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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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 234; no. 3; pp. 812 - 824
Main Authors: Wang, Kuo-Hsiung, Yang, Dong-Yuh, Pearn, W.L.
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 01.06.2010
Elsevier
Subjects:
( [formula omitted], [formula omitted])-policy
Calculus of variations and optimal control
Comparison
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Optimization
Sciences and techniques of general use
Second optional service
( p , N )-policy
Second optional service
Comparison
( T , p )-policy
Optimization
(T, p)-policy
Optimization method
Optimal policy
Numerical analysis
Queueing system
Applied mathematics
Optimal solution
(p, N)-policy
Variational calculus
Cost function
Queue
Mathematical programming
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary: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