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.
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:
Queuing Analysis is performed.