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Reed, Josh; Ward, Amy; Zhan, Dongyuan

On the generalized drift Skorokhod problem in one dimension. (English) Zbl 1262.90048

J. Appl. Probab. 50, No. 1, 16-28 (2013).
Summary: We show how to write the solution to the generalized drift Skorokhod problem in one-dimension in terms of the supremum of the solution of a tractable unrestricted integral equation (that is, an integral equation with no boundaries). As an application of our result, we equate the transient distribution of a reflected Ornstein-Uhlenbeck (OU) process to the first hitting time distribution of an OU process (that is \(not\) reflected). Then, we use this relationship to approximate the transient distribution of the \(GI/GI/1 + GI\) queue in conventional heavy traffic and the \(M/M/N/N\) queue in a many-server heavy traffic regime.

Cited in 4 Documents

MSC:

90B22 Queues and service in operations research
90B15 Stochastic network models in operations research
60G17 Sample path properties
60J60 Diffusion processes

Keywords:

Skorokhod map; reflected Ornstein-Uhlenbeck process; abandonment; queueing
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\textit{J. Reed} et al., J. Appl. Probab. 50, No. 1, 16--28 (2013; Zbl 1262.90048)
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