Charles Knessl, Charles Tier, "Mean time for the development of large workloads and large queue lengths in the queue", International Journal of Stochastic Analysis, vol. 9, Article ID 515492, 36 pages, 1996. https://doi.org/10.1155/S1048953396000147
Mean time for the development of large workloads and large queue lengths in the queue
We consider the queue described by either the workload (unfinished work) or the number of customers in the system. We compute the mean time until reaches excess of the level , and also the mean time until reaches . For the and models, we obtain exact contour integral representations for these mean first passage times. We then compute the mean times asymptotically, as and , by evaluating these contour integrals. For the general model, we obtain asymptotic results by a singular perturbation analysis of the appropriate backward Kolmogorov equation(s). Numerical comparisons show that the asymptotic formulas are very accurate even for moderate values of and .
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