Cyclic Queue Models of Fleet Operations

Abstract

Fleets of liquid natural gas vessels operating between one loading and one or two discharge ports are an example of vehicles that operate in closed cycles between a small number of terminals. We extend previous work to develop a cyclic queue model that represents such fleet operations. For any specific system we obtain the expected number of vessels in each stage, the expected number waiting in each stage, and, most important, the expected waiting time in port. Exponential service time distributions are assumed, but a series of parallel simulation computations examines the effects of other distributions. The results for exponential service are obtained in closed form, so that the simulation model can be tested and the confidence interval of the simulations estimated. Both analytic and simulation results are presented for the exponential service case under several sets of system parameters. Simulation results for the same sets are presented for normally distributed service and travel times. We restrict the detailed analysis to balanced systems but discuss extensions to more general systems.

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