What does an Operations Research (OR) analyst think about before cycling 125 miles?
It was a beautiful sunny September day in New Bern, NC. I trained all summer for this ride. I was on the starting line with 2,000 other cyclists waiting to begin the first day of a two day BikeMS charity ride. The goal of the event was to raise money to fund research to find a cure for multiple sclerosis. My goal over the next two days was to survive a 50 mile ride on Saturday and followed by a 75 mile ride on Sunday.
As I leaned against my bicycle waiting for the start of the event, I realized that the event organizers were sending out riders in waves approximately every five minutes. This stimulated my OR brain into thinking about why organizers would do this. I quickly decided to use simulation to answer my question; formulating this model kept my mind off the 125 miles ahead.
After successfully completing the ride (thanks to everyone who supported me, especially the CANA Foundation!) I built a simulation in ExtendSim. The actual New Bern BikeMS event had four riding distances a day (30, 50, 75, and 100 miles) and multiple rest stops. I simplified the model to demonstrate the effects of the wave start. A diagram of the model is in Figure 1 below.
Figure 1. ExtendSim simulation model with seven ten mile cycling segments and six rest stop queues
One day event
2,000 riders mass start
10 waves of 200 riders released in 5 minute intervals
6 rest stops
70 miles (7x10 miles segments)
1,000 simulation runs for each scenario
Departure times for the cyclists. There is a 0.9 second separation between cyclists crossing the start line. Given this gap it will take 30 minutes for 2,000 cyclist to start in one mass wave and approximately 50 minutes for 10 waves of 200 cyclist departing at 5 minute intervals (still individually at 0.9 seconds).
Rest stops have a constant service rate of one rider every 3.6 seconds. This equates to 500 cyclists over a 30 minute time frame. Some riders stop to fill a water bottle, others for food and many to use the bathroom.
Bicycling time distribution for each 10 mile segment is a triangle distribution with a minimum of 30 minutes (20 mph average), maximum of 60 minutes (10 mph average) and a most likely of 40 minutes (15 mph average). Remember this is a charity ride and not the Tour de France.
There is a probability of 0.5 for a cyclist to stop at a rest stop. Therefore each rest stop should expect approximately 1,000 cyclists during one day.
For those lucky few that ride in charity cycling events, you know that the first rest stop is usually overwhelmed (especially the bathrooms).
So what were the results of the two scenarios?
The results are very convincing and displayed in Table 1 below. Starting in waves reduces the average queue wait time from 10 minutes to under a minute. The max line for Rest Stop 1 with the 2,000 cyclist start was 335 cyclists. With the 200 wave start, it was 11 cyclists.
Table 1. Results for Rest Stop 1 for the two starting wave scenarios. The Wait times are in minutes.
By the time cyclists reached Rest Stop 2, the riders had spread out enough to eliminate any queuing at Rest Stops 2 through 6.
Given that the wave starts take slightly longer to implement at the beginning of the day (40 extra minutes for all cyclists to start), the overall performance of the wave start strategy is impressive. This strategy reduces the workload on Rest Stop 1 and decreases the time cyclists spend on the course as displayed in Table 2 below. And, for us cyclists, we are always infinitely happier pedaling our bicycles than standing in line for the bathroom.
Table 2. Results for all cyclists completing the 70 mile ride with six rest stops.
I did stop both days at Rest Stop 1 and was impressed with the short lines. Perhaps the BikeMS event organizers had figured out the wave start method through years of experience or maybe some OR designed a simulation for them….