Business

City Cab, Inc., uses two dispatchers to handle requests for service and to dispatch the cabs.  The telephone calls that are made to City Cab use a common telephone number.  When both dispatchers are busy, the caller hears a busy signal; no waiting is allowed.  Callers who receive a busy signal can call back later or call another cab company for service.  Assume that the arrival of calls follows a Poisson distribution, with a mean of 40 calls per hour, and that the call handling time follows an exponential probability distribution with a mean service time of 2 minutes.  Based on this information, answer the following questions.

What percentage of the time are both dispatchers idle?

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What percentage of the time are both dispatchers busy?

What is the probability that a caller will receive a busy signal if 2, 3, or 4 dispatchers are used?

If management wants no more than 12% of the callers to receive a busy signal, how many dispatchers should be used?

Suppose the service time distribution is not exponential, it follows some other distribution such as a normal, but the mean service time remains at 2 minutes.  Does this make any difference in the model used and in the results?  Explain.

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