Jobs arrive at a machine following a Poisson process with rate λ. The machine processes jobs one at a time, and the processing times follow i.i.d. exponential distribution with mean 1/µ, independent of the arrival process. Suppose at t = 0, the machine is occupied, processing a job. Let Y be the number of jobs waiting in queue when the machine completes processing that job. Derive the mean and variance of Y.
2026-03-27 12:16:18.1774613778
Compute mean and variance waiting time of M/M/1 Queue
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