Abstract
We consider a queueing model with preferentially ordered parallel servers that models a demand assignment channel allocation scheme used in multichannel local networks. We devise a method for reducing the number of system states to construct a tractable model from which we derive, for each n, the probability distribution that k of the first n ordered servers are busy. From these distributions, utilizations of individual servers are derived. Then assuming Poisson arrivals and exponential service time distributions, we develop analytic expressions for server utilizations. For the finite population model, where analytic expressions cannot be derived, we develop an efficient polynomial algorithm to compute server utilizations. Simple expressions for calculating upper bounds on finite population model server utilizations are also derived.
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