Related papers: The Absent-Minded Passengers Problem via Computer …
We offer a formula for the probability distribution of the number of misseated airplane passengers resulting from the presence of multiple absent-minded passengers, given the number of seats available and the number of absent-minded…
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…
In (S.B. Ekhad and D. Zeilberger, 2020) an exciting case study has been initiated in which experimental mathematics and symbolic computation are utilized to discover new properties concerning the so-called Absent-Minded Passengers Problem.…
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…
This paper reconsiders the problem of the absent-minded driver who must choose between alternatives with different payoff with imperfect recall and varying degrees of knowledge of the system. The classical absent-minded driver problem…
The absent-minded driver's problem illustrates that probabilistic strategies can give higher pay-offs than deterministic ones. We show that there are strategies using quantum entangled states that give even higher pay-offs, both for the…
Gathering is a fundamental task for multi-agent systems and the problem has been studied under various assumptions on the sensing capabilities of mobile agents. This paper addresses the problem for a group of agents that are identical and…
Empty buses are standing at a bus station. $n$ passengers arrive, and they each board a bus completely at random (meaning that they choose uniformly and independently). Then all buses depart. We show that the more buses there are, the more…
A fixed number of passengers independently board one of several buses uniformly at random. The lonely passenger problem is to prove that the probability of at least one passenger being the only one in their bus is increasing in the number…
In the area of computer science focusing on creating machines that can engage on behaviors that humans consider intelligent. The ability to create intelligent machines has intrigued humans since ancient times and today with the advent of…
We formulate a statistical flight-pause model for human mobility, represented by a collection of random objects, called motions, appropriate for mobile phone tracking (MPT) data. We develop the statistical machinery for parameter inference…
We study airplane boarding in the limit of large number of passengers using geometric optics in a Lorentzian metric. The airplane boarding problem is naturally embedded in a 1+1 dimensional space-time with a flat Lorentzian metric. The…
A detailed study is made of the number of occupied seats in an unfriendly seating scheme with two rows of seats. An unusual identity is derived for the probability generating function, which is itself an asymptotic expansion. The identity…
Two sets $A$ and $B$ of points in the plane are \emph{mutually avoiding} if no line generated by any two points in $A$ intersects the convex hull of $B$, and vice versa. In 1994, Aronov, Erd\H os, Goddard, Kleitman, Klugerman, Pach, and…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
As autonomous agents become more ubiquitous, they will eventually have to reason about the plans of other agents, which is known as theory of mind reasoning. We develop a planning-as-inference framework in which agents perform nested…
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…
This paper considers a variant of the online paging problem, where the online algorithm has access to multiple predictors, each producing a sequence of predictions for the page arrival times. The predictors may have occasional prediction…
I present and discuss a model for the free-for-all passenger boarding which is employed by some discount air carriers. The model is based on the principles of statistical mechanics where each seat in the aircraft has an associated energy…
Automatic passenger counting (APC) in public transportation has been approached with various machine learning and artificial intelligence methods since its introduction in the 1970s. While equivalence testing is becoming more popular than…