Xianjun Shi

Type

Text

Type

Dissertation

Advisor

Xing, Haipeng | Hu, Jiaqiao | Gandhi, Anshul | Chen, Xinyun. | Sasansuma, Katsunobu.

Date

2017-08-01

Keywords

Applied mathematics | DCFTP | Operations research | Perfect Sampling | Queueing System | Random Assignment | Time-Varying | Vacation System

Department

Department of Applied Mathematics and Statistics.

Language

en_US

Source

This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree

Identifier

http://hdl.handle.net/11401/78367

Publisher

The Graduate School, Stony Brook University: Stony Brook, NY.

Format

application/pdf

Abstract

This thesis mainly studies perfect simulation methodology for the time-varying queueing systems including time varying queue with a single server ($M_t/G_t/1$ and G_t/G/1) and time-varying queue with multi-servers ($G_t/G/c$). Firstly, we introduce how to simulate the $M_t/G_t/1$ queue by an auxiliary process and then proposed a perfect sampling algorithm for it, which works effectively verified by numerical results. Secondly, two perfect sampling algorithms for the $G_t/G/1$ queue are proposed. One of them is based on a technique called Dominated Coupling From The Past (DCFTP), which was given by proposed by Propp and Wilson in 1996, by taking the Vacation System (VS) as a dominant queue. The other one shows how can $G_t/G/1$ be sampled directly without any dominant queues. Besides, corresponding numerical results are reported in the end to show the effectiveness of the algorithms. At last, we give two perfect sampling algorithms for $G_t/G/c$ queue. Both of them takes advantage of the DCFTP technique but with different dominant queues, which are the VS model and $G_t/G/c$ under Random Assignment (RA) discipline. The accuracy and efficiency of the algorithms are verified by corresponding numerical experiments. Moreover, the performances for VS and RA models are compared in the end, which shows that for large $c (=10)$, RA model performs better than VS. | 105 pages

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