Phase transition in a computer network model

Tretyakov, A. Yu.; Takayasu, Hideki; Takayasu, Misako

doi:10.1016/s0378-4371(97)00659-6

Cited by 77 publications

(32 citation statements)

References 5 publications

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“…There are two interesting limiting cases of equation (15). When ρ is very small, taking into account that the sum of betweennesses is proportional to the average distance, one obtains that the load is proportional to the average effective distance.…”

Section: Optimization In a General Frameworkmentioning

confidence: 99%

Search and Congestion in Complex Networks

Arenas

Cabrales

Dı́az-Guilera

et al. 2003

Statistical Mechanics of Complex Networks

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Section: Optimization In a General Frameworkmentioning

confidence: 99%

Search and Congestion in Complex Networks

Arenas

Cabrales

Dı́az-Guilera

et al. 2003

Statistical Mechanics of Complex Networks

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“…Our interest is focused on the behavior of hierarchical structures formed by elements (or agents) that interact with each other via communication processes. This framework is especially adequate to study, e.g., Internet flow [3][4][5][6][7], traffic networks [8], river networks [9], and even communication flows in organizations [10].In this Letter, we propose and study a very simple model of communication. The model includes only the basic ingredients present in a communication process between two elements: (i) information packets to be transmitted (delivered) and (ii) communication channels to transmit the packets.…”

mentioning

confidence: 99%

Communication in Networks with Hierarchical Branching

2001

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We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. The analytical results are a useful guide to forecasting the main features of real networks. DOI: 10.1103/PhysRevLett.86.3196 PACS numbers: 89.20.Ff, 05.70.Jk, 64.60.-i Nowadays, many challenging questions have arisen concerning the behavior of complex technological, economical, and social systems [1]. In particular, computer simulations of agents and their interactions (agent-based modeling) have become a widely used tool in our current understanding of their macroscopic behavior [2]. Especially interesting is the study of hierarchical branching in networks because it seems to be the basic structure underlying complex organizational systems. Our interest is focused on the behavior of hierarchical structures formed by elements (or agents) that interact with each other via communication processes. This framework is especially adequate to study, e.g., Internet flow [3][4][5][6][7], traffic networks [8], river networks [9], and even communication flows in organizations [10].In this Letter, we propose and study a very simple model of communication. The model includes only the basic ingredients present in a communication process between two elements: (i) information packets to be transmitted (delivered) and (ii) communication channels to transmit the packets. Despite its simplicity, the model reproduces the main characteristics of the flow of information packets in a network, and is general enough to allow the study of communication processes in many conditions: for example, different capabilities of agents to transmit packets, and/or heterogeneity in the communication channels (miscommunication, exogenous effects, etc.) represented by introducing disorder. We observe three different behaviors depending on the capability of agents to transmit packets. In particular, for a certain capability, we observe a continuous phase transition between a sparse and a congested regime when the number of packets to deliver reaches a critical value. Near the transition point signs of criticality arise, we find large fluctuations, critical slowing down, and power law behavior of power spectrum of the amount of information flowing in the network, in agreement with reported empirical data [5]. We provide a mean-field estimation of the critical point in good agreement with simulation results and we define analytically an order parameter to characterize the behavior of the system.The model is defined in the f...

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“…In interconnection networks, packet buffering and flow control offer non-linear characteristics. Thus, the networks show phase transition between uncongested and congested situations [14], [15], [16], [17], [18].…”

Section: Outcomes Of Physics Research 311 Knowledge From Self-drivementioning

confidence: 99%

Relaxing Heavy Congestion by State Propagation

Yokota

Ootsu

Ohkawa

2015

Journal of Information Processing

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Interconnection network is still one of the most important key issues for building massively parallel computing systems. As a general characteristic, communication performance does not always increase as the size of network grows. Furthermore, large-scale networks suffer catastrophic performance degradation since speed of spread of congestion surpasses by far suppression speed. This paper focuses discussions on relaxation of congestion so that we can expect performance enhancement even in congested situations. This paper discusses dynamical behaviors, specifically in propagation of congestion states. When a receiver buffer becomes fully occupied, it inhibits the corresponding buffer from sending any packet to avoid loss of packet. Thus, a congested area propagates against packets' traveling direction. Based on the observation results, as the second issue of this paper, we propose a new throttling method, called State-Propagation Throttling (SPTh). The method can boost communication performance in many of typical traffic patterns in both steady and unsteady communication situations. Furthermore, this paper discusses extending the throttling method to prevent congestion from a proactive point of view. In steady communications, the proposed method improves throughput two times and latency four times. The method also improves performance of collective communication at most 1.8 times.

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Phase transition in a computer network model

Cited by 77 publications

References 5 publications

Search and Congestion in Complex Networks

Search and Congestion in Complex Networks

Communication in Networks with Hierarchical Branching

Relaxing Heavy Congestion by State Propagation

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