You are managing a fast-food restaurant with three cashiers. The total arrival rate is 45 customers per hour and the service rate is 20 customers per hour. You have the option of configuring the waiting line in one of the following forms:
a. there are 3 separate queues with one cashier each. assume 15 customers per hour arrive to each line. the coefficient of variation of inter-arrival and service times is 1 (3 of M/M/1 - each cashier has his/her own line and assume 15 customers arrive in each line)
b. there is a single queue with 3 cashiers serving customers in a first come first serve manner. The coefficient of variation of inter-arrival and service times is 1 (M/M/3 - there is a single line)
c. there is a single queue with the 3 cashiers serving customers in a first come first serve manner. The coefficient of variation of inter-arrival times is 1 and it takes exactly 3 minutes to process a customers. (M/D/3 - the service time is constant and there is a single line)
The total arrival rate and the service rates in each configuration are the same.
a. calculate utilization rates for each configuration
b.calculate the number of customers waiting in line for each configuration
c. calculate the waiting time in line for each configuration
d. which configuration would you choose? Why?