HEADWAY ADHERENCE. DETECTION AND REDUCTION OF THE BUS BUNCHING EFFECT Josep Mension Camps Director Central Services and Deputy Chief Officer of Bus Network. Transports Metropolitans de Barcelona (TMB). Miquel Estrada Romeu Associate Professor. Universitat Politècnica de Catalunya- BarcelonaTECH. 1. INTRODUCTION Transit systems should provide a good performance to compete against the wide usage of cars in metropolitan areas. The level of service of these systems relies on a proper temporal and spatial coverage provision (high frequencies, low stop spacings) as well as significant regularity and comfort. In this way, bus systems in densely populated cities usually operate at short headways (10 minutes or less). However, in these busy routes, any delay suffered by a single bus is propagated to the whole bus fleet. This fact causes vehicle bunching and unstable time-headways. In real bus lines, we usually see that two or more vehicles arrive together or in close succession, followed by a long gap between them. There are many sources of potential external disruptions in the service of one bus: illegal parking in the bus lane, failure in the doors opening system, traffic jams, etc. However, some intrinsic characteristics of transit systems and traffic management may also induce delays at specific vehicles such as traffic signal coordination and irregular passenger arrivals at stops. These facts make the bus motion unstable. Therefore, bus bunching is a common problem in the real operation of buses all over the world that must be addressed. The crucial issue is that bus bunching has a great impact on both users and agency cost. From a passenger perspective, the bus bunching phenomena increases the travel time of passengers (riding and waiting time) and worsens the vehicle occupancy. The delayed vehicle is usually overcrowded since it has to pick up more passengers than expected at stops. Besides, the waiting time of passengers are increased due to this variation and the boarding problems. From the agency point of view, any less-utilized vehicle represents a waste of capacity. In fact, bus schedules often encompass recovery time or slack time at the end of the route to alleviate the propagation of disturbances in the next roundtrips. This fact increases the route's cycle time and therefore more vehicles should be deployed to guarantee a target time-headway. Bus agencies have promoted the creation of expensive ICT systems to track the fleet, calculate the bus regularity and perform control strategies to maintain the desirable headway. However, there is a wide range of metrics proposed by transit agencies to calculate and range the bus regularity. Basically: EWT (Excess Wait Time), Standard Deviation, Wait Assessment and Service © AET 2016 and contributors 1 Regularity. The bunching effect, according to the TCQSM, Transit Capacity and Quality of Services Manual, can be monitored as the coefficient of variation of headways, Cv.h: the standard deviation of headways (representing the range of actual headways), divided by the average (mean) headway. In addition to that, several control strategies have been proposed to tackle the bus bunching effect. These strategies modify the natural motion of buses in order to keep the vehicle temporal spacings constant. Traditionally, the bus bunching is addressed deploying recovery times at holding points in the bus route (Barnett, 1974; Turnquist, 1981; and Rossetti and Turitto, 1998). Nevertheless, this recovery time increases the round trip time of buses and therefore, increases the fleet size allocated to this bus route. Other studies propose dynamic strategies that hold vehicles at stops a variable amount of time to alleviate the propagation of random disruptions in a short time horizon (Eberlein et al. 2001; Dessouky et al. 2003; Adamski and Turnau, 1998). Other contributions determine control theory approaches to modify the kinematic variables of each vehicle depending on the exact location of other vehicles in the route. Daganzo (2009) defines an adaptive variable cruising speed for bus routes with good frequencies. If a vehicle is running close to the vehicle ahead, the former vehicle is slowed down. The modification of speed is proportional to the difference between the target and the actual headway. Nevertheless, control strategies generally achieve good regularity at the expenses of high operating costs. In fact, all control strategies maintain the time-headway regularity allocating slacks or slowing the motion of buses along the route. This paper has two major objectives. First of all, we want to determine the most effective way to measure and monitor the regularity of a bus fleet in real operation. A comparison of several existing metrics in real bus routes will be carried out in order to provide insights to bus agencies about how bus regularity must be monitored. The second objective is to propose a new adaptive control strategy to tackle the bus bunching effect. This strategy is based on both the modification of speed profiles of buses and the deployment of dynamic traffic light priority for delayed buses. Therefore, delayed buses are speed up since the green time is extended when they arrive at signalized intersections. This strategy may help bus agencies minimizing the operating cost of control protocols. 