A Canonical Queuing System with Heterogeneous Servers and Finite Storage: Optimality and Application

It is well known that the blocking probability of an M/M/1/1 system can be reduced by evenly splitting the capacity of its single server into two servers, which leads to an M/M/2/2 system with homogeneous servers. In this paper, we extend the analysis to an M/M/2/m
$(m \geq 2)$
system with heterogeneous servers. For this system, we analytically prove that the blocking probability can be further reduced. As a matter of fact, there exists an optimal service ratio at which the blocking probability reaches its minimum. Moreover, we prove the optimality of average system size. The analysis is accompanied by graphical profiles. Due to its compact configuration of parallel servers and finite storage, this system has direct applications to a variety of emerging communication paradigms.