A snack stand with one seller is set in a university campus. Customers arrive at the snack stand at an average of one every 5 minutes following Poisson distribution. The service of the seller for each customer can be described by an exponential distribution with a mean of 4 minutes. Q2.1 How long is the average waiting time in queue? Q2.2 What is the probability that there are at least four customers in the system? Q2.3 If the waiting cost for each customer is $200/h and the cost for each seller is $240/h, is it necessary to hire more sellers? If yes, how many new sellers should be hired? Q2.4 If one snack selling machine is set to replace the snack stand, the service time for each customer is constant (2 minute). What is the average time a customer spends in the system after the machine is used?
A snack stand with one seller is set in a university campus. Customers arrive at the snack stand at an average of one every 5 minutes following Poisson distribution. The service of the seller for each customer can be described by an exponential distribution with a mean of 4 minutes. Q2.1 How long is the average waiting time in queue? Q2.2 What is the probability that there are at least four customers in the system? Q2.3 If the waiting cost for each customer is $200/h and the cost for each seller is $240/h, is it necessary to hire more sellers? If yes, how many new sellers should be hired? Q2.4 If one snack selling machine is set to replace the snack stand, the service time for each customer is constant (2 minute). What is the average time a customer spends in the system after the machine is used?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 9P
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Marketing
Marketing
ISBN:
9780357033791
Author:
Pride, William M
Publisher:
South Western Educational Publishing
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Marketing
Marketing
ISBN:
9780357033791
Author:
Pride, William M
Publisher:
South Western Educational Publishing