Conjugate Gradient Method Approach to Multi-Channel Queuing Theory

In this paper we examine the application of the classical conjugate gradient method to queue theory. The parameters of the symmetric definite positive linear operator of a quadratic cost functional were obtained from the various characteristic features of a multi-channel queue system. The outcome was tested with numerical values and a comparison was made for systems with two, three and four service points. The numerical computations were carried out in a Maple 14 environment. The results obtained validate previous work done with a single-channel syste

An Optimal Multi-System Control Measure Using the Approach of Conjugate Gradient Algorithm (CGA)

In this paper we examine the application of the classical conjugate gradient method to queue theory. The parameters of the symmetric definite positive linear operator of a quadratic cost functional were obtained from the various characteristic features of a multi-channel queue system. The outcome was tested with numerical values and a comparison was made for systems with two, three and four service points. The numerical computations were carried out in a Maple 14 environment. The results obtained validate previous work done with a singlechannel syste

Distributed Large Scale Network Utility Maximization

Recent work by Zymnis et al. proposes an efficient primal-dual interior-point method, using a truncated Newton method, for solving the network utility maximization (NUM) problem. This method has shown superior performance relative to the traditional dual-decomposition approach. Other recent work by Bickson et al. shows how to compute efficiently and distributively the Newton step, which is the main computational bottleneck of the Newton method, utilizing the Gaussian belief propagation algorithm. In the current work, we combine both approaches to create an efficient distributed algorithm for solving the NUM problem. Unlike the work of Zymnis, which uses a centralized approach, our new algorithm is easily distributed. Using an empirical evaluation we show that our new method outperforms previous approaches, including the truncated Newton method and dual-decomposition methods. As an additional contribution, this is the first work that evaluates the performance of the Gaussian belief propagation algorithm vs. the preconditioned conjugate gradient method, for a large scale problem.Comment: In the International Symposium on Information Theory (ISIT) 200