Next Article in Journal
Total Controllability of the Second Order Semi-Linear Differential Equation with Infinite Delay and Non-Instantaneous Impulses
Previous Article in Journal
A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction
Previous Article in Special Issue
The Impact of the Implementation Cost of Replication in Data Grid Job Scheduling
Article Menu
Issue 2 (June) cover image

Export Article

Open AccessArticle
Math. Comput. Appl. 2018, 23(2), 31; https://doi.org/10.3390/mca23020031

Dual Methods for Optimal Allocation of Telecommunication Network Resources with Several Classes of Users

1
Department of System Analysis and Information Technologies, Kazan Federal University, Kazan 420008, Russia
2
Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Kazan 420008, Russia
3
Faculty of Science, University of Oulu, FI-90014 Oulu, Finland
*
Author to whom correspondence should be addressed.
Received: 6 May 2018 / Revised: 11 June 2018 / Accepted: 14 June 2018 / Published: 17 June 2018
(This article belongs to the Special Issue Applied Modern Mathematics in Complex Networks)
Full-Text   |   PDF [293 KB, uploaded 19 June 2018]

Abstract

We consider a general problem of optimal allocation of limited resources in a wireless telecommunication network. The network users are divided into several different groups (or classes), which correspond to different levels of service. The network manager must satisfy these different users’ requirements. This approach leads to a convex optimization problem with balance and capacity constraints. We present several decomposition type methods to find a solution to this problem, which exploit its special features. We suggest applying first the dual Lagrangian method with respect to the total capacity constraint, which gives the one-dimensional dual problem. However, calculation of the value of the dual cost function requires solving several optimization problems. Our methods differ in approaches for solving these auxiliary problems. We consider three basic methods: Dual Multi Layer (DML), Conditional Gradient Dual Multilayer (CGDM) and Bisection (BS). Besides these methods we consider their modifications adjusted to different kind of cost functions. Our comparison of the performance of the suggested methods on several series of test problems show satisfactory convergence. Nevertheless, proper decomposition techniques enhance the convergence essentially. View Full-Text
Keywords: telecommunication networks; wireless networks; service levels; resource allocation; optimization problem; decomposition methods; Lagrange duality telecommunication networks; wireless networks; service levels; resource allocation; optimization problem; decomposition methods; Lagrange duality
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Konnov, I.; Kashuba, A.; Laitinen, E. Dual Methods for Optimal Allocation of Telecommunication Network Resources with Several Classes of Users. Math. Comput. Appl. 2018, 23, 31.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top