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

This paper considers an M/G/l 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.