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

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