stop, but also the potential waiting time, or the time a passenger must budget to be sure they arrive on-time at their destination % of the time. This concept corresponds to the reliability buffer time method or planning time index in highway research (). Osuna & Newell () propose inferring a typical transit passenger s wait time by estimating their average wait time as half a headway, adjusted by the consistency of that headway, as shown in Equation. Scheduled Headway ( + Coefficient of Variation of Actual Headways ) () Measured this way, typical wait time would partially account for the reliability experienced by passengers, which presumably incorporates the frequency and severity of disruptions. However, these approaches do not directly measure the actual delay experienced by transit passengers. Recently, research has focused on the demand side for transit, thanks in part to the automated fare systemsthat directly measures passengers, not vehicles. London Underground reports Excess Journey Time (EJT), which it defines as the average time added to journeys by delays, crowding and queuing, over and above the nominal scheduled journey time (). Using London Underground data, Uniman () advances the idea of EJT and proposes looking not at the schedule, but at the distribution of travel times to estimate Excess Reliability Buffer Time, or aggregate actual travel times exceeding a reliability buffer of the th, th historical percentile, etc. Uniman finds there is always irreducible noise in passenger travel times in fare system data that is not real delay, and proposes statistical techniques to minimize this problem. Zhao et al. (0) further explore EJT, and conclude that EJT strikes a useful balance between the passenger's and operator's perspectives of public transport service quality. Hendren et al. () demonstrate the feasibility of counting passengers whose travel time exceeds an acceptable amount, and propose several ways of setting that threshold the schedule, the th percentile of historical averages, and more. In addition, they explore how such a metric could be incorporated into a transit agency s performance measures.

5 Antos, Eichler Other methods of estimating delay in the field of highway research also exist. Daganzo and Newell propose using techniques from queueing theory to assess delay, using the difference between cumulative arrival and departure functions as a measurement of delay (). This paper proposes a new way to quantify the impacts to rail transit passengers as a result of non-recurrent delay, by combining concepts from highway traffic queueing theory and transit EJT. CUMULATIVE DISTRIBUTION FUNCTION (CDF) COMPARISON METHOD FOR EVALUATING DELAY This section shows the advantages and disadvantages evaluating transit passenger delay using a threshold, and proposes a new method based on queueing theory that resolves some issues with this approach. The CDF Comparison method proposed here calculates the delay by comparing the cumulative distribution functions of a day with delay and a normal day. Travel time data from a rail operator s fare system does not only reflect the time the customer spent traveling on a transit vehicle, they also include walk access and egress time, which can be fairly diverse in normal circumstances. Therefore, any method to assess delay with this data must be sensitive to this diversity. Problems with Evaluating Delay Using a Threshold One way to evaluate delay in a transportation network is to count customers with a travel time greater than some cutoff value. For instance, this cutoff is the scheduled travel time for London s EJT. This approach can lead to three kinds of problems: It can flag as delayed customers who may have completed the trip in as short a time as possible, and who were not actually delayed by the operator. o Example: customer enters the system and chooses to wait for an elevator instead of taking an escalator or stairs. This customer misses a train while waiting for the elevator, and waits a full headway before boarding. This longer journey time is because the customer preferred the elevator, but could be flagged as excessive journey time. This may unfairly penalize the transit operator. It can flag as not-delayed customers who actually experienced delay. o Example: customer enters the system and immediately boards a waiting train as the doors close. Seconds later, the train pulls away but is then delayed for five minutes while a disabled train on the track ahead is moved. Upon arrival at the destination station, the customer quickly exits the system with a total travel time below the delayed-customer cutoff. The five minutes of delay experienced by this customer can go unnoticed. This is too generous to the transit operator. It may never report days with zero delay. o A transit agency would desire to be able to report zero customer delays on a day with no disruptions, and as such it is important to calculate customer delay using a metric with a possible range of delay values that includes zero. The innovative feature of the CDF assessment proposed below is that it acknowledges that individual travelers will always have different travel times, as Uniman () notes, and accommodates for them.

