Queueing model with state dependent balking and reneging

Abstract

In this paper, the concepts of complementarity and equivalence between an M/M/c/K queueing model with state dependent balking and reneging and a machine interference problem with warm standbys are formalized. The relationship provides insight into these queueing systems. Through a series of corollaries, relationships between various queueing systems are derived. It is shown that a recently reported relationship between Erlang loss system and a finite source queueing system is a trivial consequence of the more general results presented here. New results involving the arrival point probabilities and measures of performance for these two queueing systems are also presented. An example is also provided.