Comparison of two randomized policy M/G/1 queues with second optional service, server breakdown and startup
The problem addressed in this paper is to compare the minimum cost of the two randomized control policies in the M/G/1 queueing system with an unreliable server, a second optional service, and general startup times. All arrived customers demand the first required service, and only some of the arrive...
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| Vydáno v: | Journal of computational and applied mathematics Ročník 234; číslo 3; s. 812 - 824 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Kidlington
Elsevier B.V
01.06.2010
Elsevier |
| Témata: | |
| ISSN: | 0377-0427, 1879-1778 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | The problem addressed in this paper is to compare the minimum cost of the two randomized control policies in the M/G/1 queueing system with an unreliable server, a second optional service, and general startup times. All arrived customers demand the first required service, and only some of the arrived customers demand a second optional service. The server needs a startup time before providing the first required service until the system becomes empty. After all customers are served in the queue, the server immediately takes a vacation and the system operates the (
T
,
p
)-policy or (
p
,
N
)-policy. For those two policies, the expected cost functions are established to determine the joint optimal threshold values of (
T
,
p
) and (
p
,
N
), respectively. In addition, we obtain the explicit closed form of the joint optimal solutions for those two policies. Based on the minimal cost, we show that the optimal (
p
,
N
)-policy indeed outperforms the optimal (
T
,
p
)-policy. Numerical examples are also presented for illustrative purposes. |
|---|---|
| ISSN: | 0377-0427 1879-1778 |
| DOI: | 10.1016/j.cam.2010.01.045 |