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Analysis and optimal design of a multiserver, multlqueue system with finite waiting space in each queue

An analysis of a particular type of multiserver, multiqueue system is presented in which each queue has a finite number of waiting positions and the waiting positions are not vacated until service is completed. Thus, several customers in one queue can be served simultaneously. The steady-state distribution of states is derived and is used to obtain the probability of loss for each queue and the average delay of the system. This analysis is then used in the development of a design procedure to determine the minimum-cost configuration of waiting positions and servers to meet specified single-hour grade-of-service constraints. The results are applicable to the design of systems that utilize automatic call distributors. While this model does not include such effects as day-to-day variation and noncoincidence of peak loads among trunk groups, nevertheless the results properly reflect for the first time the interactions among the trunk groups terminated on the automatic call distributor and the attendants at the automatic call distributor.