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Steady-state probability of the randomized server control system with second optional service, server breakdowns and startup

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Abstract

This paper deals with the 〈N,p〉-policy M/G/1 queue with server breakdowns and general startup times, where customers arrive to demand the first essential service and some of them further demand a second optional service. Service times of the first essential service channel are assumed to follow a general distribution and that of the second optional service channel are another general distribution. The server breaks down according to a Poisson process and his repair times obey a general distribution in the first essential service channel and second optional service channel, respectively. The server operation starts only when N (N≥1) customers have accumulated, he requires a startup time before each busy period. When the system becomes empty, turn the server off with probability p (p∈[0,1]) and leave it on with probability (1−p). The method of maximum entropy principle is used to develop the approximate steady-state probability distribution of the queue length in the M/G(G, G)/1 queueing system. A study of the derived approximate results, compared to the established exact results for three different 〈N,p〉-policy queues, suggests that the maximum entropy principle provides a useful method for solving complex queueing systems.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu, 30050, Taiwan

    Dong-Yuh Yang & W. L. Pearn

  2. Department of Applied Mathematics, National Chung-Hsing University, Taichung, 402, Taiwan

    Kuo-Hsiung Wang

Authors
  1. Dong-Yuh Yang
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  2. Kuo-Hsiung Wang
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  3. W. L. Pearn
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Correspondence to Kuo-Hsiung Wang.

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Yang, DY., Wang, KH. & Pearn, W.L. Steady-state probability of the randomized server control system with second optional service, server breakdowns and startup. J. Appl. Math. Comput. 32, 39–58 (2010). https://doi.org/10.1007/s12190-009-0231-z

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  • DOI: https://doi.org/10.1007/s12190-009-0231-z

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