On performance characteristics for queueing systems with heterogeneous servers

The problem of optimal control for queueing system (QS) with heterogeneous servers was considering by many authors. In [8] it was shown that the optimal with respect to the number of jobs in the system minimization policy is a threshold type one and it obliges to use the fastest free server if necessary. However, calculation of performance characteristics under optimal policy and analysis of its preference before some other policies rest out of the investigators' interests. The purpose of this paper is to analyze a multi-server heterogeneous exponential queue. We demonstrate the methods for the calculation of the steady-state probabilities and deriving the waiting and sojourn time distributions. Some performance characteristics of such a system under the optimal control policy are calculated and compared with the same characteristics for the model under other heuristic control policies, e.g., the usage of the Fastest Free Server (FFS) or Random Server Selection (RSS).