Related papers: Excuse Me! or The Courteous Theatregoers' Problem
In the {\em Musical Chairs} game $MC(n,m)$ a team of $n$ players plays against an adversarial {\em scheduler}. The scheduler wins if the game proceeds indefinitely, while termination after a finite number of rounds is declared a win of the…
Group elevator scheduling is an NP-hard sequential decision-making problem with unbounded state spaces and substantial uncertainty. Decision-theoretic reasoning plays a surprisingly limited role in fielded systems. A new opportunity for…
If you want to fill $n \in \mathbb{N}$ seats in succession with $n$ people and the rule that each person chooses one of the seats with the maximum distance to an occupied seat, then you can ask yourself how many possibilities there are for…
We study the dynamics of pedestrian evacuations through a narrow doorway by means of controlled experiments. The influence of the pedestrians' behaviours is investigated by prescribing a selfish attitude to a fraction c\_s of the…
Passengers board a fully booked airplane in order. The first passenger picks one of the seats at random. Each subsequent passenger takes his or her assigned seat if available, otherwise takes one of the remaining seats at random. It is well…
The rational solution of the Monty Hall problem unsettles many people. Most people, including the authors, think it feels wrong to switch the initial choice of one of the three doors, despite having fully accepted the mathematical proof for…
There are many entities that disseminate in the physical space - information, gossip, mood, innovation etc. Personal spaces are also entities that disperse and interplay. In this work we study the emergence of configurations formed by…
This article presents an interdisciplinary study of physical and social psychological effects on crowd dynamics based on a series of bottleneck experiments. Bottlenecks are of particular interest for applications such as crowd management…
The reader is reminded of several puzzles involving randomness. These may be ill-posed, and if well-posed there is sometimes a solution that uses probabilistic intuition in a special way. Various examples are presented including the well…
In this work we present a model for the evacuation of pedestrians from an enclosure considering a continuous space substrate and discrete time. We analyze the influence of behavioral features that affect the use of the empty space, that can…
We give a solution of the following combinatorial problem: "Let one from $n$ married couples in the m\'enage problem (see Problem 1) be a couple of a known mathematician $M$ and his wife. After the ladies are seated at every other chair,…
Consider a population of customers each of which needs to decide independently when to arrive to a facility that provides a service during a fixed period of time, say a day. This is a common scenario in many service systems such as a bank,…
In this paper we study a variant of the Malicious Ma\^{i}tre d' problem. This problem, attributed to computer scientist Rob Pike in Peter Winkler's book "Mathematical Puzzles: A Connoisseur's Collection", involves seating diners around a…
We analyze a boarding solution for a transport system in which the number of passengers allowed to enter a transport cabin is automatically controlled. Expressions charac- terizing the stochastic properties of the passenger queue length,…
To better design safe and comfortable urban spaces, understanding the nature of human crowd movement is important. However, precise interactions among pedestrians are difficult to measure in the presence of their complex decision-making…
We study the influence of selfish vs. polite behaviours on the dynamics of a pedestrian evacuation through a narrow exit. To this end, experiments involving about 80 participants with distinct prescribed behaviours are performed;…
We analyze the pedestrian evacuation of a rectangular room with a single door considering a Lattice Gas scheme with the addition of behavioral aspects of the pedestrians. The movement of the individuals is based on random and rational…
We study maximal seating arrangements, either on a line, or in a rectangular auditorium with a fixed number of columns but an arbitrary number of rows, that obey any prescribed set of `social distancing' restrictions. In addition to…
In this paper, we present results of an entrance experiment investigating the effect of the corridor width in front of a bottleneck on the density. The idea is based on a previous study suggesting that a guiding system in front of an…
The best improvisational theatre actors can make any scene partner, of any skill level or ability, appear talented and proficient in the art form, and thus "make them shine". To challenge this improvisational paradigm, we built an…