Headway Adherence. Detection and Reduction of the Bus Bunching Effect

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.

푛 2 푛 2 ∑𝑖=1 퐴퐻𝑖 ∑𝑖=1 푆퐻𝑖 퐴푊푇 = 푛 ; 푆푊푇 = 푛 2 · ∑𝑖=1 퐴퐻𝑖 2 · ∑𝑖=1 푆퐻𝑖

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 𝑖 𝑖 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

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* (1bus 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. It is considered that bus j=j*+1 is in the rear of bus j* (j*=1,.., J-1). The corridor presents I signalized intersections controlled by the Traffic Control Center. The location of each traffic signal is given by zi, that defines the distance between intersection i to the first stop s=1.Each intersection i=1, 2, .., I is defined by the traffic signal cycle time (Ci). For the sake of simplicity,

The travel time of bus j in the segment between stops s and s+1 (Tj,(s)) can be calculated by Equation (3.1). The variable vj (s) is the cruising speed of bus j in this segment. The second term of Equation (3.1) captures all delays caused by a subset Is of traffic signals located in the segment (s;s+1). The variable dj,p is the time that bus j waits at each intersection p∈Is in the route section. It depends on the signaling settings in the whole route. The variable dj,p is 0 if the green phase is active when bus j arrives at intersection p. In a perfect regular systems, the speed of bus j in the segment (s,s+1) can be supposed to be the maximal cruising speed vb.

I x  x s s1 s Tj (s)   d j, p p1 v j (s) (3.1)

The variable Bj(s) is the time that bus j spends at stop s. This term is defined in Equation (3.2) as the sum of two components: the time devoted to opening/closing doors (toc) and the time when passengers are boarding or alighting the bus. For the sake of simplicity, we consider that boarding and alighting operations are made in independent channels. Variable bj(s) is the total number of passengers waiting at stop s for boarding at bus j, while aj (s) is the number of alighting passengers of bus j at stop s. The parameters are respectively the corresponding unit boarding and alighting times.

Bj (s)  toc  maxbj (s);a j (s) (3.2)

Finally, the departure time Dj(s) of bus j from stop s can be calculated by Equation (3.3). This formula takes into account the former temporal terms Tj(s) and Bj(s) for a given bus j. The term m represents a slack time introduced in schedule at stop m in order to compensate potential service disruptions. It should be further analyzed in Section 3.1. Finally, the term m represent the lay-over time. It lets drivers rest an amount of time at stop m before continuing the service. Since buses can perform multiple consecutive roundtrips, the stop under analysis can be labeled by s=1+(kN), 2+(kN),.., N+(kN). Parameter k (0≤k<∞) is an integer number that denotes the number of completed round trip made by bus in the period of analysis. In a perfect regular system, the departure time from the first stop is defined by Tj(s=1)= H(j-1), j=1,..J.

s Dj (s)  Tj (m)  Bj (m) m m s {s 1} (3.3) m1

The total number of buses needed (J) to operate this bus route at a given time  headway H is defined in Equation (3.4). The mathematical operatorx

© AET 2016 and contributors 5 denotes the upper integer of the term x. In a perfect regular system, these terms should be equal for any bus in a short domain of time. Therefore, we should use a representative vehicle or calculate the expected value of the former variables to determine J in dynamic systems.

  N  Tj (s)  B j (s)  s s  J   s1   H  (3.4)    

The real time headway between buses j and j-1 (ahead) at stop s is defined in Equation (3.5). The time headway adherence between two consecutive buses is evaluated by Equation (3.6). Equation (3.6a) determines this evaluation between bus j and bus j-1 (ahead) at bus stop s. It should be noted in Equation (3.6b) that the headway analysis of bus j with regard to bus j+1 (backwards) at stop s is infeasible because bus j+1 has not arrived yet at this stop. Hence, it will be made taking into account the difference of departure time of bus j and j+1at the last stop s* visited by bus j+1 up to this moment.

