Numerical methods for simulating transient, stochastic queueing networks - I: methodology

The study of stochastic networks of queues in transportation has been confined to the use of highly simplified analytical models or the development of large, computationally expensive Monte Carlo simulations. We introduce a discrete-time approach for simulating stochastic, transient networks of bulk queues that often arise in consolidation networks. This paper presents the state variables and equations required to model the problem, and introduces a set of approximations to produce a computationally tractable algorithm. A companion paper describes the results of extensive numerical experiments which test the accuracy of the approximations and the overall efficiency of the procedure.