相关论文: Lonely passenger problem: the more buses there are…

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…

This paper introduces the \textbf{detachment process}, a novel, time-inhomogeneous Markov process inspired by I. P. T\'oth's problem \cite{Toth} concerning the number of ``lonely passengers'' (those without companions) when $n$ passengers…

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…

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…

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,…

We study a queueing system with Poisson arrivals on a bus line indexed by integers. The buses move at constant speed to the right and the time of service per customer getting on the bus is fixed. The customers arriving at station i wait for…

This article considers the stochastic on-time arrival problem in transit networks where both the travel time and the waiting time for transit services are stochastic. A specific challenge of this problem is the combinatorial solution space…

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…

Bus bunching is a curse of transportation systems such as buses in a loop. Here we present an analytical method to find the number of revolutions before two buses bunch in an idealised system, as a function of the initial distance and the…

In an increasingly interconnected world, understanding congestion-related phenomena in transportation and their underlying mechanisms is crucial for improving efficiency. As the transportation system becomes denser, different modes of…

We study a bus system with a no-boarding policy, where a "slow" bus may disallow passengers from boarding if it meets some criteria. When the no-boarding policy is activated, people waiting to board at the bus stop are given the choices of…

In this paper, we consider a mobility system of travelers and providers, and propose a "mobility game" to study when a traveler is matched to a provider. Each traveler seeks to travel using the services of only one provider, who manages one…

In the traveling salesman problem, one must find the length of the shortest closed tour visiting given ``cities''. We study the stochastic version of the problem, taking the locations of cities and the distances separating them to be random…

Predicting future bus trip chains for an existing user is of great significance for operators of public transit systems. Existing methods always treat this task as a time-series prediction problem, but the 1-dimensional time series…

We consider a stylized formal model of public transportation, where a set of agents need to travel along a given road, and there is a bus that runs the length of this road. Each agent has a left terminal and a right terminal between which…

We investigate a no-boarding policy in a system of $N$ buses serving $M$ bus stops in a loop, which is an entrainment mechanism to keep buses synchronised in a reasonably staggered configuration. Buses always allow alighting, but would…

Route choice models in public transport have been discussed for a long time. The main factor why a passenger chooses a specific path is usually based on its length or travel time. However, also the ticket price that passengers have to pay…

Suppose that you're going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer - possibly much longer - than what the bus schedule suggests intuitively. This phenomenon,…

Bus bunching is ostensibly regarded as a detrimental phenomenon in bus systems. We study a bus loop with two bus stops, one regular and one spike bus stop, where bunched buses can outperform staggered buses. The spike bus stop models a bus…

Several authors have noted that in a non-regulated environment the development of public transport service is self-adjusting: Faced with a decreasing demand, operators will tend to reduce service to cut costs, resulting in a decrease in the…