2. MEASURING BUS REGULARITY Hereafter, we include the definition and description of the most common procedures for calculating bus service regularity. In section 4.2., a summary with their main strengths and weaknesses is widely detailed. 2.1. Excess Wait Time, EWT EWT is a measure of perceived regularity. It measures the average additional waiting time that passengers experience, compared to the waiting time they expect. The lower the EWT, the more likely is that passengers will not wait more than scheduled and perceive the service as regular. © AET 2016 and contributors 2 푛 2 푛 2 ∑=1 퐴퐻 ∑=1 푆퐻 퐴푊푇 = 푛 ; 푆푊푇 = 푛 2 · ∑=1 퐴퐻 2 · ∑=1 푆퐻 퐸푊푇 = 퐴푊푇 − 푆푊푇 (2.1) AH: Actual headway SH: Scheduled headway EWT: Excess Wait Time AWT: Actual Wait Time SWT: Scheduled Wait Time 2.2. Standard Deviation The second available indicator is the standard deviation of the difference between scheduled and actual headways. 푁 1 휎 = √ · ∑(퐴퐻 − 푆퐻 )2 (2.2) 푁 1 AH: actual headway SH: scheduled headway If data follows a Normal Distribution, then relates to 68% of the population. 2.3. Wait assessment The wait assessment indicator represents the regularity within absolute band. The percentage of actual headway that is within ±2 minutes of scheduled headway. The higher the percentage, the more regular the service is. 2.4. Service regularity The service regularity estimates the regularity within proportional band (20% of scheduled headway). The percentage of actual headway within ±20% of scheduled headway. The higher the percentage, the more regular the service. The width of the proportional band may vary if the scheduled headway is not constant. 2.5 Bus Bunching effect The bunching effect can be measured in terms of headway adherence, the regularity of transit vehicle arrivals with respect to the scheduled headway, and it is calculated as the coefficient of headways variation cv.h: the quotient between the standard deviation of headways (representing the range of actual headways), and the average headway. 푠(ℎ퐴) 퐶푣,ℎ = (2.5) ℎ퐴 © AET 2016 and contributors 3 Cv.h: Coefficient of variation s: Standard deviation hA: Actual headway ℎ̅퐴: Average actual headway The headway variations are calculated as the actual headway between consecutive departures at stops and the scheduled headway. The coefficient of variation is a non-dimensional and non-negative KPI. The usage of the coefficient of variation for estimating service regularity (quality offered to customers) is statistically consistent. Additionally, the use of the coefficient of variation has a physical meaning, because it simulates the overrun of the users in terms of waiting time at the tops due to the irregularity of service. The Transit Capacity & Quality of Service Manual, TCQSM, (TRB, 2009) proposes a service regularity appraising whilst setting diverse level of service based on the coefficient of variation of the headway. Table 1. Levels of service according to service regularity of a bus route. Source: TCQSM, Transit Capacity & Quality of Service Manual LoS Cvh P(abs[hi – h] > 0,5·h) Passenger and Operator Perspective A 0,00 – 0,21 ≤2% Service provided like clockwork B 0,22 – 0,30 ≤10% Vehicles slightly off headway C 0,31 – 0,39 ≤20% Vehicles often off headway D 0,40 – 0,52 ≤33% Irregular headway, with some bunching E 0,53 – 0,74 ≤50% Frequent bunching F 0,75 >50% Most vehicles bunched Note: applies to average scheduled headway of 10 minutes or less 3. BUS MOTION AND CONTROL STRATEGIES An operational model is developed for replicating the bus motion in a given route. The model is based on the current location of buses and demand at stops in order to estimate the time headway response among them. It can also estimate the effect of implementing control strategies on the headway variation and total cost. The details of this model can be find in Estrada et al. (2016). A straight bus is considered whose roundtrip length is L. The target time-headway of this line is denoted by H. It consists of N bus stops, where the position of each stop in the line is denoted by s. Stops s=1 and s=s* (1<s*<N) denote the starting points for each route direction trip. The distance from each stop s (s=2,..,N) to the first stop s=1 is given by xs, considering that x1=0m. Boarding and alighting passenger operations are allowed at each bus stop s, s=1,..N. Let J be the total number of buses operating the whole roundtrip. Each bus is labeled by j=1,…, J.