nan Karmeshu

Queue length distribution of network packet traffic: Tsallis entropy maximization with fractional moments

A framework based on maximization of Tsallis entropy constrained by fractional moments is proposed to model queue length distribution of number of packets in network traffic exhibiting long-range behavior. For appropriate range of the Tsallis entropy parameter q, it is found that the first moment of number of packets may not exist Based on Euler summation formula, explicit expressions for mean queue length and buffer overflow probability exhibiting power law behavior are obtained. It is shown that in the limiting case as q tends to 1, one recovers the asymptotic results for buffer overflow probability depicting Weibull-like tail.

Study of population heterogeneity in innovation diffusion model: Estimation based on simulated annealing

Abstract Parameter variability randomness in diffusion (PVRD) models based on random differential equations have recently been developed to study stochastic evolution of adopters. Analysis of such models is found to generate multimodal life cycle patterns (or intervening slumps) besides the conventional unimodal pattern. Application of these models to real data sets necessitate estimation of parameters of the model. Nonlinear least squares estimation problem is formulated to deal with the minimization of high-dimensional cost function. Using the simulated annealing (SA) framework, effectiveness of the estimation approach and the fitting algorithm is demonstrated in terms of “fit statistics.” An important finding from empirical studies reveal that even in unimodal life cycle patterns, parameters of innovation diffusion process are found to possess considerable variability. This finding amply demonstrates the presence of heterogeneity on account of population variability.

Power Law and Tsallis Entropy: Network Traffic and Applications

Summary. A theoretical framework based on non-extensive Tsallis entropy is proposed to study the implication of long-range dependence in traffic process on network performance. Highlighting the salient features of Tsallis entropy, the axiomatic foundations of parametric entropies are also discussed. Possible application of nonextensive thermodynamics to study the macroscopic behavior of broadband network is outlined.

q-Exponential product-form solution of packet distribution in queueing networks: maximization of Tsallis entropy

A maximum Tsallis entropy solution is presented to examine the effect of long-range dependence (LRD) of packet traffic on network of queues. An important finding is that usual product form solution of queueing networks does not hold. However, it is possible to preserve the product like structure in terms of q-product of q-exponential functions. A special case is considered when normalized q-expectation values of first moment and queue utilization at each node are available as the constraint. The joint state probability distribution is shown to depict asymptotically power law behavior

Optimal parameter trajectory estimation in parameterized SDEs: An algorithmic procedure

We consider the problem of estimating the optimal parameter trajectory over a finite time interval in a parameterized stochastic differential equation (SDE), and propose a simulation-based algorithm for this purpose. Towards this end, we consider a discretization of the SDE over finite time instants and reformulate the problem as one of finding an optimal parameter at each of these instants. A stochastic approximation algorithm based on the smoothed functional technique is adapted to this setting for finding the optimal parameter trajectory. A proof of convergence of the algorithm is presented and results of numerical experiments over two different settings are shown. The algorithm is seen to exhibit good performance. We also present extensions of our framework to the case of finding optimal parameterized feedback policies for controlled SDE and present numerical results in this scenario as well.

Bimodal packet distribution in loss systems using maximum Tsallis entropy principle

A theoretical model of loss system is proposed and analysed within the framework of maximum Tsallis entropy principle. The study provides an explicit expression for state probability distribution of packets in presence of long-range dependent traffic. The unimodal state probability distribution corresponding to well-known Erlangs loss formula is recovered for Tsallis entropy parameter q = 1. As the parameter q is lowered from unity, it is shown that the state probability distribution makes a transition from unimodal to bimodal. The emergence of bimodality can be regarded as a consequence of long-range dependence. The implication of the model in the design of loss systems is discussed.

Adaptive mean queue size and its rate of change: queue management with random dropping

The random early detection active queue management (AQM) scheme uses the average queue size to calculate the dropping probability in terms of minimum and maximum thresholds. The effect of heavy load enhances the frequency of crossing the maximum threshold value resulting in frequent dropping of the packets. An adaptive queue management with random dropping algorithm is proposed which incorporates information not just about the average queue size but also the rate of change of the same. Introducing an adaptively changing threshold level that falls in between lower and upper thresholds, our algorithm demonstrates that these additional features significantly improve the system performance in terms of throughput, average queue size, utilization and queuing delay in relation to the existing AQM algorithms.

On Identifying Marker Genes from Gene Expression Data in a Neural Framework through Online Feature Analysis

Many attempts have been made to analyze gene expression data. Typical goals of such analysis include discovery of subclasses, designing predictors/classifiers for diseases, identifying marker genes, and trying to get a deeper understanding of underlying biological process. Success of each of these tasks strongly depends on the features used to solve the problem. The high dimensional nature of expression profiles makes the task very difficult. Consequently, many researchers have used some feature selection criteria to reduce the dimensionality of the problem. These approaches are off‐line in nature, as feature selection is done in a separate phase from the system design phase. These approaches ignore the fact that utility of features depends on both the problem that is solved and the tool that is used to solve the problem. We here propose to use a novel neural scheme that picks up the necessary features on‐line when the system learns the classification task. Because it considers all the features at one go, it does not miss any subtle combination of these features. We demonstrate the effectiveness of our on‐line feature selection (OFS) scheme to distinguish between acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL) cancer expression data set. Our scheme could identify only five genes that can produce results as good as or even better than what is reported in the literature on this data set. It identifies an important marker gene that alone has a very good discriminating power. This analysis method is quite general in nature and can be effectively used in other areas of bioinformatics.

Transient Bimodality and Catastrophic Jumps in Innovation Diffusion

A new phenomenon in innovation diffusion that exhibits a transient bimodality familiar in physical sciences is predicted in this paper for the first time on the basis of an extended Bass model. This accounts for the population heterogeneity, with the parameters characterizing the ldquoword of mouthrdquo and ldquomass mediardquo processes as random. A theoretical framework based on a nonlinear random differential equation is thus introduced to develop a stochastic model for new product diffusion with parametric uncertainty. The analytical investigation of the model establishes the existence of transient bimodality, which manifests through a cusp catastrophe. Illustrations based on analytical and simulation studies are presented. Empirical validation of the proposed model based on well-known data sets where the Bass model is known to fit very well has been carried out.

Power Law Behavior of Queue Size: Maximum Entropy Principle with Shifted Geometric Mean Constraint

A theoretical framework based on the maximum Shannon entropy principle with the specification of geometric mean or shifted geometric mean is proposed to generate the power law behavior of the system size in broadband communication networks. It is shown that the equilibrium distribution of an M/M/1 queue is obtained as a limiting case when the shifted geometric mean is specified. The various quality-of-service parameters, such as the probability of exceeding buffer size, exhibit the power law behavior. It is noted that the results based on the Shannon entropy with shifted geometric mean are found to be similar to the results when the Tsallis entropy subject to expected number of jobs in the system is prescribed. This brings out a deeper issue of the relevance of shifted geometric mean within Shannon entropy framework when the input traffic has broadband characteristics. The proposed approach gives closed-form expressions for a queuing distribution in a much simpler way and thus establishes the efficacy of Shannon entropy in communication networks exhibiting power law.