Q6  Queuing

Multiple Choice -- please select the right answer

Part 1 If the average time to serve a customer is 3 minutes, then the service rate, µ, would be

a. 3 per hour

b. 12 per hour

c. 16 per hour

d. 20 per hour

Part 2 If, on average, it takes 90 seconds to serve a customer then the hourly service rate, µ, would be

a. 90 per hour

b. 40 per hour

c. 30 per hour

d. 1.5 per hour

Part 3 An espresso stand has a single server. Customers arrive to the stand at the rate of 28 per hour according to a Poisson distribution.  Service times are exponentially distributed with a service rate of 35 customers per hour.

Part 3a The probability that the server is busy is

a. 0.20

b. 0.60

c. 0.80

d. 1.00

Part 3b The average number of customers waiting in line for service is

a. 4.0

b. 3.8

c. 3.5

d. 3.2

Part 3c The average time a customer spends waiting in line for service is

a. 0.114 minute

b. 0.143 minute

c. 6.857 minutes

d. 8.58 minutes

Part 3d If the arrival rate remains at 28 customers per hour and the stand’s manager wants to have the average time a customer spends in the system (i.e., wait time line and service time) to be a maximum of 6 minutes on average, then the service rate must

a. decrease by 2 to 33 customers per hour

b. decrease by 3 to 32 customers per hour

c. increase by 3 to 38 customers per hour

d. increase by 2 to 37 customers per hour