Question 1 CWD Department Store in Kingstown maintains a successful catalog sale

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Question 1

CWD Department Store in Kingstown 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 by an answering machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 10 per hour. The clerk is capable of taking an order in an average of 4 minutes. 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, CWD loses about $25 per hour of customer time spent waiting for the clerk to take an order.

Part A Answer the following questions:

a. What is the probability that no customers are in the system (Po)? 2 marks

b. What is the average number of customers waiting for service ( Lq)? 3 marks

c. What is the average number of customers in the system (L)?-2 marks

d. What is the average time a customer waits for service(Wq)? 3 marks

e. What is the average time in the system (W) ?-3 marks

f. What is the probability that a customer will have to wait for service (Pw)?-2 marks

g What is the probability that there is exactly 2 customers in the system- 2 marks

h) What is the probability that there are more than 3 customers in the system-3 mark

Part B

CWD is considering adding a second clerk to take calls. The store would pay that person the same $10 per hour. Using appropriate formula for the multiple channel model, answer the following questions:

a. What is the probability that no customers are in the system (Po)? 3 marks

b. What is the average number of customers waiting for service (Lq)? 2 marks

c. What is the average number of customers in the system (L)? 3 marks

d. What is the average time a customer waits for service (Wq)? 2 marks

e. What is the average time in the system (W)? 2 marks

f. What is the probability that a customer will have to wait for service (Pw)? 2 marks

g. What is the probability that there is exactly 2 customers in the system 2 marks

Explanation / Answer

1. a P0=(1-lambda/mu)=(1-0.17/4)=0.9575 [lambda=10 calls/hour=0.17 calls/minute, mu=4 minutes/call]

b. Lq=lambda^2/{mu(mu-lambda)}=0.17^2/{4(4-0.17)}=0.0019

c. L=lambda/(mu-lambda)=0.17/(4-0.17)=0.0444

d. Wq=lambda/{mu(mu-lambda)}=0.17/{4(4-0.17)}=0.0111

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