In this section, we provide examples of how simulation models can be used for Queuing System.
People arrive at the New Delhi Railway station to buy tickets according to the following distribution.
|Inter-arrival Time (Min.)||Frequency|
The service time is 5 minutes and there is only one ticket counter. The Railway station incharge is interested in predicting the operating characteristics of this counter during a typical operating day from 10.00 a.m. to 11.00 a.m. Use simulation to determine the average waiting time before service and average time a person spends in the system.
From the given distribution of arrivals, the random numbers can be assigned to the arrival times as shown in table 1.
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|2||10||0.10||0.10||0 - 09|
|3||20||0.20||0.30||10 - 29|
|4||40||0.40||0.70||30 - 69|
|5||20||0.20||0.90||70 - 89|
|6||10||0.10||1.00||90 - 99|
The first random number generated is 17, which corresponds to the inter-arrival time of 3 minutes. This implies that the first person arrives 3 minutes after the service window opens, as shown in table 2. Since the first person arrives at 10.03 a.m., therefore, the server has to wait for 3 minutes. The server takes 5 minutes and thus, the first person leaves the system at 10.08 a.m. (10.03 + .05). Similarly, other values can be calculated.
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Average waiting time before service.
= Total waiting time (person)/Total no. of arrivals
= 39/12 = 3.25 minutes.
Average time a person spends in the system.
= Service time + Average waiting time before service
= 5 + 3.25 = 8.25 minutes.