24-08-2012, 03:32 PM
Achievable Rate Region of CSMA Schedulers in Wireless Networks with
Primary Interference Constraints
Achievable Rate.PDF (Size: 86.76 KB / Downloads: 31)
Abstract
We consider Carrier Sense Multiple Access
(CSMA) schedulers for wireless networks. For networks where
all nodes are within transmission range of each other, it has
been shown that such schedulers achieve the network capacity
in the limiting region of large networks with a small sensing
delay. However the design and analysis of CSMA schedulers
for general networks has been an open problem due to the
complexity of the interaction among coupled interference constraints.
For networks with primary interference constraints, we
introduce a tractable analysis of such CSMA schedulers based
on a fixed point approximation. We then use the approximation
to characterize the achievable rate region of static CSMA
schedulers. We show that the approximation is asymptotically
accurate for the limiting regime of large networks with a small
sensing delay, and that in this case the achievable rate region
of CSMA converges to the capacity region.
INTRODUCTION
Recently, there has been a growing interest in the development
of distributed transmission policies for interferencelimited
wireless networks. A key objective of these distributed
policies is to achieve any throughput within the
capacity region1 of the network. In this paper we focus on
Carrier Sense Multiple Access (CSMA) schedulers where
nodes sense whether the channel is idle before making
an attempt to transmit a packet. For single-hop networks
where all nodes are within transmission range of each other,
it is well-known that CSMA schedulers achieve network
capacity in the limiting regime of large networks with a
small sensing time [2]. However the analysis of CSMA
schedulers for general networks has been an open problem
due to the complexity of the interaction among coupled
interference constraints. In this paper, we provide an analysis
of CSMA schedulers for networks with primary interference
constraints.
LARGE NETWORKS WITH A SMALL SENSING TIME
In this section, we study the behavior of the CSMA fixed
point under the limiting regime where the number of nodes
N increases to infinity and the sensing time b decreases to
zero. For this case, we show that the CSMA fixed point
description of the operating point is asymptotically accurate.
This result states that for large networks with a small sensing
time b , the CSMA fixed point approximates well the actual
performance of the static CSMA policy.
Consider a sequence of networks for which the number
of nodes N increases to infinity. Let L(N) be the set of all
links in the network with N nodes, and let N (N)
i be the set
of neighbours of node i. As the network size increases, we
assume that the sensing time decreases as follows.
CONCLUSIONS
In this paper we introduced the CSMA fixed point approximation
to study static CSMA schedulers in wireless
networks with primary interference, and showed that the
approximation is asymptotically accurate for large networks
with a small sensing time. There are three important issues
that are not addressed in this paper, but are being investigated
in our ongoing work. First, while we showed that the
CSMA fixed point approximation is asymptotically accurate,
we did not investigate “how large” a network.