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On the Generalized Drift Skorokhod Problem in One Dimension

  • Josh Reed (a1), Amy Ward (a2) and Dongyuan Zhan (a2)

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.

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Copyright

Corresponding author

Postal address: Stern School of Business, New York University, New York, NY 10012, USA. Email address: jreed@stern.nyu.edu
∗∗ Postal address: Marshall School of Business, University of Southern California, Los Angeles, CA 90089-0809, USA.

References

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On the Generalized Drift Skorokhod Problem in One Dimension

  • Josh Reed (a1), Amy Ward (a2) and Dongyuan Zhan (a2)

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