Introduction

Our first case study for mathematical modelling is an every-day situation in urban settings: taking an elevator. Through a simple computational simulation of elevator arrivals in a multi-elevator lobby, we seek decision support for choosing a spot at which to wait. The goal is to minimize the walking we need to do once one of the elevators arrives, assuming that the arrivals occur uniformly at random (each elevator is equally likely to be the one to arrive). The data generated by such a simulation put us face to face with descriptive statistics, since we now need to make sense of that data.

Learning outcomes

This module will help you do the following:

• Employ pseudo-randomness to simulate a real-world phenomenon
• Gather observed data from replicas
• Quantify likelihood through frequency
• Interpret an average
• Compare an average to a median
• Examine the effects of changes in configuration
• Minimize an objective

Warm-up

Sometimes when we wait, we have extra time to (over)think of things. This blog post will point us into the type of thinking this module will induce.

Warm-up assessment

Make a list of a handful of mathematical and statistical concepts that come to mind when thinking of how to model and optimize the choices we make when waiting for elevators. For each, rate on a scale of 1 (just know the word, no clue what it means) to 5 (completely comfortable with the concept) how much you feel you know of each one.

Concepts

After this module, you should be familiar with the following concepts:

• Simulation
• Pseudo-randomness
• Mean (average)
• Distribution
• Median

Remember that you can always look concepts up in the glossary. Should anything be missing or insufficient, please report it.