An M/M/∞ system

Topic: Birth–death chains and queues · more questions on this topic
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An M/M/∞ system has \lambda=6 and \mu=2 per hour. Find the stationary mean and the probability that the system is empty.

Worked answer (click to show)

The stationary number is Poisson with mean \lambda/\mu=3. The probability of an empty system is the Poisson probability at 0, which is e^{-3}.