Related papers: Lonely passengers: a short proof
We consider the stochastic transport equation where the randomness is given by the symmetric integral with respect to stochastic measure. For stochastic measure, we assume only $\sigma$-additivity in probability and continuity of paths. The…
This contribution provides a microscopic experimental study of pedestrian motion in front of the bottleneck. Identification of individual pedestrians in conducted experiments enables to explain the high variance of travel time by…
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…
Public transport networks(PTNs)are difficult to use when the user is unfamiliar with the area they are traveling to.This is true for both infrequent users(including visitors)and regular users who need to travel to areas with which they are…
We introduce a sharpened version of the well-known Lonely Runner Conjecture of Wills and Cusick. Given a real number $x$, let $\Vert x \Vert$ denote the distance from $x$ to the nearest integer. For each set of positive integer speeds $v_1,…
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…
The remaining travel time of a plane shortens with every minute that passes from its departure, and a flame diminishes a candle with every second it burns. Such everyday occurrences bias us to think that processes which have already begun…
Suppose $k+1$ runners having nonzero constant speeds run laps on a unit-length circular track starting at the same time and place. A runner is said to be lonely if she is at distance at least $1/(k+1)$ along the track to every other runner.…
A theorem is proved on the uniform estimation of the residual term of the asymptotic expansion with respect to a small parameter of the solution of the initial problem for a singularly perturbed differential operator weakly nonlinear…
Consider~\(n\) nodes~\(\{X_i\}_{1 \leq i \leq n}\) distributed independently across~\(N\) cities contained with the unit square~\(S\) according to a distribution~\(f.\) Each city is modelled as an~\(r_n \times r_n\) square contained…
In this work the results of a bottleneck experiment with pedestrians are presented in the form of total times, fluxes, specific fluxes, and time gaps. A main aim was to find the dependence of these values from the bottleneck width. The…
This contribution provides microscopic experimental study of pedestrian motion in front of the bottleneck, explains the high variance of individual travel time by the statistical analysis of trajectories. The analysis shows that this…
Reorganizing bus frequency to cater for the actual travel demand can save the cost of the public transport system significantly. Many, if not all, existing studies formulate this as a bus frequency optimization problem which tries to…
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…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions…
We consider the stochastic transport linear equation and we prove existence and uniqueness of weak $L^{p}-$solutions. Moreover, we obtain a representation of the general solution and a Wong-Zakai principle for this equation. We make only…
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…
Understanding passengers' path choice behavior in urban rail systems is a prerequisite for effective operations and planning. This paper attempts bridging the gap by proposing a probabilistic approach to infer passengers' path choice…
The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents simple Bayesian solutions to different versions of the blue bus hypothetical. In addition, the author expresses his…