(3.5) h (s)  T (s) T (s)  s j j j1

forward comparison to bus j-1

 j1, j (s)  hj (s)  H (3.6a)

backward comparison to bus j+1 (3.6b)  (s)  h (s)  H j, j1 j1

The former equations are sufficient to describe the bus motion in perfect regular systems. The conditions to suppose the former statement are: i. Target headway H is a multiple number of the traffic light cycle times Ci. ii. Constant arrival rate of boarding passengers at stops iii. Constant travel time of buses in all segments (s;s+1), i.e. vj(s)=vb.

Under these conditions, the time headway adherence is supposed to be perfect (i.e.  j1, j (s)  0 and cv=0).

However, when any of the former conditions (i-iii) does not happen or when we include a time delay Uj(s)>0 at the travel time of bus j between stops (s,s+1), the bus motion would become unstable. The time disturbance would propagate along the whole route. The former model is able to reproduce this

I s xs1  xs fact just replacing Tj(s)=  d j, p + Uj(s). p1 v j (s)

The model is also able to reproduce the effect of control strategy implementation on the bus performance. This fact is addressed in the following subsections. A part from the well-known static allocation of slack times at holding points, other dynamic control strategies are considered. These dynamic strategies require the real-time headway monitoring of bus departures at stops and a robust methodology to measure the headway variation. This is addressed in the following subsections.

3.1 Slack Time Strategy (ST) Slack time strategy (strategy ST) is based in the inclusion of an additional amount of time s at stop s in the bus schedule. Vehicles are held a maximum time before departing from stop s. Although this term can be implemented at any stop s (s=1, …, N), it is generally performed only at the ending stop of each direction of service in the whole roundtrip (s=s’ and s=N). At these stops, all onboard passengers must alight, so the term does not infer any additional travel time for passengers. However, we can notice in Equation (3.4) that this term increases the operating costs of the agency. Moreover, this strategy is not adaptive since the term is determined myopically. Slacks are calculated off-line, based on the historic disruptions data sets and before the provision of service.

3.2 Adaptive Strategy Based On Speed Modification (SM)

This strategy (referred in this paper as Strategy SM) is aimed at keeping a constant headway among vehicles by means of modifying the cruising speed of each bus. If one bus j is moving away from the vehicle at rear and, at the same time, bus j is catching up the vehicle ahead, the cruising speed of bus j is reduced. The modification of cruising speeds is defined in Equation (3.7). In the first case of Equation (3.7), the term ( j, j1  j1, j ) is a positive number. It represents an extra control time to run the segment between stops s and s+1 to adjust the headway adherence. The parameter fb (fb>0) represents the marginal increase in expected bus delay caused by a unit increase in headway (Daganzo, 2009). All speed modifications are proportional to the headway variation so that this strategy is scalable. On the contrary, when bus j is delayed and it is moving away from the vehicle ahead

(j-1), the term is a negative number. Therefore, the cruising speed of bus j in this segment is increased regarding the speed of the previous section s-1. This speed increment is limited to a maximum value of vb.

  xs  xs1    minvb ;  if  j, j1  0 ;  j1, j  0 xs  xs1     f b ( j, j1  j1, j )   v j (s 1)   v j (s)   (3.7) v otherwise  b    

3.3 Adaptive Strategy Based On Traffic Light Priority (TLP) The strategy referred as TLP is aimed at skipping potential stops of buses at signalized intersections. Green extension and red truncation measures at intersections are provided just for those buses delayed from their schedule. These measures need the dynamic modification of traffic signals (red and green times) depending on the arrival of buses at intersections. Let Ci be the cycle time of the traffic signal i. We assume that this cycle time consists of a green signal (gi green time) followed by the red signal (ri, red time). If a delayed vehicle (  j1, j   j, j1; j1, j >0) arrives at intersection i in the first G seconds of the red signal, we assume that the green signal is extended by gi+G. Alternatively, when this vehicle arrives at the last G seconds of the red signal, the red signal is truncated. In both situations, the bus does not stop at intersections and can reduce the spacing with the bus ahead, reducing the bus bunching effect.

