Abstract
SUMMARY In a queueing system with m servers, customers arrive at random, each customer being given a desired service time. If all the servers are busy, the newly arrived customer displaces that customer with smallest unexpired service time. The efficiency of the system is measured by the ratio, I, of mean achieved service time to mean desired service time under conditions of statistical equilibrium. Cox (1961) determined I when the desired service time had an exponential distribution for the case m = 2, and for general m when the service time was of fixed length. The solution for a general service time distribution and for general m is given in this paper. A conditional replacement system is also considered and a numerical comparison is given.
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