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Minimum cost routing is considered on multiclass multihop wireless networks influenced by stochastic arrivals, inter-channel interference, and time-varying topology. Endowing each air link with a cost factor, possibly time-varying and different for different classes, we define the Dirichlet routing cost as the square of the link packet transmissions… (More)

—A new routing policy, named Heat-Diffusion (HD), is developed for multihop wireless networks subject to stochastic arrivals, time-varying topology, and inter-channel interference, using only current queue congestion and current channel states, without requiring the knowledge of topology and arrivals. Besides throughput optimality, HD minimizes a quadratic… (More)

—Negative curvature in the relatively new Ollivier-Ricci sense of a wireless network graph is shown to be the culprit behind large queue occupancy, large routing energy, and restricted capacity region under any throughput optimal protocol. This is the wireless counterpart of the congestion phenomenon occurring in a Gromov negatively curved wired network… (More)

—We propose a new scheduling and routing approach, the Heat Diffusion (HD) protocol, using combinatorial analogue of the heat equation in mathematical physics. The algorithm holds for systems subject to time-varying network conditions with general packet arrivals and random topology states, including ad-hoc networks with mobility. Compared to the well-known… (More)

reliability of a power network is investigated from a topological viewpoint. Inspired from Riemannian geometry of manifolds, it is claimed that extreme load at specific parts of a large power grid can occur as a consequence of the local negative curvature in its hidden metric space. This paper contributes to four areas: (1) It draws a new course in the… (More)

—This paper considers the problem of average network delay minimization on multiclass, multihop, stochastic wireless networks subject to inter-channel interference and time-varying topology. We present a network control policy that solves this problem in the class of all policies whose control decision is a function only of current queue congestion and… (More)

- Edmond Jonckheere, Reza Banirazi, Rajit Chatterjea
- 2012

—In this paper, we develop a continuous-geometry/continuous-time model of a sensor network, which under a variant of the back-pressure protocol—the so-called diffusion protocol—sends data received from the various sensors to a central " sink. " This model is motivated by the necessity to understand how the wireless link graph topology affects network… (More)

Heat-Diffusion (HD) routing is our recently-developed queue-aware routing policy for multi-hop wireless networks inspired by Thermodynamics. In the prior theoretical studies, we have shown that HD routing guarantees throughput optimality, minimizes a quadratic routing cost, minimizes queue congestion on the network, and provides a trade-off between routing… (More)

- Reza Banirazi, Edmond Jonckheere, Bhaskar Krishnamachari
- 2014

—Concepts of temperature, heat, and entropy are extended to packet routing on multiclass wireless networks with particular challenges including network directionality, channel interference, channel capacity, time-varying topology, and stochastic arrivals. Applying thermodynamic principles in the framework of combinatorial geometry, a novel physics-oriented… (More)

- Reza Banirazi, Edmond Jonckheere, Bhaskar Krishnamachari
- 2013

—A new routing policy, named Heat-Diffusion (HD), is developed for multiclass, multihop wireless networks subject to stochastic arrivals, randomly varying topology, and channel interference. The new policy uses only current queue backlogs and current channel states, without requiring the knowledge of topology and arrivals. We show that HD is… (More)