This problem is intended to show that one can analyze the long term behavior of queueing problems by using just notions of means and variances, but that such analysis is awkward, justifying...

This problem is intended to show that one can analyze the long term behavior of queueing problems by using just notions of means and variances, but that such analysis is awkward, justifying understanding the strong law of large numbers. Consider an M/G/1 queue. The arrival process is Poisson with λ = 1. The expected service time, E [Y ], is 1/2 and the variance of the service time is given to be 1.

f) Combine (e) and (b) to estimate the expected length of a busy period.