A tandem queue with delayed server release

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Nawijn, W.M. (1997)
  • Publisher: Universiteit Twente

We consider a tandem queue with two stations. The rst station is an s-server queue with Poisson arrivals and exponential service times. After terminating his service in the rst station, a customer enters the second station to require service at an exponential single server, while in the meantime he is blocking his server in station 1 until he completes service in station 2, whereupon the server in station 1 is released. An analysis of the generating function of the simultaneous probability distribution of the queue lengths is given. An explicit expression for the stability condition and the solution for s = 2 is obtained.
  • References (3)

    [1] Loynes, R.M. (1962), Stationary waiting-time distributions for single-server queues, Ann. Math. Statist., 33, 1323{1339.

    [2] Neuts, M.F. (1968), Two queues in series with a nite intermediate waitingroom, J. of Appl. Prob., 5, 123{142.

    [3] Neuts, M.F. (1994), Matrix-Geometric Solutions in Stochastic Models, Dover, New York.

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