Question: Consider the M/M/1 queueing system with arrival rate > 0 and service rate > 0. (a) Compute the expected number of arrivals during

Consider the M/M/1 queueing system with arrival rate λ > 0 and service rate μ > 0.

(a) Compute the expected number of arrivals during a service time (also called service period).

(b) Compute the probability that no customers arrive during a service period.

You may use the trick of computing expectation/probability by conditioning, i.e., “unconditional expectation (or probability) is equal to the expectation of conditional expectation (or probability)”.

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