Question 4 A petrol station in the capital Kingstown has a single pump manned by one attendant. Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an average. Assume the arrival rate is Poisson probability distribution and service rate is exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and sales, station loses about $15 per hour of customer time spent waiting for the attendant to service and order. Part A Answer the following questions based on single channel model: 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)?❤❤ s f. What is the probability that a customer will have to wait for service (Pw)?-S g What is the probability that there is exactly 2 customers in the system-s h) What is the probability that there are more than 3 customers in the system- Part B The Petrol station is considering adding a second pump with an attendant to service customers. The station 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)? 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)2 g. What is the probability that there is exactly 2 customers in the system h. Should it hire another clerk? Explain by showing the cost savings

Understanding Business
12th Edition
ISBN:9781259929434
Author:William Nickels
Publisher:William Nickels
Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
Section: Chapter Questions
Problem 1CE
icon
Related questions
Question
Question 4
A petrol station in the capital Kingstown has a single pump manned by one attendant.
Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an
average. Assume the arrival rate is Poisson probability distribution and service rate is
exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times
tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and
sales, station loses about $15 per hour of customer time spent waiting for the attendant to
service and order.
Part A
Answer the following questions based on single channel model:
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)?❤❤
s
f. What is the probability that a customer will have to wait for service (Pw)?-S
g What is the probability that there is exactly 2 customers in the system-s
h) What is the probability that there are more than 3 customers in the system-
Part B
The Petrol station is considering adding a second pump with an attendant to service
customers. The station 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)?
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)2
g. What is the probability that there is exactly 2 customers in the system
h. Should it hire another clerk? Explain by showing the cost savings
Transcribed Image Text:Question 4 A petrol station in the capital Kingstown has a single pump manned by one attendant. Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an average. Assume the arrival rate is Poisson probability distribution and service rate is exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and sales, station loses about $15 per hour of customer time spent waiting for the attendant to service and order. Part A Answer the following questions based on single channel model: 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)?❤❤ s f. What is the probability that a customer will have to wait for service (Pw)?-S g What is the probability that there is exactly 2 customers in the system-s h) What is the probability that there are more than 3 customers in the system- Part B The Petrol station is considering adding a second pump with an attendant to service customers. The station 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)? 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)2 g. What is the probability that there is exactly 2 customers in the system h. Should it hire another clerk? Explain by showing the cost savings
AI-Generated Solution
AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.
steps

Unlock instant AI solutions

Tap the button
to generate a solution

Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Understanding Business
Understanding Business
Management
ISBN:
9781259929434
Author:
William Nickels
Publisher:
McGraw-Hill Education
Management (14th Edition)
Management (14th Edition)
Management
ISBN:
9780134527604
Author:
Stephen P. Robbins, Mary A. Coulter
Publisher:
PEARSON
Spreadsheet Modeling & Decision Analysis: A Pract…
Spreadsheet Modeling & Decision Analysis: A Pract…
Management
ISBN:
9781305947412
Author:
Cliff Ragsdale
Publisher:
Cengage Learning
Management Information Systems: Managing The Digi…
Management Information Systems: Managing The Digi…
Management
ISBN:
9780135191798
Author:
Kenneth C. Laudon, Jane P. Laudon
Publisher:
PEARSON
Business Essentials (12th Edition) (What's New in…
Business Essentials (12th Edition) (What's New in…
Management
ISBN:
9780134728391
Author:
Ronald J. Ebert, Ricky W. Griffin
Publisher:
PEARSON
Fundamentals of Management (10th Edition)
Fundamentals of Management (10th Edition)
Management
ISBN:
9780134237473
Author:
Stephen P. Robbins, Mary A. Coulter, David A. De Cenzo
Publisher:
PEARSON