Page 106 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling

Notes arriving customers are distributed to the n channels. Therefore, the arrival rate to each channel
is scaled down by a factor of n. As for converting a multiple channels queue to a single-channel
queue, the arrival rate is multiplied by n due to the merging effect. The service rate remains
unchanged for the conversions.

Tasks Analyze different examples for arrival and departure.

Results

Tables 7.3 and 7.4 show the simulation results. As observed in both tables, the server utilization
remains fairly constant as the total workload does not changed. As for converting from a multiple-
channels queue to a single-channel queue, Table 7.3 shows that the queue length is reduced by
48%. More significantly, the wait probability is reduced from 0.68 to 0.35, and the average queue
time is reduced from 106 seconds to 11 seconds. This implies that the probability that a customer
coming to the McDonalds will have to wait for service is significantly reduced by half, and even
if the customer is not immediately served the waiting time is reduced by 9 folds.
As such, the change from a multiple-channels queue to single-channel will make a substantial
improvement in the queuing performance.

Table 7.3: Comparison of Queuing Performance for McDonalds

Queue Type Average Queue Ave. Queue Wait Server
Length Time (sec) Probability Utilization
Multiple-channels 1.52 106.36 0.68 0.69
(existing)
Single-channel 0.78 10.86 0.35 0.68

On the other hand, Table 7.4 shows that the average queue length, average queue time and the
wait probability all become worse if the POSB is to convert its single channel queue to multiple-
channels.

Table 7.4: Comparison of Queuing Performance for POSB

Queue Type Average Queue Ave. Queue Wait Server
Length Time (sec) Probability Utilization

Single-channels 4.25 127.34 0.68 0.86
(existing)
Multiple-channels 5.91 883.63 0.87 0.84

7.2 Rudiments of Queuing Theory

As you know that a queue is a waiting for service. In general form of model of a queue, you
assume that customers arrive randomly. There is only one service counter, which can serve only
one customer at a time. The amount of time it takes to serve a customer also varies randomly. If
the service counter is busy, arriving customers join the queue. From the queue the customers are
served on a FCFS means first-come-first-served basis. As soon as a customer is served he gets out
of the system like first-in-first-out system.

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