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The transient solution of time-dependent M/M/1 queues

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2 Author(s)
Zhang, J. ; Rensselaer Polytech. Inst., Troy, NY, USA ; Coyle, E.J., Jr.

The transient behavior of time-dependent M/M/1 queues is studied. The boundary probability function π0(t), which is the probability that the queue is empty at time t, is shown with analyticity arguments to satisfy a Volterra-type integral equation. The boundary integral equation is derived, and a numerical algorithm is used to solve the integral equation and to find the expected queue size from π0(t). The approach can be applied to many other types of time-dependent queues. Examples are given

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Information Theory, IEEE Transactions on  (Volume:37 ,  Issue: 6 )