THE TRANSIENT SOLUTION OF M/M/1 QUEUES UNDER (M,N)-POLICY - A COMBINATORIAL APPROACH

It has been demonstrated by several authors, that combinatorial methods can be successfully applied to derive certain probability distributions in queuing theory. Recently the authors have obtained the transient solution of (0,N)-policy M/M/1 queues with an arbitrary number of initial customers, by considering their discrete-time analogue and by using combinatorial arguments. In this note, we derive the transient solution of M/M/1 queues under (MN)-policy by an alternative combinatorial method in which lattice paths with diagonal steps are counted. As a special case the result for ordinary M/M/1 queues is checked.