Abstract
We investigate a no-boarding policy in a system of N buses serving M bus stops in a loop, which is an entrainment mechanism to keep buses synchronised in a reasonably staggered configuration. Buses always allow alighting, but would disallow boarding if certain criteria are met. For an analytically tractable theory, buses move with the same natural speed (applicable to programmable self-driving buses), where the average waiting time experienced by passengers waiting at the bus stop for a bus to arrive can be calculated. The analytical results show that a no-boarding policy can dramatically reduce the average waiting time, as compared to the usual situation without the no-boarding policy. Subsequently, we carry out simulations to verify these theoretical analyses, also extending the simulations to typical human-driven buses with different natural speeds based on real data. Finally, a simple general adaptive algorithm is implemented to dynamically determine when to implement no-boarding in a simulation for a real university shuttle bus service.
Highlights
In many bus systems, bus bunching is a natural repercussion where an initially staggered configuration of buses ends up with multiple buses getting closer to each other [1,2,3,4,5,6]
An intuitive mechanism that explains this phenomenon is that if there is some perturbation in the spacing between buses or the number of people at bus stops waiting to board a bus, a bus may have to stop a bit longer to pick up people as well as allow people to alight
A bus is assumed to have only one door for one person to alight or board at a time, at a rate of l. This simplifies our calculations for the average waiting time of people at the bus stop for a bus to arrive, as it eliminates the possibility for multiple passengers simultaneously alighting or boarding
Summary
Bus bunching is a natural repercussion where an initially staggered configuration of buses ends up with multiple buses getting closer to each other [1,2,3,4,5,6]. The leading bus has to pick up the majority of the people (which increases the required stoppage time for it to allow more people to alight), whilst the trailing bus picks up relatively fewer people These two buses inevitably end up bunching, due to the positive feedback which tends to slow down the leading bus and speed up the trailing bus. [23]: A bus would allow passengers who wish to alight at a bus stop (where it would otherwise skip) to do so, and if so it would allow boarding at that bus stop The performance of this policy, is quite susceptible to the passenger distribution patterns especially if every bus stop generally has people who would like to visit. Some other work considered optimising some objective function, involving various algorithms to enhance the bus system [33,34,35], as well as being data driven [36]
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