A small mail order firm seas beginnings has one phone line an average of 60 peop

Question

A small mail order firm seas beginnings has one phone line an average of 60 people per hour call in orders, and it takes an average of 1 minute to handle a call. Time between calls and time to handle calls are exponentially distributed. If the phone line is busy, Seas Beginings can put up to c-1 people on hold. If c-1 people are on hold, a caller gets a busy signal and calls a competitor (Air End). Seas Beginnings wants only 1% of all callers to get a busy signal. How many people should the company be able to put on hold?

Explanation / Answer

We now consider the M/M/s/GD/?/?system. We assume that interarrival times are exponential (with rate l), service times are exponential (with rate m), and there is a single line of customers waiting to be served at one of sparallel servers. If j scustomers are present, then all jcustomers are in service; if j scustomers are present, then all s servers are occupied, and j scustomers are waiting in line. Any arrival who finds an idle server enters service immediately, but an arrival who does not find an idle server joins the queue of customers awaiting service. Banks and post office branches in which all customers wait in a single line for service can often be modeled as M/M/s/GD/?/?queuing systems. To describe the M/M/s/GD/?/?system as a birth

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