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  1. E. Kuumola, J. Resing and J. Virtamo, Analytical Results on the Stochastic Behaviour of an Averaged Queue Length, in Proceedings of the Sixteenth Nordic Teletraffic Seminar, NTS 16, pp. 88-99, 2002 (pdf)(bib)
    Abstract: The joint dynamics of the instantaneous and exponentially averaged queue length in an M/M/1/K queue is studied. A system of ordinary differential equations is derived for the joint stationary distribution of the instantaneous and the exponentially averaged queue length. The equations are similar to those governing an MMRP driven uid queue. An analytical solution to the equations is obtained in a few special cases. Mean and variance of the marginal distribution of the averaged queue length, both unconditional and conditional on the value of the instantaneous queue length, are derived for the general case.