Recently there has been considerable interest in the design of efficient
carrier sense multiple access(CSMA) protocol for wireless network. The basic
assumption underlying recent results is availability of perfect carrier sense
information. This allows for design of continuous time algorithm under which
collisions are avoided. The primary purpose of this note is to show how these
results can be extended in the case when carrier sense information may not be
perfect, or equivalently delayed.
Motivated by applications of distributed linear estimation, distributed
control and distributed optimization, we consider the question of designing
linear iterative algorithms for computing the average of numbers in a network.
Specifically, our interest is in designing such an algorithm with the fastest
rate of convergence given the topological constraints of the network. As the
main result of this paper, we design an algorithm with the fastest possible
rate of convergence using a non-reversible Markov chain on the given network
graph.
There has recently been considerable interest in design of low-complexity,
myopic, distributed and stable scheduling policies for constrained queueing
network models that arise in the context of emerging communication networks.
Here, we consider two representative models. One, a model for the collection of
wireless nodes communicating through a shared medium, that represents randomly
varying number of packets in the queues at the nodes of networks.