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On the generalized drift Skorokhod problem in one dimension

Reed, J; Ward, A; Zhan, D; (2013) On the generalized drift Skorokhod problem in one dimension. Journal of Applied Probability , 50 (1) pp. 16-28. 10.1239/jap/1363784421. Green open access

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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.

Type: Article
Title: On the generalized drift Skorokhod problem in one dimension
Open access status: An open access version is available from UCL Discovery
DOI: 10.1239/jap/1363784421
Publisher version: https://doi.org/10.1239/jap/1363784421
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Skorokhod map; reflected Ornstein–Uhlenbeck process; abandonment; queueing
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > UCL School of Management
URI: https://discovery.ucl.ac.uk/id/eprint/1575577
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