Comparison of two randomized policy M/G/1 queues with second optional service, server breakdown and startup

Authors:
Kuo-Hsiung Wang;Dong-Yuh Yang;W. L. Pearn
Affiliations:
Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan;Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu 30050, Taiwan;Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu 30050, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 12
Cited 0

An M/G/1 queue with second optional service

Queueing Systems: Theory and Applications
A Single Server Poisson Input Queue with a Second Optional Channel

Queueing Systems: Theory and Applications
Sensitivity analysis of the optimal management policy for a queuing system with a removable and non-reliable server

Computers and Industrial Engineering
Randomized control of T-policy for an M/G/1 system

Computers and Industrial Engineering
A discrete-time Geo/G/1 retrial queue with starting failures and second optional service

Computers & Mathematics with Applications
An M/G/1 retrial queueing system with two phases of service subject to the server breakdown and repair

Performance Evaluation
Analysis of a retrial queue with two-phase service and server vacations

Queueing Systems: Theory and Applications
Optimization of the T policy M/G/1 queue with server breakdowns and general startup times

Journal of Computational and Applied Mathematics
A repairable queueing model with two-phase service, start-up times and retrial customers

Computers and Operations Research
An M/G/1 queue with second optional service and server breakdowns

Computers & Mathematics with Applications
A batch arrival retrial queueing system with two phases of service and service interruption

Computers & Mathematics with Applications
Modified T vacation policy for an M/G/1 queueing system with an unreliable server and startup

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	7.29

Visualization

Abstract

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.