Srikanth K. Iyer

Improved genetic algorithm for the permutation flowshop scheduling problem

Genetic algorithms (GAs) are search heuristics used to solve global optimization problems in complex search spaces. We wish to show that the efficiency of GAs in solving a flowshop problem can be improved significantly by tailoring the various GA operators to suit the structure of the problem. The flowshop problem is one of scheduling jobs in an assembly line with the objective of minimizing the completion time or makespan. We compare the performance of CA using the standard implementation and a modified search strategy that tries to use problem specific information. We present empirical evidence via extensive simulation studies supported by statistical tests of improvement in efficiency.

Approximate self consistency for middle-censored data

Middle censoring refers to data that becomes unobservable if it falls within a random interval. The lifetime distribution of such data is defined via the self-consistency equation. We propose an approximation to this distribution function for which an estimator and its asymptotic properties are very easy to establish.

Topological properties of random wireless networks

Wireless networks in which the node locations are random are best modelled as random geometric graphs (RGGs). In addition to their extensive application in the modelling of wireless networks, RGGs find many new applications and are being studied in their own right. In this paper we first provide a brief introduction to the issues of interest in random wireless networks. We then discuss some recent results for one-dimensional networks with the nodes distributed uniformly in (0,z). We then discuss some asymptotic results for networks in higher dimensions when the nodes are distributed in a finite volume. Finally we discuss some recent generalisations in considering non uniform transmission ranges and non uniform node distributions. An annotated bibliography of some of the recent literature is also provided.

Evolving Random Geometric Graph Models for Mobile Wireless Networks

We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.

Queues with Dependency Between Interarrival and Service Times Using Mixtures of Bivariates

We analyze queueing models where the joint density of the interarrival time and the service time is described by a mixture of joint densities. These models occur naturally in multiclass populations serviced by a single server through a single queue. Other motivations for this model are to model the dependency between the interarrival and service times and consider queue control models. Performance models with component heavy tailed distributions that arise in communication networks are difficult to analyze. However, long tailed distributions can be approximated using a finite mixture of exponentials. Thus, the models analyzed here provide a tool for the study of performance models with heavy tailed distributions. The joint density of A and X, the interarrival and service times respectively, f(a,x), will be of the form where p i > 0 and . We derive the Laplace Stieltjes Transform of the waiting time distribution. We also present and discuss some numerical examples to describe the effect of the various parameters of the model.

On the clustering properties of exponential random networks

We consider the clustering properties of one-dimensional sensor networks where the nodes are randomly deployed. Unlike most other work on randomly deployed networks, ours assumes that the node locations are drawn from a non uniform distribution. Specifically, we consider an exponential distribution. We first obtain the probability that there exists a path between two labeled nodes in a randomly deployed network and obtain the limiting behavior of this probability. The probability mass function (pmf) for the number of components in the network is then obtained. We show that the number of components in the network converges in distribution. We also derive the probabilities for different locations of the components. We then obtain the probability for the existence of a k-sized component and components of size /spl ges/k. Asymptotics in the number of nodes in the network are computed for these probabilities. An interesting result is that, as the number of nodes, n, in the network tends to infinity, a giant component, in which a specific fraction, /spl alpha/, of the nodes form a component, almost surely does not exist for any 0</spl alpha/<1. However, the probability converges to a non-zero value for /spl alpha/=1. Another result is that for 0</spl alpha/<1, we can find an n/sub 0/ such that for n>n/sub 0/, the network almost surely does not have a giant component.

Correlated Bivariate Sequences for Queueing and Reliability Applications

Abstract We derive bivariate exponential, gamma, Coxian or hyperexponential distributions. To obtain a positive correlation, we define a linear relation between the variates X and Y of the form Y = aX + Z where a is a positive constant and Z is independent of X. By fixing the marginal distributions of X and Y, we characterize the distribution of Z. To obtain negative correlations, we define X = aP + V and Y = bQ + W where P and Q are exponential antithetic random variables. Our bivariate models are useful in introducing dependence between the interarrivals and service times in a queueing model and in the failure process in multicomponent systems. The primary advantage of our model in the context of queueing analysis is that it remains mathematically tractable because the Laplace Transform of the joint distribution is a rational function, that is a ratio of polynomials. Further, the variates can be very easily generated for computer simulation. These models can also be used for the study of transmission controlled queueing networks.

Estimation of frequencies in presence of heavy tail errors

In this paper, we consider the problem of estimating the sinusoidal frequencies in presence of additive white noise. The additive white noise has mean zero but it may not have finite variance. We propose to use the least-squares estimators or the approximate least-squares estimators to estimate the unknown parameters. It is observed that the least-squares estimators and the approximate least-squares estimators are asymptotically equivalent and both of them provide consistent estimators of the unknown parameters. We obtain the asymptotic distribution of the least-squares estimators under the assumption that the errors are from a symmetric stable distribution. We propose different methods of constructing confidence intervals and compare their performances through Monte Carlo simulations. We also discuss the properties of the estimators if the errors are correlated and finally we discuss some open problems.

In-Network Computation in Random Wireless Networks: A PAC Approach to Constant Refresh Rates with Lower Energy Costs

We propose a method to compute a probably approximately correct (PAC) normalized histogram of observations with a refresh rate of Θ(1) time units per histogram sample on a random geometric graph with noise-free links. The delay in computation is Θ(√n) time units. We further extend our approach to a network with noisy links. While the refresh rate remains Θ(1) time units per sample, the delay increases to Θ(√n log n). The number of transmissions in both cases is Θ(n) per histogram sample. The achieved Θ(1) refresh rate for PAC histogram computation is a significant improvement over the refresh rate of Θ(1/log n) for histogram computation in noiseless networks. We achieve this by operating in the supercritical thermodynamic regime where large pathways for communication build up, but the network may have more than one component. The largest component however will have an arbitrarily large fraction of nodes in order to enable approximate computation of the histogram to the desired level of accuracy. Operation in the supercritical thermodynamic regime also reduces energy consumption. A key step in the proof of our achievability result is the construction of a connected component having bounded degree and any desired fraction of nodes. This construction may also prove useful in other communication settings on the random geometric graph.

Criticality of the exponential rate of decay for the largest nearest-neighbor link in random geometric graphs

Let n points be placed independently in d-dimensional space according to the density f(x) = A d e−λ||x||α , λ, α > 0, x ∈ ℝ d , d ≥ 2. Let d n be the longest edge length of the nearest-neighbor graph on these points. We show that (λ−1 log n)1−1/α d n - b n converges weakly to the Gumbel distribution, where b n ∼ ((d − 1)/λα) log log n. We also prove the following strong law for the normalized nearest-neighbor distance d̃ n = (λ−1 log n)1−1/α d n / log log n: (d − 1)/αλ ≤ lim inf n→∞ d̃ n ≤ lim sup n→∞ d̃ n ≤ d/αλ almost surely. Thus, the exponential rate of decay α = 1 is critical, in the sense that, for α > 1, d n → 0, whereas, for α ≤ 1, d n → ∞ almost surely as n → ∞.