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Published online by Cambridge University Press: 18 December 2007
We use induction to derive the distribution of the waiting time of the ith waiting customer in a busy period for a G/M/1 queue with a first come–first serve service. A trivial implication gives the law for the ith waiting time in a busy period for a G/M/c queue. Finally, we use the Lindley recursion to relate our results to the distribution of random walks.