Queue-dependent vehicle dispatching with options and optimal fleet size

A queue-dependent vehicle dispatching rule, with options to use special vehicles (rented, reserve, shared etc.) for relieving long waiting lines, is considered. The transportation system under consideration has one source terminal and a fleet of N regular vehicles. Passengers are assumed to arrive individually at the source terminal according to a Poisson process. An efficient recursive algorithm is derived to analyse the performance of the system. An average cost criterion is used to determine the firm's fleet size and dispatching strategy for a simpler system. This is a variant of a "Random vehicle dispatching with options" rule proposed by Zuckerman and Tapiero (1980).