Abstract
We obtain the time dependent probabilities for the joint distribution of the number of arrivals and departures in [0,t] for theM/M ij/1 queue. This queue has the exponential service with parametersμ ij, depending on the types of the successive customers attended. We provide an intuitive interpretation of the solution and also present some numerical results, including time dependent event probabilities and queue length.
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Daigle, J.N., Magalhães, M.N. Transient behavior ofM/M ij/1 queues. Queueing Syst 8, 357–377 (1991). https://doi.org/10.1007/BF02412260
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DOI: https://doi.org/10.1007/BF02412260