Buffer overflow calculations using an infinite-capacity model

Paul J. Schweitzer and Alan G. Konheim

Stochastic Processes and their Applications, 1978, vol. 6, issue 3, 267-276

Abstract: Sufficient conditions are established for approximation of the overflow probability in a stochastic service system with capacity C by the probability that the related infinite-capacity system has C customers. These conditions are that (a) the infinite-capacity system has negligible probability of C or more customers; (b) the probabilities of states with exactly C customers for the infinite-capacity system are nearly proportional to the same probabilities for the finite- capacity system. Condition (b) is controlling if the probabilities for the infinite-capacity system are rescaled so that the probability of at most C customers is unity. For systems with precisely one state with C customers, such as birth-and-death processes, the latter approximation is exact even when condition (a) does not hold.

Date: 1978
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