Abstract
Given conditions, which concern the infinitesimal parameters of two birth and death processes, the processes are constructed on the same probability space such that one process is almost surely larger than the other. Application is made to M/M/s queueing systems. Stochastic comparisons of queue length and virtual waiting time in two M/M/s systems are obtained.
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Bhaskaran, B.G. Almost sure comparison of birth and death processes with application to M/M/s queueing systems. Queueing Syst 1, 103–127 (1986). https://doi.org/10.1007/BF01149330
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DOI: https://doi.org/10.1007/BF01149330