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A dual tandem queueing system with GI service time at the first queue

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  • In this paper we consider the analysis of a tandem queueing model $M/G/1 -> ./M/1$. In contrast to the vast majority of the previous literature on tandem queuing models we consider the case with GI service time at the first queue and with infinite buffers. The system can be described by an M/G/1-type Markov process at the departure epochs of the first queue. The main result of the paper is the steady-state vector generating function at the embedded epochs, which characterizes the joint distribution of the number of customers at both queues. The steady-state Laplace-Stieljes transform and the mean of the sojourn time of the customers in the system are also obtained.
        We provide numerical examples and discuss the dependency of the steady-state mean of the sojourn time of the customers on several basic system parameters. Utilizing the structural characteristics of the model we discuss the interpretation of the results. This gives an insight into the behavior of this tandem queuing model and can be a base for developing approximations for it.
    Mathematics Subject Classification: Primary: 60K25, 68M20; Secondary: 90B22.

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