Queue Length in a Queuing System with Dependent Service Times


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Abstract

A single-server queuing system with infinite capacity and a recurrent input flow is considered. Service times of the customer units have an exponential distribution with random parameter. The current value of the parameter is chosen from a finite set with given probabilities at the time the service of a certain customer is completed. Sequential values of the parameters form a special kind of Markov chain. The nonstationary behavior of the queue length is studied.

About the authors

V. G. Ushakov

Department of Computational Mathematics and Cybernetics; Institute of Informatics Problems, Federal Research Center Computer Science and Control

Author for correspondence.
Email: vgushakov@mail.ru
Russian Federation, Moscow, 119991; Moscow, 119991

N. G. Ushakov

Department of Mathematical Sciences

Author for correspondence.
Email: ushakov@math.ntnu.no
Norway, Trondheim, 7491

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