The average service time of the drive-in teller and the inside-bank teller?











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A bank has one drive-in teller (who can serve customers without leaving their
cars). The drive-in teller has a room (i.e., a queue) for one additional customer to
wait. Customers arriving when the drive-in teller queue is full will park their cars
and go inside the bank to transact business. Inside the bank, the waiting area is
sufficient to accommodate all customers, and there is one teller who is as
efficient as the drive-in teller in terms of serving the customers. The time enter image description herebetween-
arrivals and service-time distributions are given below.



The problem is to estimate the system measures of performance in terms of the
following:
1- The average service time of the drive-in teller and the inside-bank teller.
2- The average waiting time in the drive-in teller queue and the inside-bank
teller queue.
3- The maximum inside-bank teller queue length.
4- The probability that a customer wait in the inside-bank teller queue.
5- The portion of idle time of the inside-bank teller.
Moreover, the policy maker requires answers for the following questions:
6- Does the theoretical average service time of the service time distribution
match with the experimental one?
7- Does the theoretical average inter-arrival time of the inter-arrival time
distribution match with the experimental one?
8- If the drive-in teller queue can accommodate for two cars instead of one
car, how does this affect the average waiting time in the drive-in teller
queue and the inside-bank teller queue?










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A bank has one drive-in teller (who can serve customers without leaving their
cars). The drive-in teller has a room (i.e., a queue) for one additional customer to
wait. Customers arriving when the drive-in teller queue is full will park their cars
and go inside the bank to transact business. Inside the bank, the waiting area is
sufficient to accommodate all customers, and there is one teller who is as
efficient as the drive-in teller in terms of serving the customers. The time enter image description herebetween-
arrivals and service-time distributions are given below.



The problem is to estimate the system measures of performance in terms of the
following:
1- The average service time of the drive-in teller and the inside-bank teller.
2- The average waiting time in the drive-in teller queue and the inside-bank
teller queue.
3- The maximum inside-bank teller queue length.
4- The probability that a customer wait in the inside-bank teller queue.
5- The portion of idle time of the inside-bank teller.
Moreover, the policy maker requires answers for the following questions:
6- Does the theoretical average service time of the service time distribution
match with the experimental one?
7- Does the theoretical average inter-arrival time of the inter-arrival time
distribution match with the experimental one?
8- If the drive-in teller queue can accommodate for two cars instead of one
car, how does this affect the average waiting time in the drive-in teller
queue and the inside-bank teller queue?










share|cite|improve this question







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Optimus Artifex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • Hi and welcome to the Math.SE. In order to help other users help you, please provide context for your question: why it is interesting for you? What dit you tried to solve it?
    – Daniele Tampieri
    Nov 15 at 5:42













up vote
0
down vote

favorite









up vote
0
down vote

favorite











A bank has one drive-in teller (who can serve customers without leaving their
cars). The drive-in teller has a room (i.e., a queue) for one additional customer to
wait. Customers arriving when the drive-in teller queue is full will park their cars
and go inside the bank to transact business. Inside the bank, the waiting area is
sufficient to accommodate all customers, and there is one teller who is as
efficient as the drive-in teller in terms of serving the customers. The time enter image description herebetween-
arrivals and service-time distributions are given below.



The problem is to estimate the system measures of performance in terms of the
following:
1- The average service time of the drive-in teller and the inside-bank teller.
2- The average waiting time in the drive-in teller queue and the inside-bank
teller queue.
3- The maximum inside-bank teller queue length.
4- The probability that a customer wait in the inside-bank teller queue.
5- The portion of idle time of the inside-bank teller.
Moreover, the policy maker requires answers for the following questions:
6- Does the theoretical average service time of the service time distribution
match with the experimental one?
7- Does the theoretical average inter-arrival time of the inter-arrival time
distribution match with the experimental one?
8- If the drive-in teller queue can accommodate for two cars instead of one
car, how does this affect the average waiting time in the drive-in teller
queue and the inside-bank teller queue?










share|cite|improve this question







New contributor




Optimus Artifex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











A bank has one drive-in teller (who can serve customers without leaving their
cars). The drive-in teller has a room (i.e., a queue) for one additional customer to
wait. Customers arriving when the drive-in teller queue is full will park their cars
and go inside the bank to transact business. Inside the bank, the waiting area is
sufficient to accommodate all customers, and there is one teller who is as
efficient as the drive-in teller in terms of serving the customers. The time enter image description herebetween-
arrivals and service-time distributions are given below.



The problem is to estimate the system measures of performance in terms of the
following:
1- The average service time of the drive-in teller and the inside-bank teller.
2- The average waiting time in the drive-in teller queue and the inside-bank
teller queue.
3- The maximum inside-bank teller queue length.
4- The probability that a customer wait in the inside-bank teller queue.
5- The portion of idle time of the inside-bank teller.
Moreover, the policy maker requires answers for the following questions:
6- Does the theoretical average service time of the service time distribution
match with the experimental one?
7- Does the theoretical average inter-arrival time of the inter-arrival time
distribution match with the experimental one?
8- If the drive-in teller queue can accommodate for two cars instead of one
car, how does this affect the average waiting time in the drive-in teller
queue and the inside-bank teller queue?







queueing-theory simulation






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Optimus Artifex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question







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Optimus Artifex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









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asked Nov 15 at 5:35









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New contributor





Optimus Artifex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Optimus Artifex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • Hi and welcome to the Math.SE. In order to help other users help you, please provide context for your question: why it is interesting for you? What dit you tried to solve it?
    – Daniele Tampieri
    Nov 15 at 5:42


















  • Hi and welcome to the Math.SE. In order to help other users help you, please provide context for your question: why it is interesting for you? What dit you tried to solve it?
    – Daniele Tampieri
    Nov 15 at 5:42
















Hi and welcome to the Math.SE. In order to help other users help you, please provide context for your question: why it is interesting for you? What dit you tried to solve it?
– Daniele Tampieri
Nov 15 at 5:42




Hi and welcome to the Math.SE. In order to help other users help you, please provide context for your question: why it is interesting for you? What dit you tried to solve it?
– Daniele Tampieri
Nov 15 at 5:42















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