Two-way communication retrial queues with multiple types of outgoing calls

Hiroyuki Sakurai and Tuan Phung-Duc (tuan@is.titech.ac.jp)

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 23, issue 2, 466-492

Abstract: In this paper, we start with single server Markovian retrial queues with multiple types of outgoing calls. Incoming calls arrive at system according to a Poisson process. Service times of incoming calls follow the exponential distribution. Incoming calls that find the server busy upon arrival join an orbit and retry after some exponentially distributed time. On the other hand, the server makes an outgoing call after some exponentially distributed idle time. We assume that there are multiple types of outgoing calls whose durations follow distinct exponential distributions. For this model, we obtain explicit expressions for the joint stationary distribution of the number of calls in the orbit and the state of the server via the generating function approach. We also obtain simple asymptotic and recursive formulae for the joint stationary distribution. We show a stochastic decomposition property where we prove that the number of incoming calls in the system (server and orbit) can be decomposed into the sum of three independent random variables which have a clear physical meaning. We then consider the multiserver model for which we obtain the stability condition and derive some exact formulae by mean value analysis. Finally, we extend the single server model to the case where service time distribution of incoming calls and that of each type of outgoing calls are arbitrary. For this case, we obtain explicit expressions for the partial generating functions and recursive formulae for the joint stationary distribution of the server’s state and the number of calls in the orbit. Copyright Sociedad de Estadística e Investigación Operativa 2015

Keywords: Retrial queues; Two-way communication; Multiple classes; Embedded Markov chain; Stability condition; 60K25; 90B22 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s11750-014-0349-5

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