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.© BrainMass Inc. brainmass.com September 23, 2018, 4:21 pm ad1c9bdddf - https://brainmass.com/math/probability/queuing-analysis-356536
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.