Performance analysis of finite-source retrial queues with nonreliable heterogenous servers

Abstract

Retrial queueing models are often used for the performance and reliability modeling of computer systems and communication networks. The reason is that the return of customers plays a special role in many of these systems as well as in other practical applications, and it has a nonneglectable negative effect on the performance measures. For some applications of retrial queues, see, for example, [1–4], and for some fundamental results on finite-source retrial queueing systems, refer to [5–9]. Usually, the components of computer systems are subject to random breakdowns, which has a substantial influence on the performance measures, so it is of practical importance to investigate nonreliable retrial queueing systems, too. Nonreliable, infinite-source retrial queues were studied in [10–12] and finite-source retrial queues with a single nonreliable server were studied in [13]. The purpose of this paper is to generalize the model of [9, 13] and to give the main stationary performance measures of the nonreliable multiserver model described in the next section. Furthermore, our aim is to illustrate graphically the effect of the nonreliability of the servers on the steady-state systems’s measures. Because of the fact that the state space of the Markov chain described is very large, it is difficult to calculate the system measures in the traditional way of solving the system of steady-state equations. To simplify this procedure, we used the software tool MOSEL (Modeling, Specification, and Evaluation Language) (see [14]) to formulate the model and to obtain the performance measures. With the help of MOSEL, we can use various performance tools (such as SPNP — Stochastic Petri Net Package) to get these characteristics. The results of the tool can graphically be displayed using IGL (Intermediate Graphical Language), which is a part of MOSEL. The organization of the paper is as follows. Section 2 contains an accurate description of the investigated retrial queueing model and the derivation of the main steady-state performance measures. Section 3 is devoted to the validation of the results of the tool and some graphically displayed numerical results. The paper ends with Comments and Conclusions.