## Journal of Applied Probability

### On the generalized drift Skorokhod problem in one dimension

#### Abstract

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

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

Dates
First available in Project Euclid: 20 March 2013

https://projecteuclid.org/euclid.jap/1363784421

Digital Object Identifier
doi:10.1239/jap/1363784421

Mathematical Reviews number (MathSciNet)
MR3076769

Zentralblatt MATH identifier
1262.90048

#### Citation

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. https://projecteuclid.org/euclid.jap/1363784421

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