AN APPROXIMATE ANALYTIC MODEL OF MANY-TO-MANY DEMAND RESPONSIVE TRANSPORTATION SYSTEMSt

This paper presents an analytic model to predict average waiting and ridii times in urban transportation systems (such as dial-a-bus and taxicabs), which provide non-transfer door-to-door transportation with a dynamically dispatched fleet of vehicles. Three diierent dispatching algorithms are analyzed with a simple deterministic model, which is then generalized to capture the most relevant stochastic phenomena. The formulae obtained have been successfully compared with simulated data and are simple enough for hand calculation. They are, thus, tools which enable analysts to avoid cumbersome simulation models when contemplating implementing or modifying many-to-many demand responsive transportation systems. Many-to-many demand responsive transportation systems consist of one or more multiple occupant vehicles which take passengers from their origins to their destinations within a service area. They differ from many-to-one systems in that all origin-destination pairs are served without requiring a transfer. Many-to-many transportation systems can be divided into two main categories on the basis of whether or not ride sharing is permitted. In conventional tuxicab systems, once a vehicle picks up a customer, it proceeds non-stop to the customer’s destination. In this case, at all times each vehicle has at most one request on board (a request is a group of passengers traveling together from a common origin to a common destination) and the maximum total number of request-miles per hour that can be accommodated (i.e. the capacity of the system) cannot exceed the maximum achievable number of vehicle-miles per hour with the available vehicle fleet. Thus, the capacity of a taxicab system is severely limited by the number of vehicles in operation. In dial-u-bus systems, in order to circumvent this undesirable feature of taxicab systems, vehicles are allowed to deviate from their direct route to serve other passengers and the emphasis is on building efficient tours to increase vehicle productivity. This strategy increases riding times but also increases average occupancy and productivity of the vehicles, and hence decreases average waiting tunes. Models of demand responsive transportation systems have been developed in the past; Daganxo, Hendrickson and Wilson (1977) developed an analytic model of manyto-one service where buses periodically visit a fixed point (which is either the origin or the destination of every trip in the service area). They obtained formulae for waiting and riding times, showed that the total time spent in the system by customer was minimized for a specific period between visits to the tixed point, and validated the model with simulated and real data. Although many-to-many tBesearch supported in part by University of California Faculty Research Grant 615 and by NSF Grant ENG 77-05701 to the University of California, Berkeley. systems have also been studied-models of taxicab operations have been reported in the literature (Fargier and Cohen, 1972; Gerrard, 1974)-a satisfactory analytical model of dial-a-bus operations has yet to be developed. This is perhaps because dial-a-bus routing algorithms have become so complicated (especially when they try to accommodate customers with diierent preferences and/or advance service requests) that they seem to defy mathematical modellii. One such algorithm is described by Wilson et al. (1971). At present, simulation models (Heathingt?n et al. 1968; Wilson ef of. 1971) or empirical models based on simulated or real data (Arillaga and Medville, 1974; Flusberg and Wilson, 1976) seem to be the only alternatives open to the planner. However, the former are expensive, time consuming, and not suitable for parametric analysis, and the latter require careful calibration and are limited in range. This paper develops a simple analytic model to predict average waiting and riding times of many-to-many demand responsive transportation systems. In order to model different operating strategies corresponding to the operations of taxicab and dial-a-bus systems, three diierent routing algorithms are studied applying the same modelling technique used by Daganzo et al. (1977) for the many-to-one case. The resulting model is simple enough to facilitate parametric analysis of these systems and model results agree well with the results of simulation. Section 1 develops asymptotic formulae with a deterministic model, Section 2 investigates some refinements of these formulas, and Section 3 discusses the results obtained.