Abstract
In this note the complete monotonicity of the waiting time density in GI/G/k queues is proved under the assumption that the service time density is completely monotone. This is an extension of Keilson's [3] result for M/G/1 queues. We also provide another proof of the result that complete monotonicity is preserved by geometric compounding.
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References
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Szekli, R. On the complete monotonicity of the waiting time density in some GI/G/k systems. Queueing Syst 1, 401–406 (1987). https://doi.org/10.1007/BF01150672
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DOI: https://doi.org/10.1007/BF01150672