In a grocery store there are two cashier counters (M/M/1 system). Customers arrive at the cashier counter according to a Poisson process. The arrival rate is 20 customers per hour per each cashier counter. The service time is exponentially distributed. The mean service time is 2 minutes for both cashiers. Run model using QTS Plus to answer the followings. Don’t need to solve this problem by hand.
a) Once you arrived at a cashier counter, what is the expected number of customers in the waiting line?
b) What is the expected waiting time before you get served (unit in minutes)?
c) Now, you consider changing this cashier service as M/M/2 (see the lecture note). With the M/M/2 system, what are the utilization rate, number of customer in waiting line and total time spent in the line including serve time? If you need assumption(s), please state before you use and it should be reasonable.
d) Which system do you prefer, M/M/1 or M/M/2? Why?
e) If you want to change this system to M/M/2, what factors should be considered? And discuss how you can achieve this change (considering the factors)