Showing papers by "Ravi R. Mazumdar published in 2012"

Delay minimization in multihop wireless networks: Static scheduling does it

Abstract: In this paper, we address two issues in multihop wireless networks—poor end-to-end delay performance and high per-slot computational overhead of the classical max-weight algorithm. To reduce the end-to-end delay, we first propose a simple modification to the classical maximum weight scheduling algorithm that promotes the use of shorter paths by the packets. The significantly lower delays are shown via simulation. The modification that we suggest does not reduce the schedulable region and has the same complexity as the classical algorithm. Next, we propose a static routing and scheduling scheme that is obtained by adapting the classical optimal routing problem of wireline networks to multihop wireless networks. The static scheme slows the timescale of routing and scheduling computations from per-slot to the timescale of change in the network traffic pattern; thus the computation complexity is reduced. We also show, via simulations, that the delay performance in the static scheme is comparable to that of the dynamic scheme that we have proposed.

Processor sharing and pricing implications

Abstract: We study pricing models for bandwidth sharing that do not depend on detailed statistical knowledge of network traffic. For a multiclass, processor sharing server, we show that three common pricing models, namely fixed rate pricing, Vickrey-Clarke-Groves pricing, and congestion-based pricing, are linked to the zeroth, first, and second moments, respectively, of the number of users in the system. We derive expressions for these quantities and provide insights into the operator's revenue and user payments.

Predictable revenue under processor sharing

Abstract: This paper considers the case of a single service provider employing processor sharing discipline and serving randomly arriving users with random service requirements. The operator is assumed to charge a user based on the service rate allocated. The pricing mechanisms considered in this paper are the fixed rate pricing, Vickrey-Clarke-Groves (VCG) auctions, and congestion-based pricing (or the Lagrange shadow prices). Under such a model, we explicitly calculate the mean revenue of the operator and the mrean payments made by the users by exploiting the property of insensitivity associated with processor sharing. We also consider the effect of imposing a minimum rate requirement of a user on the revenue (a Quality of Service constraint). This paper presents our results and draws insights on the structure of the mean user payments and on the relation between the mean operator revenue and the zeroth, first, and the second moment of the total number of users present in the system under the three pricing mechanisms.

Heavy traffic approximation for the stationary distribution of stochastic fluid networks

Abstract: It has recently been shown that in the heavy traffic limit, the stationary distribution of the scaled queue length process of a Generalized Jackson Network converges to the stationary distribution of its corresponding Reflected Brownian Motion limit. In this paper, we show that this "interchange of limits" is valid for Stochastic Fluid Networks with Levy inputs. Furthermore, under additional assumptions, we extend the result to show that the interchange is valid for moments of the stationary distribution and for state-dependent routing. The results are obtained using monotonicity and sample-path arguments.

On the convergence of the spectral density of autoregressive approximations via empirical covariance estimates

Abstract: The problem of estimating discrete time stochastic processes by autoregressive models is encountered in many applications In most practical scenarios, the autoregressive model is derived using estimated values of the covariance sequence (known as the sample covariance) in lieu of the actual covariance sequence of the process The present paper explores the asymptotic behavior of the spectral density of such approximations, as both the number of samples N and the model order p approach infinity It is shown that under certain mild assumptions, when p= o{N1 over 3}, spectral density of the approximating autoregressive sequence converges at the origin in mean It is also shown that under the same condition, the spectral density of the autoregressive approximation converges in mean with respect to an L2 norm