相关论文: More Absent-Minded Passengers
In a delightful article that recently appeared in the American Mathematics Monthly, Norbert Henze and Guenter Last discuss the "Absent-Minded Passengers" Problem, but left open finding an explicit expression for the probability generating…
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 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…
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…
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…
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…
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…
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…
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…
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…
In the asymmetric simple exclusion process on the integers each particle waits exponential time, then with probability p it moves one step to the right if the site is unoccupied, otherwise it stays put; and with probability q=1-p it moves…
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…
In this paper we consider a set of origin-destination pairs in a mixed model in which a network embedded in the plane represents an alternative high-speed transportation system, and study a trip covering problem which consists on locating…
Ride-hailing services have expanded the role of shared mobility in passenger transportation systems, creating new markets and creative planning solutions for major urban centers. In this paper, we consider their use for the first-mile or…
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…
Airlines use different boarding policies to organize the queue of passengers waiting to enter the airplane. We analyze three policies in the many-passenger limit by a geometric representation of the queue position and row designation of…
We show that airplane boarding can be asymptotically modeled by 2-dimensional Lorentzian geometry. Boarding time is given by the maximal proper time among curves in the model. Discrepancies between the model and simulation results are…
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…
Ride-sharing can reduce traffic congestion and thus reduce gas emissions and save travel time. However, transportation system with ride-sharing is currently inefficient due to low occupancy rate, high travel demand and some other factors.…
The timely handling of passengers is critical to efficient airport and airline operations. The pandemic requirements mandate adapted process designs and handling procedures to maintain and improve operational performance. Passenger…