Towards Understanding Complex Communication Networks: Performance, Phase Transitions and Control

Published

June 13, 2007

Author(s)

Vladimir V. Marbukh

Abstract

Micro dynamics of large-scale communication networks is often described by a Markov process with a large number of locally interacting components. Due to astronomically high number of the Markov process states even for moderate-size networks, finding the entire micro distribution by solving the corresponding Kolmogorov equations is computationally infeasible. The paper proposes mean-field approximations for evaluating macro variables representing measurable and practically important network performance criteria without solving the corresponding Kolmogorov equations for TCP/IP networks under random flow arrivals/departures and multiservice mobile wireless cellular networks. Bifurcations of the non-linear mean-field equations are naturally associated with phase transitions and metastability.

Proceedings Title

Mathematical Performance Modeling and Analysis | 9th | 2007 | MAMA07

Conference Dates

June 13, 2007

Conference Location

San Diego, CA

Conference Title

MAMA 07, ninth annual workshop on MAthematical performance Modeling and Analysis

Pub Type

Conferences

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Keywords

Complex Communication Networks, Mean-Field Approximation, Phase Transitions, Metastability

Citation

Marbukh, V. (2007), Towards Understanding Complex Communication Networks: Performance, Phase Transitions and Control, Mathematical Performance Modeling and Analysis | 9th | 2007 | MAMA07, San Diego, CA, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=51184 (Accessed October 12, 2025)