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Computation of the steady state distribution for multi-server retrial queues with phase type service process

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Abstract

We consider a multi-server retrial queueing system with the Batch Markovian Arrival Process and phase type service time distribution. Such a general queueing system suits for modeling and decision making in many real life objects including modern wireless communication networks. Behavior of such a system is described by the level dependent multi-dimensional Markov chain. Blocks of the generator of this chain, which is the block structured matrix of infinite size, can have large size if the number of servers is large and distribution of service time is not exponential. Due to this fact, the existing in literature algorithms allow to compute key performance measures of such a system only for a small number of servers. Here we describe the algorithm that allows to compute the stationary distribution of the system for larger number of servers and numerically illustrate its advantage. Importance of taking into account correlation in the arrival process is numerically demonstrated.

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Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. 2010-0003269). This paper was also supported by research funds of Sangji University in 2011.

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Authors and Affiliations

  1. Department of Industrial Engineering, Sangji University, Wonju, 220-702, Republic of Korea

    Che Soong Kim

  2. Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus

    Vilena V. Mushko & Alexander N. Dudin

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  1. Che Soong Kim
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  2. Vilena V. Mushko
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  3. Alexander N. Dudin
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Correspondence to Alexander N. Dudin.

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Kim, C.S., Mushko, V.V. & Dudin, A.N. Computation of the steady state distribution for multi-server retrial queues with phase type service process. Ann Oper Res 201, 307–323 (2012). https://doi.org/10.1007/s10479-012-1254-7

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  • DOI: https://doi.org/10.1007/s10479-012-1254-7

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