2017
DOI: 10.1287/15-ssy175
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Heavy-traffic Limit for the Initial Content Process

Abstract: To understand the performance of a queueing system, it can be useful to focus on the evolution of the content that is initially in service at some time. That necessarily will be the case in service systems that provide service during normal working hours each day, with the system shutting down at some time, except that all customers already in service at the termination time are allowed to complete their service. Also, for infinite-server queues, it is often fruitful to partition the content into the initial c… Show more

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Cited by 10 publications
(6 citation statements)
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“…We have assumed that the system starts from empty. It remains to study general initial conditions as in [37,51,2]. That requires tracking the status (in service or in the waiting buffer for synchronization) of each task of jobs initially in the system.…”
Section: Discussionmentioning
confidence: 99%
“…We have assumed that the system starts from empty. It remains to study general initial conditions as in [37,51,2]. That requires tracking the status (in service or in the waiting buffer for synchronization) of each task of jobs initially in the system.…”
Section: Discussionmentioning
confidence: 99%
“…We furthermore assume that the system starts empty at time −t 0 ≤ 0. That avoids having to carefully treat the initial conditions, but for a way to do so, see [20]. LetĀ…”
Section: Review Of the Msht Fwlln For G T /Gi/∞ Queuesmentioning
confidence: 99%
“…We conjecture that the relevant many-server heavy-traffic limit for the stationary departure process is a Gaussian process with the covariance function of the stationary renewal processes associated with the service times, as in the CLT for renewal processes in Theorems 7.2.1 and 7.2.4 of [143]. Partial support comes from [10], Appendix F of [11] and [65].…”
Section: Extensionsmentioning
confidence: 90%