Journal of Applied Probability

On the generalized drift Skorokhod problem in one dimension

Josh Reed, Amy Ward, and Dongyuan Zhan

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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.

Article information

J. Appl. Probab., Volume 50, Number 1 (2013), 16-28.

First available in Project Euclid: 20 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90B22: Queues and service [See also 60K25, 68M20]
Secondary: 90B15: Network models, stochastic 60G17: Sample path properties 60J60: Diffusion processes [See also 58J65]

Skorokhod map reflected Ornstein–Uhlenbeck process abandonment queueing


Reed, Josh; Ward, Amy; Zhan, Dongyuan. On the generalized drift Skorokhod problem in one dimension. J. Appl. Probab. 50 (2013), no. 1, 16--28. doi:10.1239/jap/1363784421.

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