140 research outputs found
Efficient Distributed Medium Access
Consider a wireless network of n nodes represented by a graph G=(V, E) where
an edge (i,j) models the fact that transmissions of i and j interfere with each
other, i.e. simultaneous transmissions of i and j become unsuccessful. Hence it
is required that at each time instance a set of non-interfering nodes
(corresponding to an independent set in G) access the wireless medium. To
utilize wireless resources efficiently, it is required to arbitrate the access
of medium among interfering nodes properly. Moreover, to be of practical use,
such a mechanism is required to be totally distributed as well as simple. As
the main result of this paper, we provide such a medium access algorithm. It is
randomized, totally distributed and simple: each node attempts to access medium
at each time with probability that is a function of its local information. We
establish efficiency of the algorithm by showing that the corresponding network
Markov chain is positive recurrent as long as the demand imposed on the network
can be supported by the wireless network (using any algorithm). In that sense,
the proposed algorithm is optimal in terms of utilizing wireless resources. The
algorithm is oblivious to the network graph structure, in contrast with the
so-called `polynomial back-off' algorithm by Hastad-Leighton-Rogoff (STOC '87,
SICOMP '96) that is established to be optimal for the complete graph and
bipartite graphs (by Goldberg-MacKenzie (SODA '96, JCSS '99))
Interference Queueing Networks on Grids
Consider a countably infinite collection of interacting queues, with a queue
located at each point of the -dimensional integer grid, having independent
Poisson arrivals, but dependent service rates. The service discipline is of the
processor sharing type,with the service rate in each queue slowed down, when
the neighboring queues have a larger workload. The interactions are translation
invariant in space and is neither of the Jackson Networks type, nor of the
mean-field type. Coupling and percolation techniques are first used to show
that this dynamics has well defined trajectories. Coupling from the past
techniques are then proposed to build its minimal stationary regime. The rate
conservation principle of Palm calculus is then used to identify the stability
condition of this system, where the notion of stability is appropriately
defined for an infinite dimensional process. We show that the identified
condition is also necessary in certain special cases and conjecture it to be
true in all cases. Remarkably, the rate conservation principle also provides a
closed form expression for the mean queue size. When the stability condition
holds, this minimal solution is the unique translation invariant stationary
regime. In addition, there exists a range of small initial conditions for which
the dynamics is attracted to the minimal regime. Nevertheless, there exists
another range of larger though finite initial conditions for which the dynamics
diverges, even though stability criterion holds.Comment: Minor Spell Change
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