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QUEUING SIMULATION 517

Table 12.11 Simulation Results for Ten Customers for a Two-ATM System
Time
Available
Service
Interarrival Arrival Start Waiting Service Completion Time in ATM ATM
Customer Time Time Time Time Time System System 1 2
1 1.7 1.7 1.7 0.0 2.1 3.8 2.1 3.8 0.0
2 0.7 2.4 2.4 0.0 2.0 4.4 2.0 3.8 4.4
3 2.0 4.4 4.4 0.0 1.4 5.8 1.4 5.8 4.4
4 0.1 4.5 4.5 0.0 0.9 5.4 0.9 5.8 5.4
5 4.6 9.1 9.1 0.0 2.2 11.3 2.2 5.8 11.3
6 1.3 10.4 10.4 0.0 1.6 12.0 1.6 12.0 11.3
7 0.6 11.0 11.3 0.3 1.7 12.0 2.0 12.0 12.0
8 0.3 11.3 12.0 0.7 2.2 14.2 2.9 14.2 12.0
9 3.4 14.7 14.7 0.0 2.9 17.6 2.9 14.2 17.6
10 0.1 14.8 14.8 0.0 2.8 17.6 2.8 17.6 17.6
Totals 14.8 1.0 19.8 20.8
Averages 1.48 0.1 1.98 2.08

Table 12.11 shows that customer 7 is the first customer who has to wait to use an
ATM. We describe how customers 6, 7 and 8 are processed to show how the logic of
the simulation run for two ATMs differs from that with a single ATM.

Customer 6
l An interarrival time of 1.3 minutes is generated, and customer 6 arrives
9.1 þ 1.3 ¼ 10.4 minutes into the simulation.
l From the customer 5 row, we see that ATM 1 frees up at 5.8 minutes, and
ATM 2 will free up at 11.3 minutes into the simulation. Because ATM 1 is free,
customer 6 does not wait and begins service on ATM 1 at the arrival time of
10.4 minutes.
l A service time of 1.6 minutes is generated for customer 6. So customer 6 has a
completion time of 10.4 þ 1.6 ¼ 12.0 minutes.
l The time ATM 1 will next become available is set at 12.0 minutes; the time
available for ATM 2 remains 11.3 minutes.

Customer 7
l An interarrival time of 0.6 minute is generated, and customer 7 arrives
10.4 þ 0.6 ¼ 11.0 minutes into the simulation.
l From the previous row, we see that ATM 1 will not be available until 12.0
minutes, and ATM 2 will not be available until 11.3 minutes. So customer 7
must wait to use an ATM. Because ATM 2 will free up first, customer 7 begins
service on that machine at a start time of 11.3 minutes. With an arrival time of
11.0 and a service start time of 11.3, customer 7 experiences a waiting time of
11.3 11.0 ¼ 0.3 minute.
l A service time of 1.7 minutes is generated leading to a completion time of
11.3 þ 1.7 ¼ 12.0 minutes.
l The time available for ATM 2 is updated to 12.0 minutes, and the time
available for ATM 1 remains at 12.0 minutes.

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