Physica A 253 (1998) 315–322 Phase transition in a computer network model A.Yu. Tretyakov a; ∗ , H. Takayasu b , M. Takayasu c a Graduate School of Information Sciences, Tohoku University Aramaki, Aoba-ku, Sendai, 980-77, Japan b Sony Computer Science Lab 3-14-13 Higashi-Gotanda, Shinagawa, Tokyo 151, Japan c Research for the Future Project, Keio University Shin-Kawasaki-Mitsui Bldg. W-3F, 890-12 Kashimada, Saiwai-ku, Kawasaki 221, Japan Received 21 November 1997 Abstract The existence of a phase transition in a computer network model is indicated by an abrupt change in packet density, critical slowing down and fractal properties of the characteristic time series. The network operates most eciently in the vicinity of the critical point. c  1998 Elsevier Science B.V. All rights reserved PACS: 89.80+h; 05.45+b; 64.60Fr Keywords: Computer network; Dynamical phase transition; Simulation The enormous importance of computer networks hardly needs to be explained. Present day wide-area networks can connect millions of users, indeed, the whole Internet net- work can be considered as a single system, comprising most of the existing computers. Each computer on the Internet can interact with any other computer belonging to the system. Especially, with the advent of the World Wide Web, there is a tendency to access resources all over the world, with a little regard to the actual geographic location. A system consisting of millions of elements that is governed, at lower levels, by well- dened rules (networks protocols) is certain to attract attention of statistical physicists. Indeed, in a number of recent publications an attempt is made to analyze the network information trac using methods and approaches of statistical physics [1– 4], with attention mostly centered on spectral properties of packet (unit of information that can be sent in one transmission) delivery times and packet ow time series. In [4], based on the integral distributions of level sets for packet delivery time measurements, it has been suggested that the transition to a jammed state in a real network can be described as a second-order phase transition. * Corresponding author. Tel., fax: +81 22 217 7016; e-mail: alex@fractal.is.tohoku.ac.jp. 0378-4371/98/$19.00 Copyright c  1998 Elsevier Science B.V. All rights reserved PII S0378-4371(97)00659-6