M/G/1-FIFO Queue with Uniform Service Times

2022/06/21 by Finch, Steven
#34Kxx #44A10 #60K25 (Primary) 60-03 #68Q87 #90-03 (Secondary) #90B22 #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #History and Overview (math.HO) #Probability (math.PR)

paper · doi:10.48550/arxiv.2206.11108

Abstract

An exact formula for the equilibrium M/U/1 waiting time density is now effectively known. What began as a numeric exploration became a symbolic banquet. Inverse Laplace transforms provided breadcrumbs in the trail; delay differential equations subsequently gave clear-cut precision. We also remark on tail probability asymptotics and on queue lengths.

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