It is known that the Large Deviations of a counting process and its adjoint are closely related. We present very simple and general conditions, mainly on the rate-functions, which suuce to ensure that, if two processes are adjoint, then one will satisfy a Large Deviation principle if and only if the other does. We also present an application of this result to some problems in queuing theory.

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The aim of this paper is to investigate a multiserver retrial queueing system with a finite number of heterogeneous sources of calls. The novelty of the investigation is the heterogeneity of the sources, that is every source is characterized by different arrival, retrial and service rates. All random variables involved in the model construction are assumed to be exponentially distributed and in...

Many successful modelling studies are conducted without venturing beyond the techniques described in Part II. In other words, the system characteristics considered in these studies are restricted to those that can be represented directly using the parameters of separable queueing networks. There are, of course, situations in which the analyst will wish to represent a specific subsystem in great...

Stochastic network calculus is the probabilistic version of the network calculus, which uses envelopes to perform probabilistic analysis of queueing networks. The accuracy of probabilistic end-to-end delay or backlog bounds computed using the elegant theory of network calculus has been always a concern. In this paper, we propose novel bounds based on Doob’s maximal inequality for N-demisupermar...

In the queueing theory we usually ignore the fact that utility server is often a technical device and its breakdown can occur. Common analytic models (see for example in [1] or [2]) assume that the server works reliably without failures causing its deficit. If failures of the server occur often and we would use an analytic model of reliable queueing system for modeling studied system, reached o...

The aim of this paper is to provide a more realistic description of priority-discipline queueing models by using Fuzzy Set Theory. It develops and optimizes two fuzzy queueing models with priority-discipline, a model with nonpreemptive priorities system and a model with preemptive priorities system, denoted by M̃i /M̃i /1 and M̃i /Fi /1. The first symbol is for a queueing system where arrivals and...

Data flows in modern networks have exhibited increasingly complex prospect along with the evolving network infrastructures and emerging diverse applications. Performance evaluation must adequately consider this trend. The tractable queueing network as a traditional theoretical tool for performance evaluation can not satisfy the new requirement anymore. One reason is that the important assumptio...