Birth-Death Models for a Class of Service Systems

W. Feng and R.T. Hurley (Canada)

Keywords

Birth-Death process, server utilization, mean response time, Poisson process, system throughput.

Abstract

In this paper, we discussed three Birth-Death models for service systems, such as telephone call centers or Internet access points. The first model assumes that customers have no information about the system and so they may balk or renege upon arrival. The other two models assume that customers receive the state information as they arrive and thus, the balking probability is state-dependant. Model 2 uses the assumption that the balking probabilities depend on a waiting time threshold while Model 3 assumes that the balking probabilities depend directly on the number of customers in the waiting queue. Both analysis and simulation are used to investigate the performance of the systems based on the three models. We compare the server utilization and mean response time. Our results indicate that Model 2 tends to have a lower response time than Model 1 and the performance of a system based on Model 3 greatly depends on the sequence of balking probabilities. We show the results for two such scenarios.

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