Investigating Multiplier Effects Created by Combinations of Transit Signal Priority Measures

Investigating multiplier effects created by combinations of transit signal priority measures on arterials

Long Tien Truong1, Majid Sarvi1, and Graham Currie1

1Institute of Transport Studies, Department of Civil Engineering, Monash University

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Abstract

Transit signal priority (TSP) has proven to be a cost-effective solution for public transport vehicles at signalised intersections as it usually does not require substantial infrastructure upgrades, while improving bus travel time and reliability.Numerous studies have focused on the design and operation of TSP,while few have considered the optimum combination of TSP at a corridor and a network level. However, it is unclear whether the combination of TSP on an arterial or a network creates a multiplier effect on public transportbenefits, i.e. benefits from providing TSP at multiple intersections are higher than the sum of benefits from providing TSP at each of those individual intersections.This paper investigates the effects of combinations of TSP measureson signalised arterials to establish if a multiplier effect exists. Results of a modelling test-bed reveal that combinations of TSP measures on signalised arterials can create a multiplier effect on bus delay savings when signal offsets are optimised to minimise bus delays. The existence of the multiplier effect suggests considerable impacts of TSP on a network-wide scale.

1.Introduction

TSP strategies can be identified as passive, active, and adaptive priority (Baker et al., 2004; Smith et al., 2005). Passive priority usually involves offline signal timing optimisationin favour of public transport vehicles. For instance, optimising traffic signal offsets canreduce bus travel times substantially (Estrada et al., 2009). Active priority dynamically adjusts signal timings to facilitate the movements of public transport vehicles following theirdetection.A number of active priority strategies are used, including green extension, early green, actuated transit phases, phase insertion, and phase rotation. The activations of these strategies usually rely on the prediction of arrival times. Various arrival prediction models can be found in previous studies, which use historical travel time data (Ekeila et al., 2009; Wadjas and Furth, 2003), a combination of historical and real-time GPS data (Tan et al., 2008), rule-based micro-simulation (Lee et al., 2005), and analytical methods using time-space or flow-time diagrams (Skabardonis and Geroliminis, 2008; Li et al., 2011). Adaptive priority provides priority to public transport vehicles while optimising certain performance criteria. For example, a mixed-integer nonlinear program is formulated in a traffic responsive signal control system to minimise the total person delay (Christofa et al., 2013). In another real-time TSP model, a stochastic mixed-integer nonlinear program isdeveloped to minimise bus delays and deviations of TSP signal timing from a background timing (Zeng et al., 2014). In addition, TSP can be provided either unconditionally to all requested buses or conditionally to requested buses that are behind schedule.

Numerous studies have focused on the design and operation of TSP, while a few have considered the optimum combination of TSP at a corridor and a network level. For instance, traffic micro-simulation is used to optimise signal timings and TSP settings on anurban corridor and a suburban network(Stevanovic et al., 2008). In another study, a simulation-based planning framework is proposed to optimise locations for TSP implementation in a grid network (Shourijeh et al., 2013). However, it is unclear whether the combination of TSP on an arterial or a network creates a multiplier effect on benefits to public transport, i.e. benefits from providing TSP at multiple intersections are higher than the sum of benefits from providing TSP at each of those individual intersections.If a multiplier effect exists, it suggests considerable impacts ofTSP on a network-wide scale. Since the research literature has highlighted the impact of signal coordination on the performance of priority measures on arterials (Skabardonis, 2000; Truong et al., 2015a, b), it is essential to examine combination effects in typical offset settings as well as optimised offsets that maximise benefits for public transport.

This paper investigates effects of combinations of TSP on a signalised arterial to establish if a multiplier effect exists. The rest of this paper is organised as follows. Section 2 presents a modelling test-bed for examining combinations effects and models for bus and traffic delay estimation and signal offset optimisation. In section 3, delay estimation and offset optimisation models are then evaluated using traffic micro-simulation. Next, section 4 presents results of the test-bed, followed by a discussion of the multiplier effect. Conclusions and direction for future research are presented in section 5.

2. Methodology

2.1Test-bed

2.1.1 Case study

A hypothetical arterial is used as a case study for exploring effects of TSP combinationson bus delays and traffic delays. The 5km hypothetical arterial is designedwith typical suburban arterial settings in Melbourne, Australia. Five fixed-time signalised intersections are equally spaced on the arterial. The layout of the arterial is presented in Figure 1. Turning flows from the arterial to side streets are set to equal to the turning flows from side streets to maintain similar traffic demands on each link. A summary of test-bed characteristics is presented in Table 1. For simplicity, the eastbound direction is selected for the analysis since the westbound direction can be considered in a similar way. A bus line is eastbound with 15 bus stops. Bus dwell times are assumed to be normally distributed with a mean of 15s and a standard deviation of 10s. Stop skipping is considered when a random bus dwell time is non-positive. To capture random variations in bus entrance times to the arterial, it is assumed thatdeviations between actual and scheduled entrance times follow a normal distribution with a zero mean and a 20s standard deviation. The assumptions of bus dwell times and entrance times are made in agreement with previous studies (TCRP, 2003; Estrada et al., 2009).

