Some new results on waiting time and busy time in M/G/1 queue |
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Institution: | Department of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China |
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Abstract: | This paper considers an M/G/1 queue with Poisson rate λ > 0 and service time distribution G(t) which is supposed to have finite mean 1/μ. The following questions are first studied: (a) The closed bounds of the probability that waiting time is more than a fixed value; (b)The total busy time of the server, which including the distribution, probability that are more than a fixed value during a given time interval (0, t], and the expected value. Some new and important results are obtained by theories of the classes of life distributions and renewal process. |
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Keywords: | waiting time bound total busy time NBUE(NWUE) class 60K25 |
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