Obviously, the definition of the total amount of green time extended (G) should be constrained to guarantee safety conditions at intersections as well as a minimal traffic flow discharge in the other adjacent streets.

4. RESULTS AND DISCUSSION

4.1. Description of Test Instance The performance of the previous control strategies has been tested in the H6 route of the Barcelona bus network by simulation. It is the new bus route with the highest ridership in the city. This line is 19.3 km long and it runs along highly congested streets and avenues with 39 bus stop locations (Figure 1). The line has a time headway of H= 5 min and a total trip flow of q=1400 pax/h. It is operated by 21 vehicles of 134 pax/veh capacity. The line has a mandatory layover time of =3 minutes and an additional slack time of several minutes to tackle bus bunching (s= 1, 3 and 6 min). The unit boarding and alighting time are respectively =3.7 s/pax and = 2.1 s/pax; while the opening and closing door time is toc= 2s. The maximal cruising speed in the bus lane is considered to be v= 30 km/h.

© AET 2016 and contributors 8  (s) The activation of strategies SM and TLP is only considered when j1, j > E, (E≥0). Therefore, the modification of bus speeds and green extension/red truncation measures are only performed if the time headway deviation is greater than a target threshold E. The potential values considered are E (sec)= {0; 15; 30}. Moreover, the maximal red truncation/green extension time was G= 20 seconds.

The simulation was performed considering the stabilization parameter to be equal to fb= 0.1. The sensitivity analysis of this parameter can be consulted at Estrada (2016).

Figure 1. Layout of H6 bus route

4.2. Comparison of Bus Regularity Metrics Table 2 gives a comparison of the several methodologies to calculate bus service regularity, described in chapter 2:

Table 2. Summary of features of the 4 service regularity calculation methodologies

EWT SD WA SR Easy of communication Good Marginally only Good Good

Subjective / objective Objective Objective Subjective Subjective

Partially: input, Customer focus Yes yes; output, No No only 68%

Long headways Penalizes Penalizes No penalizes No penalizes

Not to be used Headways at Similar with irregular Normal least longer Condition requirements scheduled scheduled distribution than regularity headways headways threshold

usually: 2 Assumes A sufficiently usually: ± 20 % minutes of Other uniform arrival large data is of scheduled scheduled of passengers necessary headway headway

EWT: Excess Wait Time, SD Standard Deviation, WA: Wait Assessment & SR Service Regularity

In 2010, a comparison of these 4 methodologes was made on 12 worldwide bus operators, including TMB Barcelona, in the framework of the International Bus Benchmarking Group. Each bus operator analyzes the regularity of 3 bus lines estimating the four proposed metrics. Table 3 ranks the regularity of each bus agency within the subset of all 12 cities for each metric (#1 best regularity, #12 worst regularity).

Table 3. Service regularity: bus operator performance ranking

Bus 1 2 EWT SD WA SR Operator A 1 1 1 4 B 2 3 6 3 C 3 6 7 2 D 4 4 2 1 E 5 2 4 8 F 6 5 5 11 G 7 7 3 6 H 8 9 8 5 I 9 10 9 7 J 10 11 11 9 K 11 8 12 12 L 12 12 10 10 1 +/- 2 minutes of scheduled headway 2 +/- 20% of scheduled headway

As it can be noticed from the Table 3, the ranking strongly depends on the metric selected to analyse regularity. Despite the fact that bus operator A is the most regular for metrics EXT, SD and WA, it falls to the 4th position when we monitor SR metric.

Concerning Bus Bunching measurement, as it has been previously quoted and explained in Section 2, our source is the TCQSM, that issues a table (Table 1) with various levels of service according to service regularity of a bus route. But the coefficient of variation of headways can be also related to the probability, P that a given transit vehicle's headway, hi will be off-headway by more than one-half the scheduled headway h. This probability is measured by twice the area to the right of Z on one tail of a normal distribution curve, where Z in this case is 0.5 divided by Cv,h.

