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A Queue with Periodic Arrivals and Constant Service Rate
 In Chapter 10 of Probability, Statistics and Optimization a Tribute
, 1994
"... : Consider a queueing system in which K sources each generate 1=M units of work once every time unit. The phases of the sources are mutually independent, and each phase is uniformly distributed over the unit interval. The queue is served at unit rate. The distribution of the typical work and the max ..."
Abstract

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: Consider a queueing system in which K sources each generate 1=M units of work once every time unit. The phases of the sources are mutually independent, and each phase is uniformly distributed over the unit interval. The queue is served at unit rate. The distribution of the typical work and the maximum work are studied both for finite K and M and in the limit of large K and M . The limiting maximum work is identified as the maximum of a reflecting Brownian motion over the unit interval given that its local time at zero first reaches a specified value at the end of the interval. The analysis is expedited by a tie to the empirical process arising in KolmogorovSmirnov statistical tests. 1