Excerpt from Transient and Busy Period Analysis of the Gi/G/1 Queue: Part II, Solution as a Hilbert Problem

In this subsection we define the random variables and establish the notation we are using. We assume that the system is initially idle and the first customer's arriving time is the forward recurrence interarrival time. Although this assumption is restrictive for the waiting time distribution, it is not restrictive for the busy period distribution, since the busy period regenerates.

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