Optimization of the T policy M/G/1 queue with server breakdowns and general startup times

Authors:
Tsung-Yin Wang;Kuo-Hsiung Wang;Wen Lea Pearn
Affiliations:
Department of Accounting Information System, National Taichung Institute of Technology, Taichung 404, Taiwan;Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan;Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu 30050, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 3
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Abstract

This paper investigates the T policy M/G/1 queue with server breakdowns, and startup times. Customers arrive at the system according to a Poisson process. Service times, repair times, and startup times are assumed to be generally distributed. The server is turned on after a fixed length of time T repeatedly until at least one customer is present in the waiting line. The server needs a startup time before starting the service. We analyze various system performance measures and develop the total expected cost function per unit time in which T is a decision variable. We determine the optimum threshold T^* and derive analytical results for sensitivity investigations. The sensitivity analysis is particularly valuable to the system analyst when evaluating future conditions. We also present extensive numerical computation for illustration purpose.