SYS-611 - Systems Modeling and Simulation Engineering

Assignment Task

1. Introduction

1.1 Problem statement and study objectives

The World Triathlon Union (WTU) has imposed new transition area requirements for WTU-sanctioned races. The new rules require each athlete to have access to a volunteer in their swim-to-bike transition area (also known as T1). Each volunteer must be positioned at a transition area station that will accommodate one triathlete at a time as they exit the swim portion of the race and prepare for the bike portion. The race director of the Multi-Sport 611 Triathlon, a 140.6-mile ironman distance event, must determine how many transition stations she will accommodate for the race at the Tempe Town Lake in Arizona. The race director’s cost per volunteer is negligible, however she would like to maintain average transition times from previous races prior to the new regulations taking effect. Based on past data, the average transition times for athletes was around 13.5 minutes (see section 2.1) with the faster professionals transitioning in as little as 3 minutes. What is the minimum number of stations the race director should plan for to maintain comparable transition times and still meet the new WTU regulations?

1.2 System Boundary The boundary for the system under study is graphically

The system inputs are the athletes as they finish the swim portion of the race and arrive in transition (i.e. their arrival times). Because transition stations can only serve one athlete at a time, athletes can Transition Station Transition Station Transition Station Transition Station N number of stations w/ 1 volunteer each System Boundary: T1 Transition Area Time athlete departs transition Input: Time athlete arrives at transition (arrival rate) Athlete 1 Athlete 2 Athlete N Time athlete starts using a station Athletes waiting to use a station Time athlete takes using a station Athlete Using a Station Athlete Using a Station Athlete Using a Station Athlete Using a Station Athlete Finished using a station Input: System Runtime Output: Athlete Total Transition Time Output: Athlete Queue Length Over time Input: Transition Station Service rate Giselle Bonilla-Ortiz December 17, 2018 2 approach stations that are currently unoccupied by other athletes or they wait in queue for the next available station. Care-abouts here for the system are the number of athletes waiting to use a station, which stations are currently occupied, and which become available, the time athletes approach an unoccupied station and the amount of time the athlete spends utilizing a station. It is also important to track the time an athlete departs the transition area as this will be the total transition time (wait time) of an athlete. The number of stations is the variable under study. It must be greater than 1 and the number of stations must satisfy the constraint of providing transition times similar to those from prior races.

The scope of this system simulation is stochastic and dynamic. Input variables such as the athlete interarrival times and station service times will be random based on determined probability distributions. The system is dependent on time passing, and different events being triggered (such as arrivals and departures) so it will be of dynamic scope.

1.3 Key Performance Measures (KPM) The Key Performance Measures (KPM) for the simulation developed are the average transition time for each athlete and the queue length as athletes wait to use a transition station.

The race director wants to use average transition time of the 2018 Ironman Arizona event held in the same venue. For that race, the average transition time was approximately 13.5 minutes (see section 2 for data collected). This includes all divisions: professional, age group and gender. Because these transition rules are new, no other triathlon has yet experimented with the 1-station per athlete configuration. Due to this constraint, the queue length KPM is somewhat more difficult to quantify. The race director has expressed that a queue length of 0 is unacceptable since that means there are too many stations, but that the queue length should be short enough to allow for the average 13.5-minute transition time.

2 Modeling Approach

2.1 Collecting and Processing Real Data Data was collected online for the results for the 2018 Ironman Arizona event. 1 Coach Russell Cox gathers Ironman results from multiple races and organizes the data into MS Excel format. The data includes the times for all portions of the event for the approximately 2,400 athletes: swim, bike, run and both transitions. I compared the data collected from Coach Cox’s website to the data provided on the official Ironman web page2 and determined Cox’s data was accurate. For this particular study the following data was used: swim split time for all athletes and total transition 1 (T1) time.

The swim split time was used to determine when each athlete arrives at transition (i.e. determine the average interarrival time) and the transition time was used to determine what the average wait time would be for an athlete in the ideal conditions of a real-world system.

2.2 Formulating, Developing and Documenting   the Model

A conceptual representation of the triathlon transition model is presented in Figure 5. In this model, multiple triathletes can enter the system in parallel and proceed to available transition stations where they will be “serviced”. As triathletes finish using a station, they exit the system and those stations become available to the next athletes in the queue. Note that athletes proceed to an unoccupied station in order of arrival to the transition area.

