Note: Formulas to solve the following problems are given in the class and example problems were solved in the class. Follow the examples described in the class and read the literature posted on blackboard. 1. Huntsville Bank (a fictitious one) has a drive-through teller window and observed that customers arrive for service one every three minute, on an average, and the average service time per customer is 2.4 minutes. Assume inter-arrival time and service time follow a negative Exponential distribution. The bank hires you as a consultant. You guess that this is an M|M|1 system and you are required to determine the following: a. Probability (teller is busy) b. Probability (teller is idle) c. Average number of customers waiting for service, that is, number of autos in the line excluding the one at the teller window. d. Average number of customers in the system, that is, number of autos in the line including the one at the teller window. e. Average time a customer spends in the waiting line before reaching the teller window. f. Average time a customer spends in the system, that is, waiting time plus service time. g. The bank manager realized that too many autos are in the line for service and there have been complaints recently. In view of your knowledge of queuing analysis, you would advise as a consultant to open another teller window so that the arrival rate is shared by two windows and of course, autos will be in two lines. Now having two teller windows installed, determine again (a) to (f) above.
Note: Formulas to solve the following problems are given in the class and example problems were solved in the class. Follow the examples described in the class and read the literature posted on blackboard. 1. Huntsville Bank (a fictitious one) has a drive-through teller window and observed that customers arrive for service one every three minute, on an average, and the average service time per customer is 2.4 minutes. Assume inter-arrival time and service time follow a negative Exponential distribution. The bank hires you as a consultant. You guess that this is an M|M|1 system and you are required to determine the following: a. Probability (teller is busy) b. Probability (teller is idle) c. Average number of customers waiting for service, that is, number of autos in the line excluding the one at the teller window. d. Average number of customers in the system, that is, number of autos in the line including the one at the teller window. e. Average time a customer spends in the waiting line before reaching the teller window. f. Average time a customer spends in the system, that is, waiting time plus service time. g. The bank manager realized that too many autos are in the line for service and there have been complaints recently. In view of your knowledge of queuing analysis, you would advise as a consultant to open another teller window so that the arrival rate is shared by two windows and of course, autos will be in two lines. Now having two teller windows installed, determine again (a) to (f) above.
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...
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Transcribed Image Text:Note: Formulas to solve the following problems are given in the
class and example problems were solved in the class. Follow the
examples described in the class and read the literature posted on
blackboard.
1. Huntsville Bank (a fictitious one) has a drive-through teller
window and observed that customers arrive for service one
every three minute, on an average, and the average service
time per customer is 2.4 minutes. Assume inter-arrival time
and service time follow a negative Exponential distribution.
The bank hires you as a consultant. You guess that this is an
M|M|1 system and you are required to determine the
following:
a. Probability (teller is busy)
b. Probability (teller is idle)
c. Average number of customers waiting for service, that is,
number of autos in the line excluding the one at the teller
window.
d. Average number of customers in the system, that is,
number of autos in the line including the one at the teller
window.
e. Average time a customer spends in the waiting line before
reaching the teller window.
f. Average time a customer spends in the system, that is,
waiting time plus service time.
g. The bank manager realized that too many autos are in the
line for service and there have been complaints recently. In
view of your knowledge of queuing analysis, you would
advise as a consultant to open another teller window so that
the arrival rate is shared by two windows and of course,
autos will be in two lines. Now having two teller windows
installed, determine again (a) to (f) above.
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