Question: Q: Counter processes. Suppose that particles arrive at a counter according to a Poisson processwith rate . An arriving particle that finds the counter free

Q: Counter processes. Suppose that particles arrive at a counter according to a Poisson processwith rate . An arriving particle that finds the counter free gets registered and then locksthe counter for an amount of time . Particles that arrive while the counter is locked haveno effect (i.e., are not counted).

(a) Find the limiting probability the counter is locked at time t.

(b) Compute the limiting fraction of particles that get registered

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