# Queuing Analysis

The Bay City Police Department has eight patrol cars that are on constant call 24 hours a day. A patrol car requires repairs every 20 days, on average, according to an exponential distribution. When a patrol car is in need of repair, it is driven into the motor pool, which has a repair person on duty at all times. The average time required to repair a patrol car is 18 hours (exponentially distributed). Determine the average time a patrol car is not available for use and the average number of patrol cars out of service at any one time. Indicate whether the repair service seems adequate.

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#### Solution Preview

Please see the attached files.

In this problem we are dealing with an M/M/s queuing model with finite calling population.

The parameters of the model are as follows:

1. Size of the population = N = 8

2. Number of servers = s = 1

3. Arrival rate = = 0.0021 per hour

4. Service rate = = 0.0556 per hour

As per the theory, the steady state probability distribution of the model is as follows:

Queue ...

#### Solution Summary

Queuing Analysis is performed.