Problem

A supermarket has two checkout stations, regular and express, with a single checker per st...

A supermarket has two checkout stations, regular and express, with a single checker per station; see Fig. 1.51. Regular customers have exponential interarrival times with mean 2.1 minutes and have exponential service times with mean 2.0 minutes. Express customers have exponential interarrival times with mean 1.1 minutes and exponential service times with mean 0.9 minute. The arrival processes of the two types of customers are independent of each other. A regular customer arriving to find at least one checker idle begins service immediately, choosing the regular checker if both are idle; regular customers arriving to find both checkers busy join the end of the regular queue. Similarly, an express customer arriving to find an idle checker goes right into service, choosing the express checker if both are idle; express customers arriving to find both checkers busy join the end of the express queue, even if it is longer than the regular queue. When either checker finishes serving a customer, he takes the next customer from his queue, if any, and if his queue is empty but the other one is not, he takes the first customer from the other queue. If both queues are empty, the checker becomes idle. Note that the mean service time of a customer is determined by the customer type, and not by whether the checker is the regular or express one. Initially, the system is empty and idle, and the simulation is to run for exactly 8 hours. Compute the average delay in each queue, the time-average number in each queue, and the utilization of each checker. What recommendations would you have for further study or improvement of this system? (On June 21, 1983, the Cleveland Plain Dealer, in a story entitled “Fast Checkout Wins over Low Food Prices,” reported that “Supermarket shoppers think fast checkout counters are more important than attractive prices, according to a survey [by] the Food Marketing Institute.… The biggest group of shoppers, 39 percent, replied ‘fast checkouts,’ … and 28 percent said good or low prices … [reflecting] growing irritation at having to stand in line to pay the cashier.”)