Question

Consider a single server ,poison input queue with mean arrival rate of 12/hr .currently the server works according to an exponential distribution with mean service time of 6 minutes .Management has a training course which will result in an improvement in the variance of service time but a slight increase in the mean .After completion of course its estimated that the service time is now normally distributed and that the mean service time will increase to 4.5 minutes ,but the standard deviation will decrease from 5 minutes to 4 minutes .Management would like to know ,whether they should have the server undergo further training .

Explain and solve

Answer 1

In exponential distribution, mean = 6 minutes, variance()

After Management training course mean is slightly increase and improvement in variance( variance is decrease). I think this better is better because variance is decreases.

In Normal Distribution , mean value is increases 4.5 times and variance = 5 to 4 minutes , we can say in exponential distribution variance is decreases and mean is slightly increases but in Normal distribution mean is 4.5 time increases it mean my distribution more likely right shifted since variance is decreases this is good but mean is more increases  . Therefore , They should have go under further training for improvement of your model . And doing untill when you got less variance and mean is nearly same.