In this paper, we consider a retrial queue with two types of calls: incoming and outgoing calls. The input flow is Markovian arrival process and the service times are arbitrary distributed random variables. In its idle time the server can initiate the service itself and make outgoing calls. We consider the system with multiple types of outgoing calls. We use asymptotic analysis method under the condition of low rate of retrials to study such system and propose the approximation of the stationary probability distribution of the number of calls in the orbit.

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Diffusion Approximation for the MAP/GI/1 Retrial Queue with Two-Way Communication

  • Anatoly Nazarov,
  • Olga Lizyura

摘要

In this paper, we consider a retrial queue with two types of calls: incoming and outgoing calls. The input flow is Markovian arrival process and the service times are arbitrary distributed random variables. In its idle time the server can initiate the service itself and make outgoing calls. We consider the system with multiple types of outgoing calls. We use asymptotic analysis method under the condition of low rate of retrials to study such system and propose the approximation of the stationary probability distribution of the number of calls in the orbit.