s s Judy to pleier h 3 Sharp Discounts Wholesale Club has two service desks, one
ID: 2923114 • Letter: S
Question
s s Judy to pleier h 3 Sharp Discounts Wholesale Club has two service desks, one at each entrance of the ce rate Customers arrive at each service desk at an average of one every six minutes. The servi at each service desk is four minutes per customer. How often (what percentage of time) is each service desk idle? a. b. What is the probability that both service clerks are busy? c. What is the probability that both service clerks are idle? d How many customers, on average, are waiting in line in front of each service desk? e. How much time does a customer spend at the service desk (waiting plus service time)? 4 Sharp Discounts Wholesale Club is considering consolidating its two service desks (see Problem 3) into one location, staffed by two clerks. The clerks will continne to work at the same individual speed of four minutes per customer a. What is the probability of waiting in line? b. How many customers, on average, are waiting in line? c. How much time does a customer spend at the service desk (waiting plus service time)? d. Do you think the Sharp Discounts Wholesale Club should consolidate the service desks?Explanation / Answer
: mean rate of arrival. = 1/6 (here we have considered arrival rate will not change)
µ: mean service rate. = 1/4
= /µ = 4/6 = 0.6667
for single server queues: utilization of the server; also the probability that the
server is busy or the probability that someone is being served.
b) Average Number of customers in the Queue = Lq = ^2/(1-) = 1.33
c)
Wait in the Queue = Wq = Lq/ = 1.33/0.1667 = 7.98 minutes = 0.133 hours
Wait in the System = W = Wq + 1/µ = 7.98 + 4 = 11.98 minutes = 0.2 hours
d) Here we have considered that the arrival rate of custormes do not change and hence consolidation can happen.
But if this value of arrival rate is less than 4 minutes per customer then this queue will grow infinite.
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