Long examples

4x100m relay

Description:

We want to simulate a 4x100m relay, and are interested in predicting the finish time. For each athlete in the relay, we look up their personal best time on the individual 100m and calculate their speed in meter per second. In this example, we choose the four athletes at the time of writing (May 1st, 2021) holding the world record on the 4x100m relay [WR]:

1. Nesta Carter: 100m / 9.78s = 10.2 m/s [WA1]

2. Michael Frater: 100m / 9.88s = 10.1 m/s [WA2]

3. Yohan Blake: 100m / 9.69s = 10.3 m/s [WA3]

4. Usain Bolt: 100m / 9.58s = 10.4 m/s [WA4]

Of course, this is an example, so yes: we could just add their times together and get an answer. However, as a model becomes more and more complex to account for new factors, discrete event simulation is a useful tool to maintain an overview. For this example, one could extend the model to include varying wind conditions over time, reaction times, technological improvements in shoes, etc.: whatever factors might be influential.

The smallest simulation time unit we set to 1 nanosecond (1 second = 1e9 nanoseconds). Be aware that floating point operations (such as the time calculation in this example) can be less accurate than the simulation time precision as it depends on the number of significant digits (not on the number of decimal digits, in which we define our simulation time unit). See the floating point arithmetic documentation for more information. Keep in mind that our speed estimates only have three significant digits.

Code:

from discrevpy import simulator

def relay_finished():
    print("Last athlete finished: 4x100m relay in %.3gs" % (simulator.now() / 1e9))

class Athlete:
    def __init__(self, idx, athletes, speed_m_per_s):
        self.idx = idx
        self.athletes = athletes
        self.speed_m_per_s = speed_m_per_s

    def receive_stick_and_run(self):
        print("Athlete %d receives stick and starts run at t=%.3gs" % (self.idx, simulator.now() / 1e9))
        if self.idx != len(self.athletes) - 1:
            simulator.schedule(
                int(100.0 / self.speed_m_per_s * 1e9),
                self.athletes[self.idx + 1].receive_stick_and_run
            )
        else:
            simulator.schedule(
                int(100.0 / self.speed_m_per_s * 1e9),
                relay_finished
            )

athletes = []
athletes.append(Athlete(0, athletes, 10.2))  # Nesta Carter
athletes.append(Athlete(1, athletes, 10.1))  # Michael Frater
athletes.append(Athlete(2, athletes, 10.3))  # Yohan Blake
athletes.append(Athlete(3, athletes, 10.4))  # Usain Bolt
# All Athlete instances will now have a complete athletes list
# because Python objects are passed by reference

simulator.ready()
simulator.schedule(0, athletes[0].receive_stick_and_run)
print("Simulating a 4x100m relay")
simulator.run()
simulator.reset()

Output:

Simulating a 4x100m relay
Athlete 0 receives stick and starts run at t=0s
Athlete 1 receives stick and starts run at t=9.8s
Athlete 2 receives stick and starts run at t=19.7s
Athlete 3 receives stick and starts run at t=29.4s
Last athlete finished: 4x100m relay in 39s

References:

WR

https://www.worldathletics.org/records/all-time-toplists/relays/4x100-metres-relay/outdoor/men/senior (accessed May 1st, 2021)

WA1

https://www.worldathletics.org/athletes/jamaica/nesta-carter-14201894 (accessed May 1st, 2021)

WA2

https://www.worldathletics.org/athletes/jamaica/michael-frater-14202005 (accessed May 1st, 2021)

WA3

https://www.worldathletics.org/athletes/jamaica/yohan-blake-14201842 (accessed May 1st, 2021)

WA4

https://www.worldathletics.org/athletes/jamaica/usain-bolt-14201847 (accessed May 1st, 2021)