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# Queuing Analysis

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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.

https://brainmass.com/math/probability/queuing-analysis-356536

#### Solution Preview

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.

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## Linear Programming, Queueing Analysis, Simulations, Decision Analysis and Forecasting

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B) Briefly describe how simulation could be used to assist decision makers in regards to new product development?

C) Give an example of how Decision analysis could be used to determine an optimal strategy? Briefly describe several decision alternatives a decision maker would be faced with and possible uncertain future events to consider.

D) What is the difference between quantitative forecasting methods and qualitative forecasting methods?

E) Under what circumstances would it be more appropriate to use quantitative rather than qualitative forecasting methods?

F) Give an example of a situation when using quantitative forecasting would be appropriate?

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