6 Antos, Eichler 0 Comparing Cumulative Distribution Functions to Calculate Delay Take a single origin-destination station pair in a rail network, and suppose that on each day, ten customers made the trip from this origin to this destination. Let Normal, Event and Event be three days that have different travel time profiles for a given origin/destination station pair. On the Normal day there is no external delay to the customer, and wait time, walk speed and elevator use are the only variables that result in a distribution of travel times. Under Event, a slow-zone was implemented all day that added three minutes to every customer s travel time. Under Event, a slight disruption only impacted a handful of customers by a few minutes. Let the minimum travel time between these stations equal tt, and each day have the travel time profiles in minutes listed below (Table ). TABLE : Example arrival profiles (number of customers arrived by time interval) Travel Time Arrivals-Normal Arrivals-Event Arrivals-Event tt 0 tt+ 0 tt+ 0 tt+ tt+ tt+ tt+ 0 0 tt+ 0 0 tt+ 0 0 tt tt Taking Normal and Event first, the histogram of travel time shows some overlap between the travel time profiles (Figure ). Given that this example is using a total of 0 trips, the th percentile would fall between the eighth and ninth arrivals as illustrated. Using the th percentile as the threshold for delay, the first customer under Event with a travel time of tt+

7 # of Customers Antos, Eichler would be considered on-time, even though by definition of Event, all customers experienced minutes of delay. th Percentile of "Normal" Normal Event 0 0 Travel Time FIGURE Histogram of Normal and Event Travel Times Converting these histograms into cumulative distributions helps better illustrate the actual delay experienced by each customer (Figure ). The delay experienced by each person is the horizontal distance between the Normal and Event curves, three minutes each. And therefore the total delay will be ( minutes 0 persons) 0 person-minutes. The total number of customers delayed is the vertical height of the region made by the space between the two curves. FIGURE CDFs of Arrival Profiles of Normal and Event

8 # of Customers Antos, Eichler 0 This pair of CDFs is analagous to input-output diagram used in transportation operations analysis as described in Daganzo (). To map this pair of CDFs to Daganzo and Newell s work, the Normal curve is the desired output flow of the uncongested system and the Event curve is the actual output flow of the congested system. In fact, the only difference between the methodology proposed here is that Daganzo and Newell evaluate cumulative, concecutive arrivals and departures, using linear time as the X-axis. Under this methodology, the X-axis is travel time instead of time of day. In contrast with the EJT method, this assessment of delay accurately describes that all customers were delayed and provides total delay and delay per person. Evaluating Event provides an additional histogram and an additional CDF (Figures & ). th Percentile of "Normal" Normal Event 0 FIGURE Travel Time Histogram of Normal and Event Travel Times FIGURE CDFs of Arrival Profiles of Normal and Event

9 Antos, Eichler Here the delay caused by Event is not as straightforward, but it can be easily calculated by evaluating each travel time and comparing the expected and actual number of arrivals. In fact, the area of the curve can be achieved by summing the product of the change in the y-axis (percentile of customers) and the change in the x-axis (minutes) (Table ). TABLE Calculation of Delay for Event Using CDF Comparison Travel Time (A) Normal CDF (B) Event CDF (C) Delta-X (D) [B-C] Delta-Y (E) [Ai - A(i-)] Delay [D E] tt tt tt tt tt tt Since this arithmetic was performed on a cumulative distribution function to ensure the heights of the curves match, summing the Delay column provides total delay for the dataset under evaluation in units of ridership-percentage-minutes. The subsequent delay total must be multiplied by the ridership (0 in this example) to achieve a total delay of minutes. Recall that the number of delayed customers is the height of the region between the two curves. In this case, the height of the region is given by the Normal percentile value before the curves reunite (Bt+) minus the Event percentile value after the curves depart (Ct+), or 0. minus 0., resulting in 0. percent of the customers being delayed. Delay per person is therefore one minute each. (Table and Figure ) The EJT method would have counted the last two customers under Event as delayed, arriving and minutes past the shortest possible time, if the Normal day were used to calculate the th percentile. However, this method has illustrated that three customers were delayed. Delayed But Not Late? It is perhaps useful to consider the difference between delay and late. Passengers are delayed when the performance of the transit system makes their travel times lengthier than they otherwise would have been. Passengers are late when they arrive at their destination later than they expected. An individual customer primarily cares that they arrive at their destination within a reasonable travel time. The customer would consider themselves late if their travel time exceeded an expected, normal travel time, because it likely meant they arrived at their destination later than they expected. As such, a customer who moves quickly through a transit station but experiences minor delay on the train may not consider herself late if arriving within an acceptable number of minutes. The transit operator certainly delayed this customer, but she was not necessarily late.

