Question

Timing-Waiting Lines

Joe Hammer is thinking about setting up a special counter for the do-it-yourself customers at which they can get, not only help where to find products in the store, but also some quick advice about the best way to handle their upcoming projects. Experience has taught Joe that six minutes is a good figure to allow for the average time required to serve a “do-it-yourselfer” and that these customers will arrive every 15 minutes throughout the day.

a.) If joe sets up the counter under these conditions, what operating characteristics might he expect?

b.) What might Joe do to avoid the costs of idleness?

c.) What is the likelihood(probability) that three or more customers will be at the counter, either waiting or being served, at any given time?

Calculate the Utilization rate, idleness rate, Average time in queue, Average time in system, Average number in queue, Average number in system, and probability that three or more customers will be in the counter system at the same time.

Please show calculation for each question, thank you.

Answer 1

A. The characteristics are as below

Utilization rate

Idleness rate

Average customers in the system

Average Queue Length

Average Waiting time for customer in queue

Wq = 4 minutes

Average waiting time for customer in system = queue + service

B. To avoid the cost of idleness, Joe can either decrease the mean service time or the mean arrival rate of the customers should increase.

C. Probability that there are 3 or more cusromers in counter system is