# probability distribution of the model

Alice Tanner is a nurse on the night shift from 10:00 P.M. to 6:00 A.M. at Community Hospital. She has 15 patients for whom she is responsible in her area. She averages two calls from each of her patients every night on average (Poisson distributed) and she must spend an average of 10 minutes (exponentially distributed) with each patient who calls. Nurse Tanner has indicated to her supervisor that, although she has not kept records, she believes her patients must wait about 10 minutes on average for her to respond and she has requested that her supervisor assign a second nurse to her area. The supervisor believes 10 minutes is too long for a patient to wait but she does not want her nurses to be idle more than 40% of the time. Determine what the supervisor should do.

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#### Solution Preview

Please see the attached files.

The initial model is M/M/1 with finite capacity N = 15 Given that:

Arrival rate = 0.0625

Service rate = 0.10

= 0.6250

As per the theory of the model:

And

By using this formula the probability distribution of the model is and the average number of customers in the system can be calculated as follows:

(See the attached excel file for ...

#### Solution Summary

The probability distribution of the model and the average number of customers in the system are calculated in this solution.