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[1]     Alnowibet K. and Perros H.,The Nonstationary Loss Queue: A Survey”, K.,  Imperial College Press, 2006.

Abstract: The nonstationary loss queue is of great interest since the arrival rate in most communication systems varies over time. In view of the difficulty in solving the nonstationary loss queue, various approximation methods have been developed. In this paper, we review several of these approximation methods and present a new technique, the fixed point approximation (FPA) method. Numerical evidence points to the fact that the FPA method gives the exact solution.

[2]     Alnowibet K. and Perros H., Nonstationary Analysis of Circuit-Switched Communication Networks”, Performance Evaluation 2006

Abstract: Circuit-switched communication networks have been analyzed extensively in the stationary case, i.e. where the arrival and/or service rates are time-independent. In this paper, we study a circuit-switched network where the external arrival rates to the network are time-dependent functions. The circuit-switched network is modelled as a nonstationary queueing network with population constraints, which is analyzed approximately in order to obtain the blocking probability functions. Using this method we model two circuit-switched networks, namely, a traffic-groomed tandem optical network and a single-orbit LEO satellite network. 

[3]     Alnowibet K. and Perros H., Nonstationary Analysis of Loss Queue and of Queueing Networks of Loss Queues”, European Journal of OR, to appear

Abstract: We present an iterative scheme based on the fixed point approximation method, for the numerical calculation of the time-dependent mean number of customers and blocking probability functions in a nonstationary queueing network with multi-rate loss queues. We first show how the proposed method can be used to analyze a single-class, multiclass, and multi-rate nonstationary loss queue. Subsequently, the proposed method is extended to the analysis of a nonstationary queueing network of multi-rate loss queues. Comparisons with exact and simulation results showed that the results are consistently close to the exact results and they are always within simulation confidence intervals..

[4]     Alnowibet K. and Tadj L., A Quorum Queueing System with Bernoulli Vacation Schedule and Restricted Admission”, AMO - Advanced Modeling and Optimization1, Volume 9, 2007

Abstract: The goal of this research is to study and design an optimal management policy for the queueing system which has restricted customers admission and batch service with R-r policy. Server Bernoulli scheduled vacations are considered with generally distributed times.

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