Consider the Markov process illustrated below. The transitions are labelled by the rate q ij at which those transitions occur. The process can be viewed as a single server queue where arrivals become...

Consider the Markov process illustrated below. The transitions are labelled by the rate q_ij
at which those transitions occur. The process can be viewed as a single server queue where arrivals become increasingly discouraged as the queue lengthens. The word time-average below refers to the limiting time-average over each sample-path of the process, except for a set of sample paths of probability 0.