Implementation of a Routing Algorithm for Stochastic Transportation Networks

There are many decisions to make when trying to find the quickest way from one stop to another in bus system: the intermediate stop to go to next, the bus to board in order to go to this next stop, the bus to take at the next stop, and so on. In a transportation network where all buses run on time, the optimal decisions could be easily calculated by using a modified form of a standard shortest-paths algorithm such as Dijkstra’s algorithm. However, a more realistic model of a transportation network would account for the variability of waiting time at each stop for each bus. Datar and Ranade originally addressed the issue of optimizing a travel schedule while accounting for bus delay. They provided an algorithm that minimized travel time under the assumption that the arrival distributions of the buses were exponential. Later, Boyan and Mitzenmacher devised a bus-riding algorithm that could accept a much broader class of arrival distribution: those with increasing failure rate (IFR). Under this new criterion, uniform, normal, and gamma distributions became admissible as arrival distributions. The output of the generalized algorithm is of the form “if at stop s, take bus 1 if it arrives before t1, bus 2 if it arrives before t2, etc.” Boyan and Mitzenmacher left the implementation of their algorithm as possible future work. This thesis’s focus is an implementation of this algorithm, done in the language of Maple (a computer algebra system). I have also implemented a simulator that would test the efficacy of plans generated by this algorithm against plans which ignore the stochastic aspects of the network. Source code to these implementations are included.