A compensation method for multiprogramming queues

In this paper we study a multiprogramming system consisting of an input-output unit (IO unit) and a central processor (CP). This system can be represented by a continuous time Markov process with states (m, n), wherem andn denote the number of jobs at the CP and the IO unit respectively. The computation of the equilibrium distribution {p m,n } of this Markov process is the purpose of the analysis in this paper. The analysis consists of two parts. In the first part, we use a compensation procedure to show that the equilibrium distribution {p m,n } in those states (m, n) for whichm+n is not too small, can be expressed as an infinite linear combination of product forms. Explicit formulae are given for the product forms and the coefficients of this infinite linear combination. In the second part of the analysis, we pay attention to some numerical aspects of the computation of the equilibrium distribution.