Asymptotic analysis of the M/G/1 queue with a time‐dependent arrival rate |
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Authors: | Yang Yongzhi Knessl Charles |
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Institution: | (1) Department of Mathematics, University of St. Thomas, St. Paul, MN 55105‐1096, USA;(2) Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607‐7045, USA |
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Abstract: | We consider the M/G/1 queue with an arrival rate λ that depends weakly upon time, as λ = λ(εt) where ε is a small parameter. In the asymptotic limit ε → 0, we construct approximations to the probability p
n(t)that η customers are present at time t. We show that the asymptotics are different for several ranges of the (slow) time scale Τ= εt. We employ singular perturbation techniques and relate the various time scales by asymptotic matching.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | M/G/1 queue time‐ dependent arrival rate asymptotic analysis |
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