Waiting Lines and Queuing Theory Models
Ashley’s Department Store in Kansas City maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically with a recorded message that tells the customer that their business is important to Ashley’s and asks them to please wait for the next available clerk. As soon as the clerk is free, the party that has waited the longest is transferred and their order is the next one that the clerk takes. Calls come in at a rate of about 12 per hour. On average, it takes the clerk 4 minutes to take an order. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The clerk is paid $10 per hour, but because of lost goodwill and sales, Ashley’s loses about $50 per hour of customer time spent waiting for the clerk to take an order.
a. What is the average time that catalog customers must wait before their calls are transferred to the order clerk?
b. What is the average number of callers waiting to place an order?
c. Ashley’s is considering adding a second clerk. If the second clerk takes orders at the same rate as the first, what is the steady-state probability that there are no calls in the system?
d. If the store hires the second clerk, it would also pay that clerk $10 per hour. Should it hire the second clerk? Explain your answer.
diketahui : lamda : 12, miu : 60/4 = 15 calls/hour
(a) Wq = lamda/miu(miu – lamda) = 12/15(15-12) = 0.2666
atau 60 x 0.2666 = 15.996 = 16 minutes
jadi rata2 penelpon menunggu dalam antrian untuk disambungkan selama 16 menit.