Question

Experience the Tour de France (ETF) is a specialty travel agent. It arranges vacations for amateur cyclists who want to experience the Tour de France by riding through one or more stages in the race. It has six people who take calls from clients. Each call lasts on average 30 minutes, with a standard deviation of 60 minutes. A call arrives on average every 25 minutes with a standard deviation of 25 minutes.

On average, how many minutes does a caller wait before talking to an agent? _____ minutes

Answer 1

Question: Experience the Tour de France (ETF) is a specialty travel agent. It arranges vacations for amateur cyclists who want to experience the Tour de France by riding through one or more stages in the race. It has six people who take calls from clients. Each call lasts on average 30 minutes, with a standard deviation of 60 minutes. A call arrives on average every 25 minutes with a standard deviation of 25 minutes.

Answer: 30.0476 minutes

Explanation:

Given:

Arrival Time = a = 25 min

Service Time = p = 30 min

CV_a = 25 / 25 = 1

CV_p = 60 / 30 = 2

Now:

Utilization with 'm' server = p / a x m = 30 / 6 x 25 = 0.2

u = 0.2

Here Waiting time is given by formula:

T_q = (p / m) x (u^√2(m+1)-1 / 1 - u) x ( (CV_a² + CV_p² ) / 2 )

T_q = 30 / 6 x (0.20^{√2(6+1) -1} / 1 – 0.20) x (1² + 2² / 2)

= 5 x (0.20^2.741 / 0.8) x 2.5

= 5 x (0.0121 / 0.8) x 2.5

= 5 x 0.015125 x 2.5

T_q = 0.19

Now, T = T_q + p = 0.19 + 30 = 30.19 min

On average, a caller wait before talking to an agent = 30.19 min