a. What is the probability that no customers are in the system (Po)? b. What is the average number of customers waiting for service ( Lq, c. What is the average number of customers in the system (L)?
a. What is the probability that no customers are in the system (Po)? b. What is the average number of customers waiting for service ( Lq, c. What is the average number of customers in the system (L)?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
![Question 4
Skyline pizza is a famous restaurant operating a number of outlets. The restaurant uses a toll-free telephone
number to book pizzas at any of its outlets. If the clerk is occupied on one line, incoming phone calls
to the restaurant 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 15 per hour. The clerk is capable of taking an order in an average of 3
minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The
clerk is paid $20 per hour, but because of lost goodwill and sales, CWD loses about $50 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)?
b. What is the average number of customers waiting for service ( Lq,
c. What is the average number of customers in the system (L)?
d. What is the average time a customer waits for service(Wq):
e. What is the average time in the system (W)
f. What is the probability that a customer will have to wait for service (Pw\?
g What is the probability that there is exactly 2 customers in the system-
h) What is the probability that there are more than 3 customers in the system](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7a6b591-ea57-4f65-b236-63229553b951%2F2e6fa7b5-973d-4d1d-ad90-ea3159705132%2Ff2g6mtw_processed.png&w=3840&q=75)
Transcribed Image Text:Question 4
Skyline pizza is a famous restaurant operating a number of outlets. The restaurant uses a toll-free telephone
number to book pizzas at any of its outlets. If the clerk is occupied on one line, incoming phone calls
to the restaurant 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 15 per hour. The clerk is capable of taking an order in an average of 3
minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The
clerk is paid $20 per hour, but because of lost goodwill and sales, CWD loses about $50 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)?
b. What is the average number of customers waiting for service ( Lq,
c. What is the average number of customers in the system (L)?
d. What is the average time a customer waits for service(Wq):
e. What is the average time in the system (W)
f. What is the probability that a customer will have to wait for service (Pw\?
g What is the probability that there is exactly 2 customers in the system-
h) What is the probability that there are more than 3 customers in the system
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