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Randomized policy of a poisson input queue with J vacations

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Abstract

This paper studies the operating characteristics of an M/G/1 queuing system with a randomized control policy and at most J vacations. After all the customers are served in the queue exhaustively, the server immediately takes at most J vacations repeatedly until at least N customers are waiting for service in the queue upon returning from a vacation. If the number of arrivals does not reach N by the end of the J th vacation, the server remains idle in the system until the number of arrivals in the queue reaches N. If the number of customers in the queue is exactly accumulated N since the server remains idle or returns from vacation, the server is activated for services with probability p and deactivated with probability (1 − p). For such variant vacation model, other important system characteristics are derived, such as the expected number of customers, the expected length of the busy and idle period, and etc. Following the construction of the expected cost function per unit time, an efficient and fast procedure is developed for searching the joint optimum thresholds (N*, J*) that minimize the cost function. Some numerical examples are also presented.

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Authors and Affiliations

  1. Department of Applied Statistic, National Taichung Institute of Technology, Taichung, 404, Taiwan, China

    Jau-Chuan Ke

  2. Department of Industrial and Engineering Management, National Chiao Tung University, Hsing Chu, 300, Taiwan, China

    Kai-Bin Huang & Wen Lea Pearn

Authors
  1. Jau-Chuan Ke
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  2. Kai-Bin Huang
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  3. Wen Lea Pearn
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Correspondence to Jau-Chuan Ke.

Additional information

Jau-Chuan Ke is a professor of Applied Statistics at National Taichung Institute of Technology, Taiwan. He received his M.S. in Applied Mathematics at National Cheng-Kung University, Taiwan, and his Ph.D. in Applied Mathematics at National Chung-Hsing University, Taiwan. His research interests include stochastic process, queuing theory, reliability, and applied statistics

Kai Bin Huang received the Ph.D. degree in industrial engineering and management from National Chiao-Tung University, Hsinchu, Taiwan, China. He is currently an IT engineer in the Engineering Information System Develop Dept., Ardentec Co. Ltd., Hsinchu. His research interests include Queueing theory, Quality engineering and Applied statistics.

Wen Lea Pearn is a professor of operations research and quality assurance at National Chiao Tung University, Taiwan. He received his PhD degree in operations research from the University of Maryland, College Park, Maryland, USA. He worked at AT&T Bell Laboratories as a quality research scientist before joining National Chiao Tung University. His research interests include process capability, network optimization, production management and queuing theory. His publications have appeared in the Journal of the Royal Statistical Society, Journal of Quality Technology, Journal of Applied Statistics, Statistics, Journal of the Operational Research Society, European Journal of Operations Research, Operations Research Letters, Omega, Networks, International Journal of Production Research, International Journal of Systems Science, Journal of Computational and Applied Mathematics, Quality & Reliability Engineering International, IEEE Transactions on Semiconductor Manufacturing, IEEE Transactions on Electronics Packaging Manufacturing and others.

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Ke, JC., Huang, KB. & Pearn, W.L. Randomized policy of a poisson input queue with J vacations. J. Syst. Sci. Syst. Eng. 19, 50–71 (2010). https://doi.org/10.1007/s11518-010-5124-z

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  • DOI: https://doi.org/10.1007/s11518-010-5124-z

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