Calls arrive at Lynn Ann Fish\'s hotel switchboard at a rate of 2.5 per minute.

Question

Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2.5 per minute. The average time to handle each is 15 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation a) The probability that the operator is busy = | | (round your response to two decimal places). b) The average lime that a caller must wait before reaching he operator-? minutes round your response to two decir a,paces c) The average number of calls waiting to be answeredcalls (round your response to two decimai placos).

Explanation / Answer

Arrival rate (A) = 2.5 per minute

Service rate (S) = 15 sec or 60/15 per minute = 4 per minute

a) Probability of operator busy = A/S = 2.5/4 = 0.63

b) Average waiting time for a caller = A/(S*(S-A)) = 2.5/(4*(4-2.5)) = 0.42 minutes

c) Average number of waiting = A^2/(S*(S-A)) = 2.5^2/(4*(4-2.5)) = 1.04

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