Given the structure presented above then we can define the simulation variables as follows:

• Athlete Arrival Time: random variable sampled from an Exponential distribution. The mean interarrival time used in the simulation was selected from computing the mean interarrival time of the real data collected. Computed mean interarrival time = 0.05 minutes/athlete or 19 athletes/minute.
• Service time: This simulation variable is given by simpy request for available resource. In other words, the time of simulation when a station becomes available for an athlete.
• Queue wait time: service time – arrival time
• Departure time: This simulation variable is given by a randomly sampled delay from a Lognormal distribution. As described in Section 2.1, the lognormal delay was selected due to the real-world transition data following a lognormal distribution. It’s important to note here, that in the simulated transition, total transition area will include the time spent in the queue plus the time being serviced at the station. Therefore, it was determined that real-world transition data (which does not include queue waiting time) was an accurate representation for the simulated transition departure time.
• Total transition time = departure time – arrival time. One assumption to note here is that, because total transition time is based on the Lognormal distributed departure time, it will accurately be able to represent real-world transition data that is Lognormal distributed.

SME Consultation

I sent data of one simulation run to my triathlon coach, Jen Lynn of Desert Endurance Multisport Coaching3 . For the particular data set that I sent her, the simulated min was about 4 minutes and the max was about 33 minutes. Her assessment was as follows:

The minimum transition time looks realistic, however in small transitions areas like IM Arizona, professional triathletes transition in as little as 3 minutes.

The maximum transition time of 33 minutes seemed unrealistically large. Per Jen, most age group triathletes transition in 10-15 minutes. Based on Jen’s input I can conclude that my simulated data is realistic. However, please see sections 3 and 4 for my assessment on limitation and my conclusion regarding extreme outlying transition times.

3 Results and Analysis

3.1 Study and Design Conditions

The objective of the study is to determine the number of transition stations to provide in the transition area of the triathlon. I designed the study based on a server based discrete event model, where each station acts as a server. To execute the study, I implemented the simulation model in Simpy, based on the Queueing System example provided in class and took advantage of the environment resource availability scheme provided by Simpy.

As stated in section 1.3, the two KPMs for this study are the total transition time and the queue length.

The following conditions were established for this study:

• Simulation run time: For this particular study, the runtime was determined to be 120 minutes, the typical Ironman swim cut off time (140) minus 20 minutes4 . The reasoning behind this condition is that this would allow around 2000 athletes from swim into the transition, a detail that accurately represents the real-world amount of athletes participating an Ironman event.
• As previously stated, the input random variables of interarrival times and service times are modeled using exponential and lognormal distributions respectively.
• The selection of transition area capacity will follow trial and error, where too many stations will be determined by a queue of length
• For this study, the assumption is that 100 runs of the simulation will provide adequate mean transition times for determining the most effective number of transition stations. Some limitations to keep in mind are the following: 1) real-world data used to pre-determine random sampling parameters include times of athletes that did not continue the race, thus skewing results to somewhat unrealistically large transition times, 2) there is no real-world example of the queuing system being proposed by WTU’s requirement in this study so the assumption for success is that even when accounting for the additional queue wait, transition times should match realistic results that do not include the queuing delay, 3) triathlons usually divide their swim starts into divisions (i.e. professionals, by age, by gender) and this division is not accounted for in this simulation. The study assumes all athletes start at the same time and reach transition when they finish their swim.

Discussion and Conclusion

Based on the results of the study, the Multi-Sport 611 Triathlon race director should provide a total of 255 stations in the event’s transition area. Considering real-world impacts, with the number of athletes that participate in Ironman events (~2,400 for the Ironman AZ 2018 example), 255 stations is not an unrealistic number. That being said, this is a theoretical problem as real triathlons do not use this scheme of “1 athlete per station” and instead provide large changing tents, volunteers to hand out athlete race gear and an assigned transition space for each athlete. One thing I did not have time to study further, was an optimum queue length. In real life, a queue length of any size would annoy athletes, and it serves as a good variable to be minimized in a future study. Other extensions of this study could explore more realistic athlete arrival times that result from staggered “swim waves”, in which athletes start at different times with their own professional, gender or age group divisions. Another limitation that I briefly touched on earlier was the observation of unrealistically large transition times. The real-world data collected includes large transition times. This is due to the fact that in a real event, athletes may end up in the T1 medical tent and may later drop out of the race, providing for skewed data that does not match an appropriate transition time. This detail is not supported by the current version of this simulation and could be of interest for further study.

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