10 Antos, Eichler On the other hand, a customer who just barely misses a train and moves slowly through the transit network, for whatever reason, may experience an above-average travel time, but may not consider themselves late. Some customers may simply use multiple elevators, be more likely to wait if the first train is crowded, or willing to take a longer route to avoid a transfer. The CDF Comparison method accurately captures delay to customers that is caused by a transit operator because it accounts for this diversity among customers. The method assumes a consistent range of travel times between any two stations, depending on passengers walk speed, elevator usage, familiarity with the system, path choice, and other factors. This may be a matter of perspective. Passengers experience one travel time per commute, and thus experience a distribution of travel times across days. A rail operator records a distribution of travel times across all passengers every day. Perhaps using a threshold approach is better suited to evaluating customers with long journey times, where as the CDF Comparison method more accurately calculates delay. Limitations of the CDF Comparison Method The primary limitation of this method is that it relies on knowing each customers elapsed travel time. Rail transit systems like Metro which record both entry and exit times, and therefore and elapsed travel time. For operators without tap-out systems, other strategies could be employed. One promising strategy is tracking of Bluetooth and Wi-Fi devices as they enter and exit the rail system, similar to a similar strategy used for highway travel time monitoring as described in Young (). Another limitation of this method is that it is computationally expensive and can be time consuming when applied to large volumes of operational data. Finally, rail delays are not the only source of delay between tapping in and out. Customers may face delay in stations due to crowded escalators and elevators that would add variation and delay to customer travel times. Applications of the CDF Comparison Method WMATA is currently assessing how this method might best inform operations. This method has been used to better assess the impacts of rebuilding program planning, and may inform key performance indicators of customer delay, the financial impacts of potential service guarantee programs, and more. EVALUATING CUSTOMER DELAY FROM SERVICE CHANGES USING THE CDF COMPARISON METHOD The application of this method to actual Metrorail passenger travel times can be performed easily for individual station pairs and individual days. The following example evaluates the difference in delay for one origin/destination pair on a variety of Saturdays, including two with no service

11 Antos, Eichler changes, two with single tracking between the origin and destination stations, two with single tracking elsewhere on the line, and two with a bus bridge. Rebuilding and Its Impacts Metro is in the middle of a multi-year, multi-billion dollar capital program to return the rail system to a state of good repair. Metro focuses this rebuilding effort only on weekends when rail ridership is usually light, and only on specific sections of the network to minimize customer impact. When Metro repairs its rail infrastructure, the agency employs two strategies to provide continued service to customers: Single tracking: Trains share one segment of track around the work area. Train headways are reduced to ensure no trains queue on either side of the shared segment. Stations in the work area remain open. Bus bridges: Both inbound and outbound rail segments, and the stations are closed. Buses replace trains between end points of the rail work area. Customers traveling across the work area must exit the train and station, board a bus, reenter the rail system, and exit on the next departing train. About the Data The Metrorail system uses a distance-based fare structure that requires customers to process fare media upon entering and exiting the rail system. The entry and exit transactions are matched to create a record of origin-destination pairs that include time/date stamps and the number of minutes between system entry and exit. WMATA takes a break from its rebuilding efforts for cherry blossom season, a four-week period when tourists visit the District to witness the city s cherry trees in full bloom. This rebuilding hiatus provides a good opportunity to assess a normal distribution of travel times. While the make-up of the rider base during this period is likely different than at other times, it was assumed that the range of travel times resulting from the rebuilding hiatus would be representative of normal conditions. For this analysis, data was pulled only for days when both the origin and destination stations were in service. As such, normal entry and exit transactions were recorded at faregates. Metro attempts to maintain customer data integrity when operating bus bridges, requesting that customers walk through opened faregates instead of tapping in or out when using the bus bridge. Assessment of Impact of Rebuilding on Travel Times Using the method described above, we now assess the travel time impacts on customers traveling between one station pair, Vienna to Smithsonian, on a few different weekends where customers experienced a variety of service impacts. On two Saturdays during cherry blossom season, this origin-destination pair was unaffected and travel times were normal. On two other Saturdays, riders experienced a bus bridge. On a handful of other Saturdays, customers were affected by single-tracking either between Vienna and Smithsonian, or elsewhere on the line.

12 Antos, Eichler All subsequent analysis focuses only on customers traveling between this single station pair. On most occasions, riders on other lines did not experience service impacts. 0 0 FIGURE System Map Subset Showing Origin and Destination Stations Ridership data was extracted from the fare system database for trips from Vienna to Smithsonian for a variety of Saturdays over a three month period, from April to June of 0. These dates were cross-referenced with WMATA s rebuilding calendar to identify which dates saw rebuilding between Vienna and Smithsonian, and what type of alternative service (single tracking or bus bridge) was provided to customers. The rebuilding calendar also illustrated when planned disruptions were occurring elsewhere in the system but not directly impacting the riders between Vienna and Smithsonian (Table ). TABLE Sample Service Impacts Affecting Customers Between Vienna and Smithsonian Stations Date Service Impacts Affecting Customers on Station Pair None Normal Service 0--0 None Normal Service Shutdown - Bus Bridge 0--0 Single-tracking, 0-minute headway 0--0 Shutdown - Bus Bridge Single-tracking elsewhere on the line 0--0 Single-tracking elsewhere on the line 0--0 Single-tracking, -minute headway The raw transactions were grouped by date and number of travel minutes, counting the number of customers who made the trip per travel time increment per day, similar to the format of Table above, illustrated in Figure. Figure shows that when shutdowns or single-tracking events affect this station pair, fewer passengers take the trip. The cumulative distribution of the travel times per day were plotted and assessed for patterns (Figure ). All service impacts shown happened between the origin and destination stations unless otherwise specified as elsewhere on the line.