The relationship between P and Cvh: 푃[|ℎ𝑖 − ℎ| > 0.5 ∙ ℎ] ↔ 퐶푣,ℎ can be demonstrated this way:

|ℎ𝑖 − ℎ| ℎ𝑖 푃[|ℎ − ℎ| > 0.5 ∙ ℎ] = 푃 [ > 0.5] = 푃 [| − 1| > 0.5] = 𝑖 ℎ ℎ

ℎ𝑖 ~ 푁(휇ℎ, 휎ℎ)

휇̂ = ℎ̅ { ℎ 푖 휎̂ℎ = 푠(ℎ𝑖) ̅ ℎ𝑖 − ℎ푖 ~ 푁(0,1) 푠(ℎ𝑖)

ℎ𝑖 − ℎ𝑖 푃 [−푎 ≤ ≤ 푎 ] = 푃[−푎 · 푠(ℎ𝑖) ≤ ℎ𝑖 − ℎ𝑖 ≤ 푎 · 푠(ℎ𝑖)] 푠(ℎ𝑖)

= 푃[ℎ𝑖 − 푎 · 푠(ℎ𝑖) ≤ ℎ𝑖 ≤ ℎ𝑖 + 푎 · 푠(ℎ𝑖)] (4.2)

̅ ̅ (4.2.1) 푃[0.5 · ℎ푖 ≤ ℎ𝑖 ≤ 1.5 · ℎ푖] = 1 − 훼

(4.2.2) 푃[ℎ𝑖 − 푎1−∝ · 푠(ℎ𝑖) ≤ ℎ𝑖 ≤ ℎ𝑖 + 푎1−∝ · 푠(ℎ𝑖)] = 1 − 훼

0.5 푠(ℎ ) 0.5 · ℎ̅ = ℎ̅ − 푎 · 푠(ℎ ) ⟺ 0.5 · ℎ̅ = 푎 · 푠(ℎ ) ⇔ = 𝑖 = 퐶 푖 푖 1−∝ 𝑖 푖 1−∝ 𝑖 ̅ 푣,ℎ 푎1−∝ ℎ푖

0.5 = 푎1−∝ (4.3) 퐶푣.ℎ

P 1-a/2 Z a1-a Cvh 2% 0,990 2,33 0,21 10% 0,950 1,65 0,30 20% 0,900 1,28 0,39 33% 0,835 0,97 0,52 50% 0,750 0,67 0,74 > 50% - - ≥ 0,75

Figure 2. Normal Distribution and Cv,h associated values

4.3. Analysis of Control Strategies The implementation of each control strategy has been analyzed with regard to two key metrics: i) the total cost of the system, ZT, and ii) the coefficient of headway variation, cv. The former embraces the operating cost incurred by the agency and the temporal cost incurred by passengers. The latter allows us analysing the headway adherence obtained with each control strategy. It should be highlighted that there is a trade-off between the effectiveness of each strategy to keep the headway constant and the cost needed to do so. Strategy ST with huge slack times (>10 min) is significantly efficient to maintain the headways constant at the expenses of introducing additional vehicles in the service.

Figure 3 summarizes the results obtained by simulation (Aimsun software) in the H6 route in the peak morning time. We consider a basic scenario that the implementation of strategy ST with slack time s= 1min. Hence, the ZT variable of each control strategy is plotted as the quotient between the total cost of that strategy and the total cost of strategy ST when s =1 min. Traffic light control, variable user arrival rates at stops and car traffic flow makes the headway adherence unstable in the basic scenario (slack time s =1min). The provision of this slack time is not enough to keep the coefficient of headway variation in an acceptable domain (cv=1.043). Most of the vehicles run in bunches and the total cost of the system is ZT=35,143 €/h. The implementation of strategy ST with higher slack times cannot improve significantly both total cost and the headway adherence of the corridor. It is the result that this strategy is neither adaptive nor scalable to the potential disruptions that generate the unstable motion of the system. The coefficient of variation remains roughly constant for slack times greater than a minimum threshold. However, the total cost increases since more vehicles are needed as the total amount of slack time is incremented.

