The IE analyst at RC Regional outreach care has noticed a rise in complaints abo

Question

The IE analyst at RC Regional outreach care has noticed a rise in complaints about waiting time. Having a statistics background she collects data on inter-arrival times and service times. Using a Chi-Square goodness of fit test she determines the inter-arrival time is indeed exponential with an arrival rate of 5 per hour. However, the service time tends to follow a Weibull distribution. From the data, she has calculated a sample mean service time of 10 minutes and a sample standard deviation of 4 minutes. Model this system as an M/G/1 queue to determine average wait time for a customer.

Explanation / Answer

Avg waiting time in M-G-1 queue with poisson arrival time and variable service time

= rho + lambda. Mu . Var (S) / 2 ( mu - lambda)

= 5/6 + 30/3600 x 16 / 2 ( 6/60- 5/60)

= 29 min.

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