Figure 1: Layout of the hypothetical arterial

Table 1: Test-bed Characteristics

Feature / Options
Traffic volume on 3-lane main arterial / Three levels: 1600, 2000, 2400vph
Signal offsets / Two levels: free-flow offset and optimised offset
Traffic volumes on 2-lane side streets / 0.2 traffic volume on the arterial
Traffic composition / 95% car and 5% heavy goods vehicle (HGV)
Desired speed distributions / Car and HGV: 55-65kph. Bus: 60kph
Turning proportions / Arterial: through (95%), left (3%), and right (2%)
Side streets: through (75%), left (15%), and right (10%)
Traffic signals / Cycle = 120s, min green = 6s, yellow = 3s, all red = 2s. Split: 0.7 for the arterial and 0.3 for side streets
Bus headway / 5min
Bus dwell times / Mean = 15s, standard deviation = 10s
Bus entrance time variation / Mean =0s, standard deviation = 20s

2.1.2 TSP strategies

A typical TSP system is used in the test-bed(TCRP, 2010), which incorporatesthe following strategies: (i) green extension that extends an ending green phase to allow an approaching bus to pass through the intersection and (ii) early green that shortens the waiting time for a bus arriving during the red phase. A maximum priority time of 10s is provided for each strategy. To maintain signal coordination, the green phases for side streets will be reduced by the amount of the activated priority time. The detection system for each intersection includes a check-out detector placed at the stop line and a check-in detector placed after the near-side bus stop and 100m from the stop line. When a bus is detected at the check-in detector, a predetermined travel time with a slack time is used to predict its arrival interval at the stop line and activate either early green or green extension. If green extension is provided, the green phase is extended until either the detection of the bus at the check-out detector or the maximum green extension time is reached.

2.1.3 Combination design

All possible combinations of TSP at five intersections (25=32 combinations including the base case) along the arterial are considered. Each combination is then examined with three levels of traffic volumes (1600, 2000, 2400vph) and two offset settings (free-flow offset and optimised offset that minimises bus delay). Hence, there are 192 scenarios in total.

2.2 Delay estimation

The efficiency of delay estimation is important to the test-bed that involves optimising offset for a large number of scenarios. In this paper, the LWR shockwave theory(Lighthill and Whitham, 1955; Richards, 1956; Stephanopoulos et al., 1979; Skabardonis and Geroliminis, 2005; Liu et al., 2009; Ramezani and Geroliminis, 2014) and kinematic equations are used to estimate traffic and bus delays.Monte-Carlo simulation is then applied to account for the randomness in traffic arrivals, bus arrivals and dwell times. The following assumptions are made.

There is a triangular fundamental diagram with parameters: free-flow speed , saturation rate , jam density , and congested shockwave speed (see Figure 2).
The platoon dispersion effect is ignored.
There is no queue spillover from downstream links or turning bays (Hence vehicles can always be discharged during green times).
A bus travels with a constant acceleration rate and a constant deceleration rate.
Bus stops do not affect traffic.

2.2.1 Shockwave analysis

Figure 2 describes the development and dissipation of shockwaves on an approach of a signalised intersection as a result of signal phase changes during a signal cycle. When the red interval starts, a queue forming shockwave () is generated and moves upstream of the intersection if traffic queue has been fully discharged in the previous cycle. The speed of can be different over time. For example, in Figure 2b has a two-segment piecewise linear form as a result of two arrival traffic states () and (). When the green interval starts, a queue discharging shockwave () is generated and moves upstream as vehicles start to discharge at saturation flow rate. Since has a higher speed than , two shockwaves will meet at a specific time when the queue length is maximum. As soon as the two shockwaves intersect, a departure shockwave () is formed and moves towards the stop line. In the beginning of the next red interval, if the queue is not fully discharged, a residual queue forming shockwave () is generated moving upstream of the intersection(see Figure 2c). As soon as and intersect, a new queue forming shockwave is formed and a similar process is repeated in the following cycle. These shockwave speeds are calculated using the following equations:

/ (1)
/ (2)

Figure 2: Fundamental diagram and shockwavesonan approach of a signalised intersection

(a) fundamental diagram / (b) no residual queue
(c) residual queue

If the signal setting and arrival traffic rates are known, these shockwave speeds can be deterministically calculated using the LWR shockwave theory.A shockwave profile model for arterials, which tracks trajectories of shockwaves at every time step, can be found in a previous study (Wu and Liu, 2011). It is noted that arrival flows to the back of the queue at a specific time can be derived from the inflows at the link entrance since vehicles are assumed to travel at the free-flow speed.

