Distributed Cross-Layer Algorithms for the Optimal Control of Multihop Wireless Networks

Abstract

Abstract-In this paper, we provide and study a general framework that facilitates the development of distributed mechanisms to achieve full utilization of multi-hop wireless networks. In particular, we describe a generic randomized routing, scheduling and flow control scheme that allows for a set of imperfections in the operation of the randomized scheduler to account for potential errors in its operation. These imperfections enable the design of a large class of low-complexity and distributed implementations for different interference models. We study the effect of such imperfections on the stability and fairness characteristics of the system, and explicitly characterize the degree of fairness achieved as a function of the level of imperfections. Our results reveal the relative importance of different types of errors on the overall system performance, and provide valuable insight to the design of distributed controllers with favorable fairness characteristics.In the second part of the paper, we focus on a specific interference model, namely the secondary interference model, and develop distributed algorithms with polynomial communication and computation complexity in the network size. This is an important result given that earlier centralized throughputoptimal algorithms developed for such a model relies on the solution to an NP-hard problem at every decision. This results in a polynomial complexity cross-layer algorithm that achieves throughput optimality and fair allocation of network resources amongst the users. We further show that our algorithmic approach enables us to efficiently approximate the capacity region of a multi-hop wireless network.

Asynchronous CSMA Policies in Multihop Wireless Networks With Primary Interference Constraints

“…This observation has motivated high research activity in the recent years for the development of distributed and low-complexity implementations of queuelength-based schemes (e.g. [37], [13], [7], [25], [8], [30], [41], [9], [42], [19]). Also, random access strategies have been investigated in a number of works (e.g.…”

“…Note that the fixed point equation can be given both in terms of the fraction of idle times ρ by substituting (10) in (9) or in terms of the transmission attempt rates G by substituting (9) in (10). Given this equivalence, we refer to either one as the CSMA fixed point equation.…”

“…Hence, the expected number of transmission attempts that node i makes or receives, after it has been idle for β time units is (roughly) given by (10). Using (8) of Section VI-A, the fraction of time that node i is idle under p can then be approximated by (9).…”

Network adiabatic theorem

“…As the first non-trivial step, Modiano, Shah and Zussman [24] provided a totally distributed, simple gossip algorithm to find an approximate MW schedule each time for matching constraints (it naturally extends to independentset constraints and to cross-layer optimal control of a multihop network, e.g. see [7]). This algorithm is throughputoptimal, like the standard MW algorithm it does not require information about arrival rates, or it does not suffer from the caveat of "saturated system" analysis.…”

On the Role of Mobility for Multimessage Gossip

“…A partial list includes file sharing and rumor spreading [2]- [5], distributed computation and parameter estimation [6]- [10], and scheduling and control [11], [12]. Due to the huge centralization overhead and unpredictable dynamics in large networks, it is usually more practical to disseminate information and exchange messages in a decentralized and asynchronous manner to combat unpredictable topology changes and the lack of global state information.…”