Some Relationships Between the Distributions of Waiting Time, Idle Time and Interoutput Time in the $GI/ G/1$ Queue

Some known results on the waiting time distribution in the $GI/G/1$ queue are summarized, and a generalization of the Pollaczek-Khintchine formula is derived from these. The author gives a.direct derivation of this result and demonstrates the role played by the idle time distribution in finding the distribution of wait. The results lead to two representations of the Laplace transform of the output distribution.