2005/04/30 by Omer Angel, Alexander E Holroyd, James B Martin · 1 citation
Mathematics · #math.PR #math.CO #msc:60K35 #msc:82B43
published as Elec. Comm. Prob. 10 (2005) 167--178 · 15 pages, 5 figures; revised journal version
arxiv created 2005/08/22 · arxiv updated 2009/12/01
Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each North-facing car moves one unit North if there is a vacant site for it to move into. At even time steps, East-facing cars move East in the same way. We prove that when p is sufficiently close to 1 traffic is jammed, in the sense that no car moves infinitely many times. The result extends to several variant settings, including a model with cars moving at random times, and higher dimensions.