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In this paper, we analyze the steady state maximum overlap time in the M/M/1queue. We derive the maximum overlap time tail distribution, its moments andthe moment generating function. We also analyze the steady state minimumoverlap time of the adjacent customers and compute its moments and momentgenerating function. Our results provide new insight on how customers becomeinfected in the M/M/1 queue.

The Maximum Overlap Time in the M/M/1 Queue