title: Phase transitions in crowd dynamics of resource allocation.
abstract: We define and study a class of resource allocation processes where gN agents, by repeatedly visiting N resources, try to converge to an optimal configuration where each resource is occupied by at most one agent. The process exhibits a phase transition, as the density g of agents grows, from an absorbing to an active phase. In the latter, even if the number of resources is in principle enough for all agents (g<1), the system never settles to a frozen configuration. We recast these processes in terms of zero-range interacting particles, studying analytically the mean field dynamics and investigating numerically the phase transition in finite dimensions. We find a good agreement with the critical exponents of the stochastic fixed-energy sandpile. The lack of coordination in the active phase also leads to a nontrivial faster-is-slower effect.
authors.affiliation: TCMP Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064, India. asim.ghosh@saha.ac.in
authors.forename: Asim
authors.initials: A
authors.lastname: Ghosh
authors.forename: Daniele
authors.initials: D
authors.lastname: De Martino
authors.forename: Arnab
authors.initials: A
authors.lastname: Chatterjee
authors.forename: Matteo
authors.initials: M
authors.lastname: Marsili
authors.forename: Bikas K
authors.initials: BK
authors.lastname: Chakrabarti
mesh_terms: D000818:Animals; D003198:Computer Simulation; D003441:Crowding; D005716:Game Theory; D006801:Humans; D008962:Models, Theoretical; D044367:Phase Transition; D040841:Resource Allocation