13 Cumulative Arrival Percentage Customers Antos, Eichler 0 00 Normal Service (//0) Normal Service (//0) FIGURE FIGURE % 0% 0% 0% 0% 0% 0% 0% 0% 0% Travel Time (minutes) Customer Arrivals Diagram (Histogram) 0% Travel Time (minutes) Cumulative Distributions of Travel Times Shutdown - bus bridge (/0/0) Single-tracking, 0-min. headway (//0) Shutdown - bus bridge (//0) Single-tracking eleswhere on the line (//0) Single-tracking eleswhere on the line (//0) Single-tracking, -min. headway (//0) Normal Service (//0) Normal Service (//0) Shutdown - bus bridge (/0/0) Single-tracking, 0-min. headway (//0) Shutdown - bus bridge (//0) Single-tracking eleswhere on the line (//0) Single-tracking eleswhere on the line (//0) Figure shows two Saturdays with no service impacts, or Normal Service, illustrated as solid lines (//0 and //0). The travel time profiles for these two days will be used to define the normal profile, the basis of comparison for the other days. The dotted lines on the graph illustrate two days where single-tracking occurred on the Orange Line, but not between the origin and destination stations. The two dashed lines represent days with single tracking between the origin and destination stations. Finally, the dot-dash lines illustrate two Saturdays where buses replaced trains between the origin and destination station.

14 Antos, Eichler Using the method described above on the extracted data, Table shows total delay, delay per passenger, delayed passengers and percentage of passengers delayed for each of the sample Saturdays. TABLE Stations Estimated Customer Impact on Sample Saturdays, Vienna to Smithsonian Total Delay (personminutes) Delay Per Passenger (minutes) Delayed Passengers Percent of Passengers Delayed Date Shutdown bus bridge (/0/0),. 0 00% Single-tracking, 0-minute headway (//0). 00% Shutdown bus bridge (//0),0. 00% Single-tracking elsewhere on the line (//0). % Single-tracking elsewhere on the line (//0). 0% Single-tracking, -minute headway (//0),. 00% From both cumulative curves and the table above, the bus bridge around rebuilding causes the largest disruption to customers (around minutes per customer) and impacting 00% of them. Single tracking elsewhere on the same line appears to have very little impact on customers: a high percentage of customers are impacted but with very small average delay per passenger. Finally, a difference in headway of minutes between the single-tracking disruptions on April and June resulted in minutes of additional delay per customer, a reasonable result. Note that the analysis above only measures the impact to customers on one example origindestination pair, for illustration purposes. These few hundred riders represent a small fraction of a typical Saturday s ridership of over 00,000 boardings. In the future, this analysis could be extended to all station pairs to estimate the impact (if any) to all customers. CONCLUSION Assessment of travel time, including reliability and delay, on transit systems is still in its infancy, but holds great potential for measuring customer impacts. When using fare system data to assess delay, researchers should take care to account for the diversity and normal variation in the data. This paper shows how using a fixed threshold of acceptable travel time can both undercount and overcount delayed customers, depending on the circumstances. To address these issues, this paper proposes a new method of calculating delay on transit systems, adopted from queueing theory where a form of input-output diagram is constructed using cumulative distributions of travel times. This CDF Comparison method more accurately counts delayed customers and calculates total delay.

15 Antos, Eichler 0 This method provides a good estimate of the number of passengers delayed, and the severity of the delay. However, it focuses on the aggregate impact of a transit system s performance on riders, and may not necessarily assess whether individual passengers thought they were on-time or late. The CDF Comparison method was applied to fare system data from WMATA to quantify how customers are impacted by different strategies for providing service during track and station rebuilding. The goal of this research to demonstrate with real data how the CDF Comparison method can be used in practice, showing the real-world impacts of rebuilding on Metrorail customers. Ultimately, this research can help transit operators such as WMATA understand impacts to customers to minimize delays when performing necessary system maintenance.

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