Note: Spread sheet is pasted at bottom, If you need attchment file,
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Question:Consider the operation of a bank that has a separate waiting
line in front of each teller?s window. In this situation each window
can be considered a Single Queue Single Server System. Suppose that
both interarrival and service times are exponentially distributed.
a)Create a spreadsheet to simulate the operation of the bank teller
for 25 customers (a Single Queue Single Server system). Assume that
the mean values of the interarrival and service times are 4 and 3
minutes, respectively. Choose the seed values Z1
equal to the last digit of your College ID #, (if it is
zero, then select Z1=6) and Z2
equal to the last three digits of your College ID #.
It will display the following information:
Stream 1 Random Number Interarrival Time Stream 2 Random Number
Service Time Customer Number Arrival Time Idle Time for Teller Begin
Service Time Service Time Departure Time Time in Queue Time in System
i Z1i U1i X1i Z2i U2i X2i
and
the average waiting time for a customer=(total time customers wait in
queue)/(total number of customers)
the probability that a customer has to wait in the queue=
=(# of customers who wait)/(total
number of customers)
the probability that server is idle=
=(total idle time of server)/(total run time of simulation)
Note that total run time of simulation=departure time of last customer
the average service time =(total service time)/(total number of customers)
the average waiting time of those who wait=(total time customers wait
in queue)/(total number of customers who wait)
the average time that a customer spends in the bank=
=total time customers spend in the bank)/ ( total number of customers)
the average time between arrivals(interarrival time)=
=(sum of all times between arrivals)/(# of arrivals-1)
Note that sum of all times between arrivals= arrival time of last customer
and # of arrivals= total number of customers.
b)Investigate the effect of the interarrival and service times on the
bank teller system by repeating the part (a) for different
interarrival and service times. Create a summary table and make
comments on the findings.
c)Repeat the simulation of the operation of the bank teller for 10
times by changing the seed values and . Calculate the average of
the average of Idle Time for Teller,
the average Time in Queue and
the average Time in System.
Create a summary table and make comments on the findings.
Spread sheet:
Stream 1 Random Number Interarrival Time Stream 2 Random
Number Service Time Customer Number Arrival Time Idle Time for
Teller Begin Service Time Service Time Departure Time Time in
Queue Time in System
i Z1i U1i X1i Z2i U2i X2i 1 2 3 4 5 6=4+5 7=4-2 8=6-2
0 3 122
1 66 0.516 2.17 5 0.039 0.10 1 2.17 2.17 2.17 0.10 2.27 0.00 0.10
2 109 0.852 5.72 108 0.844 4.46 2 7.90 5.63 7.90 4.46 12.35 0.00 4.46
3 116 0.906 7.10 95 0.742 3.25 3 15.00 2.65 15.00 3.25 18.25 0.00 3.25
4 7 0.055 0.17 78 0.609 2.26 4 15.17 0.00 18.25 2.26 20.51 3.08 5.34
5 22 0.172 0.57 105 0.820 4.12 5 15.73 0.00 20.51 4.12 24.63 4.77 8.89
6 81 0.633 3.01 32 0.250 0.69 6 18.74 0.00 24.63 0.69 25.32 5.89 6.58
7 40 0.313 1.12 35 0.273 0.77 7 19.86 0.00 25.32 0.77 26.08 5.46 6.22
8 75 0.586 2.65 98 0.766 3.48 8 22.51 0.00 26.08 3.48 29.57 3.58 7.06
9 42 0.328 1.19 13 0.102 0.26 9 23.70 0.00 29.57 0.26 29.82 5.87 6.12
10 117 0.914 7.36 20 0.156 0.41 10 31.06 1.24 31.06 0.41 31.47 0.00 0.41
11 28 0.219 0.74 39 0.305 0.87 11 31.80 0.33 31.80 0.87 32.68 0.00 0.87
12 79 0.617 2.88 54 0.422 1.32 12 34.68 2.01 34.68 1.32 36.00 0.00 1.32
13 126 0.984 12.48 113 0.883 5.15 13 47.16 11.16 47.16 5.15 52.31 0.00 5.15
14 89 0.695 3.57 72 0.563 1.98 14 50.73 0.00 52.31 1.98 54.29 1.58 3.56
15 80 0.625 2.94 107 0.836 4.34 15 53.67 0.00 54.29 4.34 58.63 0.62 4.96
16 19 0.148 0.48 74 0.578 2.07 16 54.15 0.00 58.63 2.07 60.70 4.48 6.55
17 18 0.141 0.45 21 0.164 0.43 17 54.61 0.00 60.70 0.43 61.13 6.09 6.52
18 125 0.977 11.26 60 0.469 1.52 18 65.87 4.74 65.87 1.52 67.38 0.00 1.52
19 68 0.531 2.27 111 0.867 4.85 19 68.14 0.76 68.14 4.85 72.98 0.00 4.85
20 23 0.180 0.59 30 0.234 0.64 20 68.73 0.00 72.98 0.64 73.63 4.25 4.89
21 102 0.797 4.78 121 0.945 6.97 21 73.52 0.00 73.63 6.97 80.60 0.11 7.08
22 97 0.758 4.25 112 0.875 4.99 22 77.77 0.00 80.60 4.99 85.59 2.83 7.82
23 120 0.938 8.32 51 0.398 1.22 23 86.09 0.50 86.09 1.22 87.31 0.00 1.22
24 91 0.711 3.72 50 0.391 1.19 24 89.81 2.50 89.81 1.19 91.00 0.00 1.19
25 122 0.953 9.18 29 0.227 0.62 25 98.99 7.99 98.99 0.62 99.61 0.00 0.62
Average 1.67 1.94 4.26 |
