8/20/2019 Bank Teller Problem
1/16
i)
This problem deals with calculating average wait time for
customers in order to determine
whether or not to hire a second teller. However, in order to do
so, you must write a program to
approximate the average wait time of customers for n tellers. To
implement this, each customer
is considered to have an Arrival Event and a Departure Event.
Each Arrival Event holds the
incoming customers arrival time to the ban!, and the length of
his or her transaction. EachDeparture Event holds the departure
time of the specified customer "when the customer is
finished with his or her transaction and the teller he or she
was using is now available). #f the
customer is first in the ban! line, or the ban! line is empty,
the customers Arrival Event is
deleted and the customer is processed, and a Departure Event is
created. #f the ban! line is not
empty, the customer is put in the bac! of the ban! line. This
allows for the total wait time of each
customer to be calculated, as $ustomer %s wait time will be the
departure time of $ustomer A
minus the arrival time of the $ustomer % "assuming $ustomer A is
in front of $ustomer %). After
finding each customers wait time, the individual wait times are
summed up, and then divided by
the total amount of customers to find the average wait time of
each customer.
&se $ase
&ser'(resident of %an! wants to determine whether or not to
hire more tellers. &ser runs
simulation for certain data set containing arrival times and
transaction length of any number of
customers in order to determine average wait time for those
customers based on the given data.
imulation re*uests user to input number of tellers available.
&ser inputs number of tellers
available. imulation determines wait time for each individual
customer, and pushes each wait
time into a vector. &ser finds average wait time by summing
up each individual wait time in
vector and dividing by the total number of customers. &ser
compares the average wait time with
his or her standard for whether or not to hire more tellers. #f
the average wait time meets
standard to hire more tellers, more tellers are hired.
+therwise, user does nothing or runs
simulation again with a different data set.
ii)
ee scanned pdf in folder labeled (roblem , or loo! at hard copy
attached.
iii)
ee .cpp file in folder labeled (roblem -. To run this code,
simply compile it how you would
normally run a $ program. # attached a test.txt file that has a
uniform distribution of arrival
times and a transaction time of / "used in problem 0), but if
you want to test it on your own text
file, rename the file test.txt and run the program. 1+TE2 the
program will have the user input the
number of tellers.
iv)
/ Teller2 00.33 minutes or 45- seconds
Tellers2 /6.4 minutes or //54 seconds
/7 Tellers2 7 minutes or 7 seconds "ma!es sense since /7
customers arrive each minute)
%elow are screenshots of the result for / Teller, Tellers, and
/7 Tellers, respectively.
8/20/2019 Bank Teller Problem
5/16
"reference2 wi!ipedia.com)
# use lambda 8 7./, because the expected values of incoming
customers based on the uniform
distribution from problem - is 7./, since customers come every
7./ minutes, and lambda e*uals
Expected 9alue for (oisson Distribution.
An Exponential distribution is given by the e*uation2
"reference2 wi!ipedia.com)
# use lambda 8 /, because the expected values of incoming
customers based on the uniform
distribution from problem - is 7./, since customers come every
7./ minutes, and lambda e*uals
/'Expected 9alue for Exponential Distribution.
::::1+TE2 ince problem - has every person coming at every 7./
minutes, rather than /77
people coming at 7./ minutes, # calculated the arrival time of
customer i as y 8 y (oisson
Distribution of i, where y is initially 7, and i is from 7 to
66.
As one can clearly see, both of these distributions
converge to ;ero. Thus, eventually, the
incoming customers will begin to come at the exact same time.
This occurs at / minute.
![Problem Bank 200(All)[1]](https://img.pdfslide.us/doc/110x75/55cf9e08550346d033b05fa4/problem-bank-200all1.jpg)
