Abstract
AbstractThe paper is concerned with the investigation of the GI/Geom/N queue in discrete time using the method of the imbedded Markov chain. The queueing system under consideration has a general independent input, of which the interarrival times are assumed to be identically distributed positive independent random variables with a general probability distribution {an}, first-come first-served queue discipline, geometric service-time distribution and iVservers. The limiting state probability distribution, the waiting-time probability distribution and the delay probability are determined analytically. The problem is also solved for the case when the queue length is bounded by the number of servers. Of special importance is the probability oi customer loss. Erlang's delay and loss formulae are obtained using a limiting process.
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