Some new results on the waiting time and busy time in a M/G/1 queue

This paper considers an M/G/1 queue with Poisson arrival rate λ > 0 and service time distribution G(t) which is supposed to have finite mean 1/μ. The following questions are studied: (a) the probability that waiting time is more than a fixed value; (b) the cumulative probability of the busy time of the server, dependent on the service distribution. Some new and important results are obtained based on the renewal process.