In this paper, shockwave speeds at each intersection of the signalised arterial is explicitly estimated cycle by cycle to account for over-saturated situations where shockwaves generated in a cycle may still exist in the following cycle. For each time step,distances fromthe stop line to the front of each shockwave at the next time step can be calculated using estimated shockwave speeds at the current time step. Since the back of the queue follows trajectories of the queue forming and departure shockwaves (see Figure 2), the queue length in the next time step can also be updated.

Flows discharged during green time, including saturation rate if the queue is being discharged or arrival flow rate if the queue has been fully discharged, can be used to calculate inflow rates to the downstream link. It is noted that turning flows from other directions also contribute to inflow rates to the downstream link.

2.2.2 Bus movements

Once the shockwave speeds and queue length are estimated, it is possible to simulate movements of a bus approaching the intersection.In a virtual vehicle probe model for estimating travel times, a virtual probe is simulated with one of three decisionsat each time step, i.e. acceleration, deceleration, and no change in speed, depending on signal status and distances to the stop line and the last queued vehicles in front of the virtual probe (Liu and Ma, 2009).However, simulating bus movements is more complex considering decelerating and accelerating movements before and after bus stops, particularly with the presence of traffic queue.Figure 2 suggests that a bus at a specific time is in traffic queue if it is inside the delay (shaded) regions bounded by trajectories of the stop line, queue forming and residual queue forming shockwaves, and queue discharging shockwaves.For each time step, a bus can make one of the following movements: accelerate or continue to travel at the desired speed, decelerate, and stop, determined by its distances to obstacles, signal status, current speed() and dwell time status. Distances to obstacles includethe distances to the next bus stop where passengers are waiting (), the front of the queue forming shockwave (), the front of residual queue forming shockwave (), the next stop line () (see Figure 2c). One-dimension kinematic equations are used to update the location and speed of the bus at the next time step.

2.2.3 TSP control

If TSP is provided for an intersection, for each time step, the algorithm presented in Figure 3 is used to implement TSP control.

2.2.4 Monte-Carlo simulation

Traffic delays are thencalculated using the flow rate and density of each region divided by traffic shockwaves(Dion et al., 2004).Bus delay is calculated as the actual travel time minus the free-flow travel time and the total dwell times, obtaining from their simulated trajectories. A Monte-Carlo simulation method is then proposed to estimate traffic and bus delays accounting for the randomness in traffic arrivals and bus entrance times and dwell times. Traffic arrivals are assumed to follow a Poisson distribution. For each run, traffic arrivals rates, bus entrance times, and dwell times are sampled from given distributions.

Figure 3: TSP control flowchart

2.3 Offset optimisation

To investigate the maximum benefits in reducing bus delay from TSP combinations, an offset optimization model that minimises bus delay can be formulated as follows.

/ (3)

where:is mean bus delay obtained from Monte-Carlo simulation,is number of intersections on the arterial,is common cycle length, and is signal offset for intersection i on the arterial.

Given the complexity of the objective function, e.g. using Monte-Carlo simulation method, a Genetic Algorithm (GA) is proposed to solve the problem.In addition, GA has been found to be useful in optimising signal control on mixed traffic arterials (Duerr, 2000). It is noted that as both traffic and bus delay can be estimated, an offset optimisation model considering for both bus and traffic delays can be developed in a similar way.

3. Validation

Based on characteristics of the test-bed, parameters for the fundamental diagram are set to: capacity = 1800 vph per lane, free-flow speed = 60kph, jam density=140vpk per lane. Bus acceleration and deceleration rates are 1.2m/s2and 1.2m/s2 respectively. These values are consistent with values reported in the literature(Estrada et al., 2009; Skabardonis and Geroliminis, 2005). Other parameters are selected as: simulation time = 1h, time step =1s, and the number of Monte-Carlo simulation runs = 100.

The delay estimation model is coded in C++ and the offset optimisation problems are solved by using the Genetics Algorithm (GA)toolboxin Matlab(MathWorks, 2014). The crossover rate and mutation rate are set to 0.8 and 0.01 respectively. The population size and generation size of the GA are set to 100 and 50 respectively. Examples of GA results and bus trajectories in a TSP case are presented in Figure 4. A fast convergence trend of the GA is evident. The computation time for optimising offsets of one scenario is about 6 min on a personal computerwith Intel Core i7-3770 CPU (3.4GHz).

The test-bed is coded in VISSIM (PTV, 2014) for evaluation. TSP control is modelled using Vehicle Actuated Programming (VAP). It is tedious to evaluate all combination cases. Hence, six combinationsare selected for evaluation, including the base case and combinations with one to five intersections with TSP. Each combination is evaluated with the three traffic volume levels and the two offset settings. There are 36 evaluation scenarios (about 19% of all scenarios). Measures of performance include bus delay, arterial traffic delay, and mean side street traffic delays. A sequential approach is applied to calculate the minimum number of runs for each scenario to achieve a 95% confidence level for all measures of performance with percentage errors of 2% (Truong et al., 2015c, d). The root mean square error (RMSE) and the mean absolute percentage error (MAPE) are used to compare results of VISSIM and the proposed models.