185 research outputs found
Large deviations of max-weight scheduling policies on convex rate regions
Abstract—We consider a single server discrete-time system with K users where the server picks operating points from a compact, convex and co-ordinate convex set in ℜ K +. For this system we analyse the performance of a stablising policy that at any given time picks operating points from the allowed rate region that maximise a weighted sum of rate, where the weights depend upon the workloads of the users. Assuming a Large Deviations Principle (LDP) for the arrival processes in the Skorohod space of functions that are right-continuous with left-hand limits we establish an LDP for the workload process using a generalised version of the contraction principle to derive the corresponding rate function. With the LDP result available we then analyse the tail probabilities of the workloads under different buffering scenarios. I
Many-Sources Large Deviations for Max-Weight Scheduling
In this paper, a many-sources large deviations principle (LDP) for the
transient workload of a multi-queue single-server system is established where
the service rates are chosen from a compact, convex and coordinate-convex rate
region and where the service discipline is the max-weight policy. Under the
assumption that the arrival processes satisfy a many-sources LDP, this is
accomplished by employing Garcia's extended contraction principle that is
applicable to quasi-continuous mappings.
For the simplex rate-region, an LDP for the stationary workload is also
established under the additional requirements that the scheduling policy be
work-conserving and that the arrival processes satisfy certain mixing
conditions.
The LDP results can be used to calculate asymptotic buffer overflow
probabilities accounting for the multiplexing gain, when the arrival process is
an average of \emph{i.i.d.} processes. The rate function for the stationary
workload is expressed in term of the rate functions of the finite-horizon
workloads when the arrival processes have \emph{i.i.d.} increments.Comment: 44 page
Max-min Fairness in 802.11 Mesh Networks
In this paper we build upon the recent observation that the 802.11 rate
region is log-convex and, for the first time, characterise max-min fair rate
allocations for a large class of 802.11 wireless mesh networks. By exploiting
features of the 802.11e/n MAC, in particular TXOP packet bursting, we are able
to use this characterisation to establish a straightforward, practically
implementable approach for achieving max-min throughput fairness. We
demonstrate that this approach can be readily extended to encompass time-based
fairness in multi-rate 802.11 mesh networks
On a class of optimal rateless codes
Abstract—In this paper we analyze a class of systematic fountain/rateless codes constructed using Bernoulli(1/2) random variables. Using simple bounds we then show that this class of codes stochastically minimizes the number of coded packets receptions needed to successfully decode all the information packets. This optimality holds over a large class of random codes that includes Bernoulli(q) random codes with q ≤ 1/2 and LT codes. We then conclude by demonstrating asymptotic optimality for intermediate decoding of the same codes. I
- …