Monte Carlo Simulation - An Example Simulation Problem

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A small garage only has one self-service petrol pump. As a consequence, cars arriving at the garage frequently have to queue. Due to customer complaints the owner of the garage decides to investigate the characteristics of the queue in terms of average queue length and the average time customers have to wait. This problem lends itself to simulation as long as there is necessary survey data to hand. For example: the owner should be able to obtain probability distributions on car arrivals and the time taken for customers to fill their cars. Two sample tables are given below in Table 15 & 16:

In order to simulate the real situation, it is necessary to allocate one digit numbers (lying between 0 and 9) to the above tables according to the probabilities. This is shown below in Tables 17 and 18 in what are known as look-up tables:

The simulation model is conceived as a sequence of events. Inserting a column for the selection of a random number where uncertain events prevail.

To carry out the simulation, it is necessary to employ a table of random numbers to represent car arrivals and the time taken to fill a car with petrol. A row of ten random numbers, taken from a table of random numbers.

These numbers have been produced in such a way that there is no systematic relationship among them.

Random numbers: 2, 6, 1, 8, 6, 9, 4, 4, 9, 0.

A simulation is carried out covering the arrival of the first five cars, assuming that the garage opens at 9.30am.

Table 19 below shows the simulation results:

Notice that the random numbers have just been taken in sequence to simulate inter-arrival times and service (petrol-filling) times.

A normal simulation is for many hundreds of transactions in order that the probability of inter-arrival times and service times is fully revealed in the data.

This small example, however, does show how operating statistics can be gathered. It shows that the average number of cars waiting in the queue is 1, for all cars that have to queue.

If we include the first car which did not queue the average number queuing is 0.8.

The average time spent in the queue for a car is 1.75 mins, for those cars that did queue. For all cars, including the first, the average time in the queue is 1.4 mins.

This model could be elaborated to include cars leaving the garage because the queue is too long.

The model could also be altered to include two self-service pumps in order to see the effect this has on avenge queue size and waiting times.

These different models would be viewed against the background of the various costs and benefits involved in their configuration.

Thus, a choice could be made on the best system to be employed by the garage in order to maximise the net benefits.

The simulation model above is a general model for all simple single-server queuing systems. Though the values in the look-up tables may change, the general format of the model remains the same.

Thus the Simulation Model could reside in the model-base of a DSS.

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Reference(s)
	Book		Anderson, D. R., Sweeney, D. & Williams, T. (2002) An Introduction to Management Science: A Quantitative Approach to Decision Making. 10th Edition. South-Western College Publishing: United States of America (USA), California (CA), San Diego. [ISBN: 9780324145632]. [Available on: Amazon: https://amzn.to/3DrQjUY].
	Book		Campbell, D. J. & Craig, T. (2005) Organisations and the Business Environment. 2nd Edition. Elsevier: Netherlands, North Holland, Amsterdam. [ISBN: 9780750658294]. [Available on: Amazon: https://amzn.to/3VHJupz].
	Book		Pfaffenberger, B. (2002) Computers in Your Future 2003. 5th Edition. Prentice Hall: United States of America (USA), New Jersey (NJ), Bergen, Upper Saddle River. [ISBN: 9780139227820]. [Available on: Amazon: https://amzn.to/3gv8n7D].
	Book		Thesen, A. & Travis, L. (1992) Simulation for Decision Making. Thomson Reuters - West: United States of America (USA), Minnesota (MN), Dakota, Eagan. [ISBN: 9780314835499]. [Available on: Amazon: https://amzn.to/3Sqcv6g].

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Reference (or cite) Article
	Kahlon, R. S. (2013) Monte Carlo Simulation: An Example Simulation Problem [Online]. dkode: United Kingdom, England, London. [Published on: 2013-02-07]. [Article ID: RSK666-0000100]. [Available on: dkode | Ravi - https://ravi.dkode.co/2013/02/monte-carlo-simulation-example.html].

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