Related papers: Walk versus Wait: The Lazy Mathematician Wins
Moving groups are routinely faced with a choice of different routes as part of their daily lives, such as choosing between exits from a building. Differences in moving speeds and environmental constraints often lead to individuals being…
We study the biased random walk in positive random conductances on $\mathbb {Z}^d$. This walk is transient in the direction of the bias. Our main result is that the random walk is ballistic if, and only if, the conductances have finite…
This paper presents a model of pedestrian crossing decisions, based on the theory of computational rationality. It is assumed that crossing decisions are boundedly optimal, with bounds on optimality arising from human cognitive limitations.…
We prove new results on lazy random walks on finite graphs. To start, we obtain new estimates on return probabilities $P^t(x,x)$ and the maximum expected hitting time $t_{\rm hit}$, both in terms of the relaxation time. We also prove a…
This study examines the computational complexity of the decision problem modeled on the smartphone game Bus Out. The objective of the game is to load all the passengers in a queue onto appropriate buses using a limited number of bus parking…
Destination prediction is an essential task in a variety of mobile applications. In this paper, we optimize the matrix operation and adapt a semi-lazy framework to improve the prediction accuracy and efficiency of a state-of-the-art…
Consider a walk in the plane made of $n$ unit steps, with directions chosen independently and uniformly at random at each step. Rayleigh's theorem asserts that the probability for such a walk to end at a distance less than 1 from its…
In this note, we design a discrete random walk on the real line which takes steps $0, \pm 1$ (and one with steps in $\{\pm 1, 2\}$) where at least $96\%$ of the signs are $\pm 1$ in expectation, and which has $\mathcal{N}(0,1)$ as a…
We study a make-to-order system with a finite set of customers. Production is stochastic with a nonlinear dependence between the ordered quantity and the production rate. Customers may have to queue until their turn arrives, and therefore…
We consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of visits to zero. We show the existence of distinct regimes…
In some athletic races, such as cycling and types of speed skating races, athletes have to complete a relatively long distance at a high speed in the presence of direct opponents. To win such a race, athletes are motivated to hide behind…
In route selection problems, the driver's personal preferences will determine whether she prefers a route with a travel time that has a relatively low mean and high variance over one that has relatively high mean and low variance. In…
Accurate forecasting of bus travel time and its uncertainty is critical to service quality and operation of transit systems; for example, it can help passengers make better decisions on departure time, route choice, and even transport mode…
Consider a transient near-critical (1,2) random walk on the positive half line. We give a criteria for the finiteness of the number of the skipped points (the points never visited) by the random walk. This result generalizes (partially) the…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
Computer-based simulation of pedestrian dynamics reached meaningful results in the last decade, thanks to empirical evidences and acquired knowledge fitting fundamental diagram constraints and space utilization. Moreover, computational…
Humans experience small fluctuations in their gait when walking on uneven terrain. The fluctuations deviate from the steady, energy-minimizing pattern for level walking, and have no obvious organization. But humans often look ahead when…
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…
In this paper we introduce a Linear Program (LP) based formulation of a Rendezvous game with markers on the infinite line and solve it. In this game one player moves at unit speed while the second player moves at a speed bounded by vmax…
The current paper deals with the subject of shortest path routing in transportation networks (in terms of travelling time), where the speed in several of the network's roads is a function of the time interval. The main contribution of the…