You are planning the new layout for the local branch of the Sixth Ninth Bank. You are considering separate cashier windows Page 292 for the three different classes of service. Each class of service would be separate, with its own cashiers and customers. Oddly enough, each class of service, while different, has exactly the same demand and service times. People for one class of service arrive every four minutes and arrival times are exponentially distributed (the standard deviation is equal to the mean). It takes seven minutes to service each customer, and the standard deviation of the service times is three minutes. You assign two cashiers to each type of service. a. On average, how long will each line be at each of the cashier windows? b. On average, how long will a customer spend in the bank (assume they enter, go directly to one line, and leave as soon as service is complete)? You decide to consolidate all the cashiers so they can handle all types of customers without increasing the service times. c. What will happen to the amount of time each cashier spends idle? (increase, decrease, stay the same, depend on d. What will happen to the average amount of time a customer spends in the bank? (increase, decrease, stay the same, depend on
You are planning the new layout for the local branch of the Sixth Ninth Bank. You are considering separate cashier windows Page 292 for the three different classes of service. Each class of service would be separate, with its own cashiers and customers. Oddly enough, each class of service, while different, has exactly the same demand and service times. People for one class of service arrive every four minutes and arrival times are exponentially distributed (the standard deviation is equal to the mean). It takes seven minutes to service each customer, and the standard deviation of the service times is three minutes. You assign two cashiers to each type of service. a. On average, how long will each line be at each of the cashier windows? b. On average, how long will a customer spend in the bank (assume they enter, go directly to one line, and leave as soon as service is complete)? You decide to consolidate all the cashiers so they can handle all types of customers without increasing the service times. c. What will happen to the amount of time each cashier spends idle? (increase, decrease, stay the same, depend on d. What will happen to the average amount of time a customer spends in the bank? (increase, decrease, stay the same, depend on
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
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Question
I need assitance with solving Chapter 10 Question 23. I made numerous attempts to solve. however I am still having issues. Please provide a step by step explanation so, I can use it as notes for future reference. Respectfully thank you.
Transcribed Image Text:23. You are planning the new layout for the local branch of the Sixth Ninth Bank. You are considering separate cashier windows Page 292
for the three different classes of service. Each class of service would be separate, with its own cashiers and customers. Oddly
enough, each class of service, while different, has exactly the same demand and service times. People for one class of service arrive
every four minutes and arrival times are exponentially distributed (the standard deviation is equal to the mean). It takes seven minutes
to service each customer, and the standard deviation of the service times is three minutes. You assign two cashiers to each type of
service.
a. On average, how long will each line be at each of the cashier windows?
b. On average, how long will a customer spend in the bank (assume they enter, go directly to one line, and leave as soon as service is
complete)?
You decide to consolidate all the cashiers so they can handle all types of customers without increasing the service times.
c. What will happen to the amount of time each cashier spends idle? (increase, decrease, stay the same, depend on
d. What will happen to the average amount of time a customer spends in the bank? (increase, decrease, stay the same, depend on
Transcribed Image Text:Hint: for question 23 of chapter 10, we should consider using the waiting line approximation method because the service times do not follow an
exponential distribution.
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