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Infinite-server queueing tandem with Markovian arrival process and service depending on its state

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Abstract

We consider the infinite-server queueing tandem with the Markovian arrival process. The service time of requests at the first stage and the probability of their transition to the second stage are determined by the type of request that corresponds to the state of the arrival process at the time when the request arrived. A study of this system was performed under an asymptotic condition of a high rate of arrivals. A Gaussian approximation is obtained for the joint stationary probability distribution of the number of requests at the stages of the system under the condition. Based on this approximation, the problem of computing the optimal number of servers for specific values of model parameters is solved. Further, the obtained asymptotic result is extended to the case when a service at the second stage also depends on the request type, as well as on the case of systems with the number of stages greater than two.

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Authors and Affiliations

  1. Tomsk State University, 36, Lenina Str., Tomsk, Russia

    Alexander Moiseev, Maria Shklennik & Evgeny Polin

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  1. Alexander Moiseev
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  2. Maria Shklennik
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  3. Evgeny Polin
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Correspondence to Alexander Moiseev.

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Moiseev, A., Shklennik, M. & Polin, E. Infinite-server queueing tandem with Markovian arrival process and service depending on its state. Ann Oper Res 326, 261–279 (2023). https://doi.org/10.1007/s10479-023-05318-1

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