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Analysis and Simulation of Intervention Strategies against Bus Bunching by means of an Empirical Agent‐Based Model

Quek, Wei Liang, Chung, Ning Ning, Saw, Vee-Liem, Chew, Lock Yue·2021·Complexity
DOI 10.1155/2021/2606191
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Abstract

In this paper, we propose an empirically based Monte Carlo bus‐network (EMB) model as a test bed to simulate intervention strategies to overcome the inefficiencies of bus bunching. The EMB model is an agent‐based model which utilizes the positional and temporal data of the buses obtained from the Global Positioning System (GPS) to constitute (1) a set of empirical velocity distributions of the buses and (2) a set of exponential distributions of interarrival time of passengers at the bus stops. Monte Carlo sampling is then performed on these two derived probability distributions to yield the stochastic dynamics of both the buses’ motion and passengers’ arrival. Our EMB model is generic and can be applied to any real‐world bus network system. In particular, we have validated the model against the Nanyang Technological University’s Shuttle Bus System by demonstrating its accuracy in capturing the bunching dynamics of the shuttle buses. Furthermore, we have analyzed the efficacy of three intervention strategies: holding, no‐boarding, and centralized‐pulsing, against bus bunching by incorporating the rule set of these strategies into the model. Under the scenario where the buses have the same velocity, we found that all three strategies improve both the waiting and travelling times of the commuters. However, when the buses have different velocities, only the centralized‐pulsing scheme consistently outperforms the control scenario where the buses periodically bunch together.

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Figures

FIG. 1 Average velocity of the buses at different positions of the route. The path represents the 688 discretized positions of the route taken by NTU-SBS. The X and Y values represent actual GPS coordinates of the bus route. The color describes the average
FIG. 1 Average velocity of the buses at different positions of the route. The path represents the 688 discretized positions of the route taken by NTU-SBS. The X and Y values represent actual GPS coordinates of the bus route. The color describes the averageCC-BY · From the PDF
(a) Empirical distribution of velocities of the buses at position x = 542, which is the middle of a straight stretch of road.
(a) Empirical distribution of velocities of the buses at position x = 542, which is the middle of a straight stretch of road.CC-BY · From the PDF
FIG. 3 Empirical trajectories of the three buses operating on 11 Sept 18, from 1404h - 1516h. The r 2 time series is derived from the trajectories and Eq. 2.
FIG. 3 Empirical trajectories of the three buses operating on 11 Sept 18, from 1404h - 1516h. The r 2 time series is derived from the trajectories and Eq. 2.CC-BY · From the PDF
FIG. 4 Plot of empirical and simulated trajectories. Each graph is selectively aggregated based on the initial r 2 of the trajectories from [ 0.0, 0.1 ) to [ 0.9, 1.0 ] . The statistical similarity between the empirical and simulated trajectories is tabulated in Table II
FIG. 4 Plot of empirical and simulated trajectories. Each graph is selectively aggregated based on the initial r 2 of the trajectories from [ 0.0, 0.1 ) to [ 0.9, 1.0 ] . The statistical similarity between the empirical and simulated trajectories is tabulated in Table IICC-BY · From the PDF
FIG. 5 Results of the s-holding strategy in the two same-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.
FIG. 5 Results of the s-holding strategy in the two same-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.CC-BY · From the PDF
FIG. 6 The average time the bus takes to traverse each site of the route based on the number of active buses. The total time taken for a bus to reach its destination position can be derived by taking the total area under the curve between the two points.
FIG. 6 The average time the bus takes to traverse each site of the route based on the number of active buses. The total time taken for a bus to reach its destination position can be derived by taking the total area under the curve between the two points.CC-BY · From the PDF
FIG. 7 Results of the c-holding strategy in the two same-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.
FIG. 7 Results of the c-holding strategy in the two same-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.CC-BY · From the PDF
FIG. 8 Results of the distance-based no-boarding strategy on the two same-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.
FIG. 8 Results of the distance-based no-boarding strategy on the two same-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.CC-BY · From the PDF
FIG. 9 Results of the time-based no-boarding strategy on the two same-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.
FIG. 9 Results of the time-based no-boarding strategy on the two same-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.CC-BY · From the PDF
Image 10
CC-BY · From the PDF
FIG. 11 Results of simulating the s-holding strategy in the two different-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.
FIG. 11 Results of simulating the s-holding strategy in the two different-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.CC-BY · From the PDF
FIG. 12 Results of the c-holding strategy in the two different-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.
FIG. 12 Results of the c-holding strategy in the two different-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.CC-BY · From the PDF
FIG. 13 Results of the no-boarding strategy in the two different-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.
FIG. 13 Results of the no-boarding strategy in the two different-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.CC-BY · From the PDF
FIG. 14 Results of the centralized-pulsing strategy in the two different-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.
FIG. 14 Results of the centralized-pulsing strategy in the two different-velocity scenarios. Each colored point represents the mean and standard deviation of the measured quantities calculated from 100 realizations of each parameter value. The black line and grey shaded area of each graph denote the mean and standard deviation of the measured quantities from a control case, which are simulation runs of the same parameter values, without any intervention strategies.CC-BY · From the PDF
FIG. 15 Scatter plot of all ˜ x i,t +1 , with a fitted line representing the average route taken by the buses.
FIG. 15 Scatter plot of all ˜ x i,t +1 , with a fitted line representing the average route taken by the buses.CC-BY · From the PDF
FIG. 16 Graphs of normalized stopping frequency i.e. probability of bus stopping at a each position along the bus route, and velocity distributions of two different positions on the road. These graph are derived from the raw data collected over 13 weeks. Red lines on the graph are the sites where there are bus stops.
FIG. 16 Graphs of normalized stopping frequency i.e. probability of bus stopping at a each position along the bus route, and velocity distributions of two different positions on the road. These graph are derived from the raw data collected over 13 weeks. Red lines on the graph are the sites where there are bus stops.CC-BY · From the PDF
FIG. 17 Illustration of the interpolation process done to filter out false occurrence of zero velocities.
FIG. 17 Illustration of the interpolation process done to filter out false occurrence of zero velocities.CC-BY · From the PDF
FIG. 18 Graphs of normalized stopping frequency along the bus route, and velocity distributions of two different positions on the road. These graph are derived after the filtering process as described. Red lines on the graph are the sites where there are bus stops.
FIG. 18 Graphs of normalized stopping frequency along the bus route, and velocity distributions of two different positions on the road. These graph are derived after the filtering process as described. Red lines on the graph are the sites where there are bus stops.CC-BY · From the PDF

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Cited by

Metadata

Authors
Quek, W. L., Chung, N. N., Saw, V.-L., & Chew, L. Y.
ORCID
Venue
Complexity
Publisher
Wiley
Published
2021-01
Volume
2021
Issue
1
ISSN
  • 1076-2787
  • 1099-0526
DOI
10.1155/2021/2606191
Cited by
10
References
1
Language
en
Licence
creativecommons.org/licenses/by/4.0/ (vor, 7 d)
Funders
  • Joint WASP/NTU Programme (M4082189, M4082418)
  • DSAIR@NTU (M4082189, M4082418)

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