Rush Franken receives about 60 000 calls in a 3 hour period

Rush Franken receives about 60, 000 calls in a 3 hour period into his phone lines for his radio show, but he is only able to accept 15 per hour to go on the air. Discuss whether this would or would not fit into one of the 3 waiting line models discussed in the text. Why or why not? A local radio call-in show has about 30 calls arrive each hour, and the radio host spends about 1.1 minutes per caller, exponentially distributed. Assume no commercials and callers are immediately taken on the air if there is one waiting; all other appropriate assumptions also hold. Also assume that there is an infinite line possible, that is, callers will not get a busy signal but will always be put into a line to go on the air. What is the average number of callers waiting to go on the air? What is the average time to wait before going on the air? What is the utilization? An airline ticket counter has one line feeding into 2 ticket agents. The airline is considering adding a third agent. Arrivals are spaced at an average of 5 minutes, Poisson distribution. An agent spends about 7 minutes per customer, exponentially distributed. All other appropriate assumptions hold. What is the average number in line waiting for service? What is the average wait time in line waiting for service? If a third agent is added, what is the average number in line waiting for service? If a third agent is added, what is the average wait time in line waiting for service?

Solution

Answer of question number 6.

The arrival rate = 30 calls per hour

As 1.1 minutes spends on one call therefore call served in one hour is Service rate µ = 60/1.1 call per hour = 54.55 calls per hour

(a) The average number of caller waiting to go on air

= The average waiting length in queue = ^2 / µ (µ -)

= 30^2 / 54.55 * (54.55 – 30) = 0.672 callers

(b) The average time of waiting before going on air

= The average waiting time in queue = / µ (µ -)

= 30 / 54.55 * (54.55 – 30) = 30 / 54.55 *24.55 = 0.0224 hour = 1.34 minutes

(c) Average utilization = / µ = 30/ 54.55 = 0.55 = 55%