Diffusion Approximation for a Heavily Loaded Multi-User Wireless
Communication System with Cooperation
S. Bhardwaj and
R. J. Williams
A cellular wireless communication system in which data is transmitted to
multiple users over a common channel is considered.
When the base stations in this system can cooperate with each other, the
link from the base stations to the users can be considered a multi-user
multiple-input multiple-output (MIMO) downlink system.
For such a system, it is known from information theory that the total rate
of transmission can be enhanced by cooperation.
The channel is assumed to be fixed for all transmissions over the period of
interest and the ratio of anticipated average arrival rates for the users,
also known as the relative traffic rate, is fixed.
A packet-based model is considered where data for each user is queued at the
We consider a simple policy which, under Markovian assumptions, is known to
be throughput-optimal for this coupled queueing system.
Since an exact expression for the performance of this policy is not
available, as a measure of performance, we establish a heavy traffic
To arrive at this diffusion approximation, we use two key properties
of the policy; we posit the first property as a reasonable
manifestation of cooperation and the second property follows from
coordinate convexity of the capacity region.
The diffusion process is a semimartingale reflecting Brownian motion
(SRBM) living in the positive orthant of N-dimensional space (where
N is the number of users).
Nominally, this SRBM has one direction of reflection associated with each of
the 2^N-1 boundary faces.
We show that, in fact, only those directions associated with the
(N-1)-dimensional boundary faces matter for the heavy traffic limit.
The latter is likely of independent theoretical interest.
In Queueing Systems, 62 (2009), 345-382.
For a copy of a preprint for personal, scientific, non commercial use,
click here for pdf.
Last updated: August 14, 2008