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 three 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; round to two decimal places)

Answer 1

Answer :

Given data is

Number of servers (m) =3 people

Average activity time or service time (p) = 30 minutes

Standard deviation of activity time or service time = 60 minutes

Average interarrival time (a) = 25 minutes

Standard deviation of interarrival time = 25 minutes

Calculate CVa, CVp and Utilization(U) and Tq

CVp = the coefficient of variation of the service time process or activity time process

CVa = the coefficient of variation of the arrival time process

CVa = ( standard deviation of interarrival time) / ( average interarrival time)

CVa = 25/25 = 1 minute

CVa = ( standard deviation of interarrival time) / ( average interarrival time)

CVp = 60/30 = 2 minutes

Utilization (U) = ( average activity time or service time ) / ( no.of servers * average interarrival time)

= p/(m*a) = 30/(3*25) = 30/ 75 = 0.4

U = 0.4

(Tq) Time in queue  

= ( p / m) * ( ( U ^{(sqrt(2(3+1)) -1 )} ) / (1- U) ) * (  (CVa² + CVp² ) / 2 )

= ( 30/3) * ( 0.4^(1.83)/ (1-0.4 ) ) * ( 5/2)

= 7.79 minutes or 7.80 minutes