Dynamic controlling strategies (SM and TLP) implemented together with strategy ST improve the performance of the bus network. The implementation of strategy SM reduces the total cost of the system by 18-26% and cv by 41- 62% with regard to the base case (strategy ST s =1 min). The best results are obtained when we consider a slack time of s =3 min at each bus terminal stop of the line. In spite of that, the coefficient of headway variation is still bad (Level of service D). Finally, strategy TLP significantly outperforms the results obtained by the former control strategies. The total cost of the system is reduced by 40% with regard to the basic scenario. On the other hand, the time headway adherence is outstanding since cv<0.26 (level of service B according to the classification of TRB, 2003). In this strategy, the performance of strategy TLP when slack time is s =3 min is the scenario with the best total cost and headway adherence. The total cost is now 22,092 €/h and the level of service concerning regularity can be graded as A. The allocation of higher

1.2

1.043 1.0 1.000 0.890 0.898 0.817 0.8 0.750 0.84 0.85 0.735

0.630 0.629 0.637 0.6 0.64

0.4 0.42

0.38 ratios (with regard to S0 strategy)to regard (with ratios

T 0.2 0.26 0.25 Z 0.20

Cv and and Cv 0.0 ST ST ST SM SM SM SM+TLP SM+TLP SM+TLP phi=1 min phi=3 min phi=6 min phi=1 min phi=3 min phi=6 min phi=1 min phi=3 min phi=6 min J= 21 veh J= 22 veh J= 23 veh J= 21 veh J= 22 veh J= 23 veh J= 21 veh J= 22 veh J= 23 veh

Ratio (ZT)i/(ZT)ST CV

Figure 3. Comparison of control strategy performance

5. CONCLUSIONS Service Regularity is a very important KPI in the bus operation field. 4 methodologies are described for its measurement: EWT, Excess Wait Time; Standard Deviation; Wait Assessment; and Service Regularity.

Each of those methodologies has strengths and weaknesses: the EWT is the only method that fully incorporates the customer perspective as its output reflects the average experience of all passengers in the data sample. The Wait Assessment and service regularity indicators only reflect the experience of regular customers. The standard deviation method only reflects the experience of one standard deviation, approximately 68% of customers. The EWT is the only method that provides a normalization for differences in scheduled headways and thanks to its customer focus as well, makes it a suitable service regularity KPI for use in a benchmarking exercise, especially if the headways in each route are scheduled in regular intervals.

Concerning Bus Bunching measurement, the TCQSM (TRB, 2009) proposes a service regularity appraising whilst setting diverse level of service based on the coefficient of variation of the headway, that can be also related to the probability, P that a given transit vehicle's headway, hi will be off-headway by more than one-half the scheduled headway h. Despite it is difficult to explain

The strategies proposed to control the service regularity present a trade-off between headway adherence effectiveness and the cost of the resources deployed to achieve proper service regularity. Static control strategies based on slack times present higher total cost (user and agency cost) to keep the bus motion stable. Since this strategy is neither scalable nor adaptive, we would need huge slack times to maintain good headway adherence. In the test instance, the provision of slack time of s =6 min was insufficient to mitigate the effects of irregular passenger arrivals at stops and variable traffic flow states. The coefficient of headway variation is cv>0.8; it means that the level of service can be graded as F concerning the classification of TCQSM.

In order to tackle the bus bunching phenomena, it is crucial to perform dynamic control strategies based on a combination of cruising speed modification and traffic light priority. This strategy outperforms the total cost of the system by 40% and allows maintaining the coefficient of headway variation below cv<0.21 (the maximal threshold to consider a level of service A).

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