> City Cab, Inc., uses two dispatchers to handle requests for service and to dis

Question

> 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.

> 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.

Explanation / Answer

Yes there willl be a difference when normal distribution is used instead of exponential distribution

This is because a exponential distribution is generally used for describing time between 2 poisson distributions as the exponentional distribution is not affected by previous data

But normal distribution is not like the exponential distribution. Here the previous data points affect the future data points so we can say that normal distributin has potential to remember past data but exponential distribution does not remember past data

Hence the results of exponntial distribution will remain the same over a period of time , in this case mean service time will remain 2 in exponential distribution

But the mean service time will change over a period of time in normal distribution

This makes a big diffrence in the model used and the final results obtained.

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