Question: The manager of a grocery store is interested in providing good service to the senior citizens who shop in his store. The manager is considering the addition of a separate checkout counter for senior citizens. It is estimated that the senior citizens would arrive at the counter at an average of 30 per hour, with interarrival times following an exponential distribution. It is also estimated that they would be served at a rate of 35 per hour, with exponentially distributed service times.

a. What is the estimated utilization of the checkout clerk?

b. What is the estimated average length of the queue?

c. What is the estimated average waiting time in line?

d. Assess the performance of this process.

e. What service rate would be required to have customers average only 8 min in the process? (The 8 min include both waiting and service times.)

f. For the service rate calculated in part (e), what is the probability of having more than four customers in the process?

g. What service rate would be required to have only a 10% chance of exceeding four customers in the process?