This paper deals with a single server retrial queue with a finite number of homogeneous sources of calls and a single nonreliable server, which means that the server is subject to random breakdowns depending on whether it is busy or idIe. The failure of the server may block or unbloek the systems' operations and the service of the interrupted request may be resumed or the call can be transmitted to the orbit. All random variables involved in the model constructions are supposed to be exponentially distributed and independent of each other. The novelty of the investigation is the variability of this nonreliability of the server which makes the system rather complicated. The MOSEL tool was used to formulate and solve the problem and the main performance and reliability measures were derived and graphically displayed. Several numerical calculations were performed to show the effect of the nonreliability of the server on the mean response times of the calls.

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In this paper we investigate a single server retrial queue with a finite number of heterogeneous sources of calls. It is assumed when a given source is idle it will generate a primary call after an exponentially distributed time. If the server is free at the time of the request's arrival then the call starts to be served. The service time is also exponentially distributed. During the service time the source cannot generate a new primary call. After service the source moves into free state and can generate a new call again. If the server is busy at the time of the arrival of a primary call, then the source starts generating so called repeated calls with exponentially distributed times until it finds the server free. As before, after service the source becomes free and can generate a new primary call again. We assume that the primary calls, repeated attempts and service times are mutually independent. This queueing system and its variants could be used to model magnetic disk memory systems, local area networks with CSMA/CD protocols and collision avoidance local area networks. The novelty of this model is the heterogeneity of the calls, which means that each call is characterized by its own arrival, repeated and service rates. The aim of the paper is to give the usual steady-state performance measures of the system. To do so, an efficient software tool, MOSEL ( Modeling, Specification and Evaluation Language ) developed at the University of Erlangen, Germany, is used to formulate and solve the problem. Several sample numerical results illustrate the power of the tool showing the effect of different parameters on the system measures.

This paper proposes a retrial queueing model with the finite number of sources to evaluate the performance of spectrum renting in mobile cellular networks. The model incorporates necessary ingredients such as the finite number of subscribers, their impatience and a queue for the outbound service. To consider the specific feature of spectrum renting and the current mobile cellular technology, a variable number of servers that are switched on and off in groups is introduced. We present a novel way to take into account the renting * Corresponding author. 1440004-1 2nd ReadingJanuary 21, 2014 9:50 WSPC/S0217-5959 APJOR 1440004.tex T. V. Do et al.fee, which can be used to fine-tune the operation of the spectrum renting procedure. Numerical results show that it is still profitable to initiate a spectrum renting request at high loads, even if no discount is offered by the frequency bands' owners.