Abstract
This paper deals with determining an optimal sequence of service stations in a series queueing system. Optimality is defined in terms of the total time spent waiting for service. Sequences are compared on the basis of the moments of their steady-state total waiting time. In addition, the rules of stochastic dominance are applied which allow comparison of sequences on the basis of their waiting time distributions. Analytical results in the sequencing of service stations in series queues have been limited to stations with constant or exponential service times. This study extends the investigation to service distributions with varying degrees of statistical regularity given by the family of Erlang distributions.Relationships are developed for predicting optimal sequences. Validation is accomplished by simulating a number of systems and comparing the waiting time distribution functions for each sequence. The relationships are shown to be good predictors and useful in the study and design of systems of servers in series.
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