2: A Sensitivity-Based Solution Algorithm for the Network Model of Urban Taxi Services

Yang and Wong (1998) proposed a network model for urban taxi services to describe how vacant and occupied taxis cruise in a road network to search for customers and provide transportation services. It is assumed that a taxi driver, once having picked up a customer, will move to the customer’s destination by the shortest route; and a taxi driver, once having dropped a customer, will try to minimize individual expected search time required to meet the next customer. The probability that a vacant taxi meets a customer at a particular zone is specified by a logit model by assuming that the expected search time in each zone is an identically distributed random variable due to variations in perceptions of taxi drivers and the random arrival of customers. The taxi model was formulated as a system of nonlinear equations and was solved efficiently using an iterative balancing method (Wong and Yang, 1998).