In their book, Chaudhry and Templeton  present a unified approach to many problems on bulk queues. Using their analytical approach, we show how to numerically evaluate steady-state probabilities and moments for number in system (or queue) at each of three time epochs — postdeparture, prearrival and random — for several bulk and nonbulk queues. The approach can be used for other problems in queueing theory, and for similar problems in the theories of dams, inventories, etc. The present study extends the computational results available in tables, such as those produced by Hillier and Yu , and has several potential applications. The method proposed is computationally efficient, accurate, and stable. It accommodates high values of the queueing parameters. Sample numerical results and graphs are also presented.
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Chaudhry, M.L., Madill, B.R. & Brière, G. Computational analysis of steady-state probabilities of M/Ga,b/1 and related nonbulk queues. Queueing Syst 2, 93–114 (1987). https://doi.org/10.1007/BF01158395
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