Keywords: transportation, bus-routing optimization, entropy.

Urban traffic modelling and planning is a highly complex problem, especially in urban domains with a high volume of unplanned vehicular movements, such as in the case of urban regions with limited or no mass transit infrastructure. Urban transportation planning in such locales involves both the study of existing travel patterns (origins, destinations, paths) but also the determination of the underlying factors influencing these travel patterns (duration, cost, originating time, purpose of trip, transit alternatives, driver behaviour, etc.) as well as possible remediation measures. The aforementioned transportation factors are often difficult to evaluate and the underlying transportation problem resolves to a stochastic or fuzzy-estimated problem. One such approach to modelling vehicular traffic is the "entropy-maximization method"; a method that has previously been shown to have direct applications in transportation planning and by which the theoretical basis for a class of forecast models on traffic demand can be based.

The work presented herein builds on previous work by Christodoulou [1], and addresses traffic modelling and bus-routing optimization for urban regions and travellers of approximated origins and known destinations, by means of an entropy-based formulation of their vehicular movements within the domain considered. The perceived level of disorder caused by the numerous vehicle-student trips in the domain under examination is subsequently utilized for the formulation of a policy and a bus-routing scheme in order to minimize the entropy in the system. The entropy metric used in the scheduling optimization is related to the probability of student-trips by origin and destination, and an application of the method is illustrated using the case study of an urban university (with facilities in multiple locations) starting a bus-service for its students.

The proposed entropy-based model is shown to perform particularly well and to be an effective tool for evaluating the distribution of traffic loads and for appraising the level of disorder caused in a network. Furthermore, the entropy-based method is shown be an excellent metric for evaluating fluctuations in distributions (especially equi-probability). These properties can in turn be used for devising bus-routing and park-and-ride schemes for readjusting the traffic distributions in a roadway network and thus for reducing traffic loads on traffic arteries.

1

S. Christodoulou, "Traffic Modeling and College-Bus Routing Using Entropy Maximization", Journal of Transportation Engineering, 136(102), 102-109, 2010. doi:10.1061/(ASCE)TE.1943-5436.0000067

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