Monte Carlo Simulation - The Bus Delays

Monte Carlo Simulation is a very powerful way to forecast and predict situations. It works on a collection of historical data. Various data points are collected and the probability of an event is calculated. KPI's are then formed to determine future outcomes and take predictive measures.



For example, Simulations can be used at an airport to improve efficiency. The time a customer waits in a queue can be recorded and then the time taken to check his handbag/passport can be noted down. After a representative sample is collected, probabilities are assigned to all possible outcomes. Now a simulation can be run and a customers' average wait time can be calculated. It can also be determined to a great accuracy how many customers have to wait for how long. Thus remedial actions can be taken to counter the problems if any. For example, more checking counters can be added in the simulation to measure its impact on the waiting time.





Airlines use simulations to see how many check-in counters are required for different time periods. You must have observed at different airports, all the check-in counters are hardly ever operated. Customers would love to have all the counters operated but it incurs cost. Thus, simulations help airlines to predict the flow of customers, expected waiting times and thus manage the check-in counters at different times. The same principle is also applied in various other scenarios like managing aircraft landings, aircraft re-fueling etc.

Monte Carlo Simulations can be applied in almost any field be it waste management, airlines, banks, sports, ship servicing, predicting sales in a bakery etc.

A real example: 

We, MBA students at SP Jain, go to our college from hostel in a college bus. The bus usually takes 15 minutes to reach the college. It has a scheduled start time of 9:15 am, the classes start at 10:00 am. However, almost daily the students delay the bus and in the way we find a traffic jam (on a particular signal which connects to the highway). Thus we usually take 20-25 mins to reach college.
I collected around 30 data points capturing the bus start delay and the duration of traffic jam. The following screenshot shows the probabilities of the delays. The delays range from 3 mins to 10 mins.



The following table shows the delay at the traffic signal. The delay is usually between 2-7 mins.



After running out the simulation for 300 cases, the total average delay comes out to be 10.7 minutes. Moreover, most of the delays are between 10-11 minutes. The average delay for the bus is 6.2 minutes and the average delay at the traffic signal is 4.5 minutes. The following graph shows the % age of times for delays from 5-15 minutes.


X-axis shows the total delay in minutes and Y-axis shows the percentage of times the delay is likely to happen. For example, as per the graph, on a particular day there is a 20% probability that the total delay will be 10 minutes.

The graph is almost normal in shape, average is 10.7 and the median is 11. The curve is slightly skewed towards the left. The exact delay can help travel desk to plan its further trips accordingly.

The bus also takes a longer route at times which does not have a traffic jam. I will try and collect data points for that route and carry out some simulations for distance vs. time vs. cost (fuel).

Have a great day !

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