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.
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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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