Collective effects in traffic on bi-directional ant-trails

Motivated by recent experimental work of Burd et al., we propose a model of bi-directional ant-traffic on pre-existing ant-trails. It captures in a simple way some of the generic collective features of movements of real ants on a trail. Analyzing this model, we demonstrate that there are crucial qualitative differences between vehicular- and ant-traffics. In particular, we predict some unusual features of the flow rate that can be tested experimentally. As in the uni-directional model a non-monotonic density-dependence of the average velocity can be observed in certain parameter regimes. As a consequence of the interaction between oppositely moving ants the flow rate can become approximately constant over some density interval

Physics of Transport and Traffic Phenomena in Biology: from molecular motors and cells to organisms

Traffic-like collective movements are observed at almost all levels of biological systems. Molecular motor proteins like, for example, kinesin and dynein, which are the vehicles of almost all intra-cellular transport in eukayotic cells, sometimes encounter traffic jam that manifests as a disease of the organism. Similarly, traffic jam of collagenase MMP-1, which moves on the collagen fibrils of the extracellular matrix of vertebrates, has also been observed in recent experiments. Traffic-like movements of social insects like ants and termites on trails are, perhaps, more familiar in our everyday life. Experimental, theoretical and computational investigations in the last few years have led to a deeper understanding of the generic or common physical principles involved in these phenomena. In particular, some of the methods of non-equilibrium statistical mechanics, pioneered almost a hundred years ago by Einstein, Langevin and others, turned out to be powerful theoretical tools for quantitaive analysis of models of these traffic-like collective phenomena as these systems are intrinsically far from equilibrium. In this review we critically examine the current status of our understanding, expose the limitations of the existing methods, mention open challenging questions and speculate on the possible future directions of research in this interdisciplinary area where physics meets not only chemistry and biology but also (nano-)technology.Comment: 33 page Review article, REVTEX text, 29 EPS and PS figure

A Model for Collective Dynamics in Ant Raids

Ant raiding, the process of identifying and returning food to the nest or bivouac, is a fascinating example of collective motion in nature. During such raids ants lay pheromones to form trails for others to find a food source. In this work a coupled PDE/ODE model is introduced to study ant dynamics and pheromone concentration. The key idea is the introduction of two forms of ant dynamics: foraging and returning, each governed by different environmental and social cues. The model accounts for all aspects of the raiding cycle including local collisional interactions, the laying of pheromone along a trail, and the transition from one class of ants to another. Through analysis of an order parameter measuring the orientational order in the system, the model shows self-organization into a collective state consisting of lanes of ants moving in opposite directions as well as the transition back to the individual state once the food source is depleted matching prior experimental results. This indicates that in the absence of direct communication ants naturally form an efficient method for transporting food to the nest/bivouac. The model exhibits a continuous kinetic phase transition in the order parameter as a function of certain system parameters. The associated critical exponents are found, shedding light on the behavior of the system near the transition.Comment: Preprint Version, 30 pgs., 18 figures, complete version with supplementary movies to appear in Journal of Mathematical Biology (Springer

Planning and Scheduling Transportation Vehicle Fleet in a Congested Traffic Environment

Transportation is a main component of supply chain competitiveness since it plays a major role in the inbound, inter-facility, and outbound logistics. In this context, assigning and scheduling vehicle routing is a crucial management problem. Despite numerous publications dealing with efficient scheduling methods for vehicle routing, very few addressed the inherent stochastic nature of travel times in this problem. In this paper, a vehicle routing problem with time windows and stochastic travel times due to potential traffic congestion is considered. The approach developed introduces mainly the traffic congestion component based on queueing theory. This is an innovative modeling scheme to capture the stochastic behavior of travel times. A case study is used both to illustrate the appropriateness of the approach as well as to show that time-independent solutions are often unrealistic within a congested traffic environment which is often the case on the european road networkstransportation; vehicle fleet; planning; scheduling; congested traffic

Balancing building and maintenance costs in growing transport networks

The costs associated to the length of links impose unavoidable constraints to the growth of natural and artificial transport networks. When future network developments can not be predicted, building and maintenance costs require competing minimization mechanisms, and can not be optimized simultaneously. Hereby, we study the interplay of building and maintenance costs and its impact on the growth of transportation networks through a non-equilibrium model of network growth. We show cost balance is a sufficient ingredient for the emergence of tradeoffs between the network's total length and transport effciency, of optimal strategies of construction, and of power-law temporal correlations in the growth history of the network. Analysis of empirical ant transport networks in the framework of this model suggests different ant species may adopt similar optimization strategies.Comment: 4 pages main text, 2 pages references, 4 figure

Counterflow Extension for the F.A.S.T.-Model

The F.A.S.T. (Floor field and Agent based Simulation Tool) model is a microscopic model of pedestrian dynamics, which is discrete in space and time. It was developed in a number of more or less consecutive steps from a simple CA model. This contribution is a summary of a study on an extension of the F.A.S.T-model for counterflow situations. The extensions will be explained and it will be shown that the extended F.A.S.T.-model is capable of handling various counterflow situations and to reproduce the well known lane formation effect.Comment: Contribution to Crowds and Cellular Automata Workshop 2008. Accepted for publication in "Cellular Automata -- 8th International Conference on Cellular Automata for Research and Industry, ACRI 2008, Yokohama, Japan, September 23-26, Springer 2008, Proceedings