Problem 7-7 Sharp Discounts Wholesale Club has two service desks, one at each en
ID: 349496 • Letter: P
Question
Problem 7-7
Sharp Discounts Wholesale Club has two service desks, one at each entrance of the store. Customers arrive at each service desk at an average of one every six minutes. The service time at each service desk is four minutes per customer.
a. How often (what percentage of time) is each service desk idle? (Round your answer to 2 decimal places.) Percentage of time %
b. What is the probability that both service clerks are busy? (Round your answer to 4 decimal places.) Probability
c. What is the probability that both service clerks are idle? (Round your answer to 4 decimal places.) Probability
d. How many customers, on average, are waiting in line in front of each service desk? (Round your answer to 2 decimal places.) Average of customers waiting in line
e. How much time does a customer spend at the service desk (waiting plus service time)? Customer spending time minutes
Explanation / Answer
It is of 2 M/M/! system:
Kendall's notation M/M/1 Comment Arrival rate A 10 60/6 per hour Service rate S 15 60/4 U Utilization ratio U=A/S 0.66667 <1 Length of queue diminishing L Expected number of people in system Ls A/(S-A) 2.00 W Avg waiting time in the system Ws 1/(S-A) 0.20000 hours 12.0000 mins Ans E Wq Avg waiting time in the Line Wq A/S(S-A) 0.13333 hous 8.0000 mins Lq Avg no of customer waiting in line Lq A^2/S(S-A) 1.3333 Ans D Po Prob of 0 units in system Po 1-(A/S) 0.33333 33.33% Ans A Po' Prob of busy system Po' 1-Po 0.6667 Ans B 66.67% P12 Probability of both servers idle Po*Po 0.1111 Ans C