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Calculates average queue size and waiting time.

by | Dec 1, 2023 | Posted Questions

Calculates average queue size and waiting time.

ABC Airline has one reservation clerk on duty at a time. He
handles information about flight schedules and makes reservations. All calls to
ABC Airline are answered by an operator. If a caller requests information or
reservations, the operator transfers the call to the reservations clerk. If the
clerk is busy, the operator asks the caller to wait. When the clerk becomes
available, the operator transfers to him the call of the person who has been
waiting the longest. Assume that arrivals and services follow a Poisson
process. Calls arrive at a rate of 10 per hour (? = 10 per hour), and the reservations
clerk can service a call in four minutes on average (? = 15 per hour).

Part 1: What is the average number of calls waiting to be
connected to the reservations clerk?

Part 2: What is the average time a caller must wait before
reaching the reservations clerk?

Part 3: What is the average time for a caller to complete a
call (waiting time plus service time)?

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