Answer to Question #134801 in Statistics and Probability for Moffat

Question

A small company has a call center with two phone lines only. An average of 40 people per hour calls in for orders, and it takes an average of 2 minutes to handle a call. Interarrival time between call arrivals and time to serve calling customers is on phone are exponentially distributed. If there are more than two customers waiting to be served, a caller gets a busy signal and hangs up.

b)What is the average time that the phone lines stay idle?

c) Calculate the fraction of the time that the line will be busy?

d) Calculate the average number of customers on hold waiting to be answered

Answer 1

b) arrival rate - $\lambda$ - 40 people per hour

service rate - $\mu$ - 60/2=30 people per hour

arrival rate >service rate so idle time is 0

c) fraction of the time that the line will be busy

p=$\lambda/\mu$ =40/30 $\implies 1 -$ all the time

d)$L=\lambda^2/(\mu(\mu-\lambda))$ =1600/(30*10)=5.33