Acta mathematica scientia,Series B ›› 2001, Vol. 21 ›› Issue (3): 295-301.

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SOME NEW RESULTS ON WAITING TIME AND BUSY TIME IN M/G/1 QUEUE

 TANG Ying-Hui   

  1. Department of Applied Mathematics, University of Electronic Science and Technology of China,Chengdu 610054, China
  • Online:2001-07-06 Published:2001-07-06
  • Supported by:

    This work was supported by the National Outstanding Youth Science Foundation (79725002) and the supporting program of the National Education Ministry for Chinese University Excellent Teachers ([2000]65).

Abstract:

This paper considers an M/G/1 queue with Poisson rate  > 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.

Key words: M/G/1, waiting time, bound, total busy time, NBUE(NWUE) class

CLC Number: 

  • 60K25
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