University of Oulu

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.

Dual methods for optimal allocation of telecommunication network resources with several classes of users

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Author: Konnov, Igor1,2; Kashuba, Aleksey2; Laitinen, Erkki3
Organizations: 1Department of System Analysis and Information Technologies, Kazan Federal University, Kazan 420008, Russia
2Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Kazan 420008, Russia
3Faculty of Science, University of Oulu, FI-90014 Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: Multidisciplinary Digital Publishing Institute, 2018
Publish Date: 2019-01-30


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.

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Series: Mathematical and computational applications
ISSN: 2297-8747
ISSN-E: 2297-8747
ISSN-L: 2297-8747
Volume: 23
Issue: 2
Article number: 31
DOI: 10.3390/mca23020031
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: I.K. and A.K. were supported by the RFBR grant, project No. 16-01-00109a. Also, I.K. and E.L. were supported by grants No. 315471 and No. 315366 from Academy of Finland.
Academy of Finland Grant Number: 315471
Detailed Information: 315471 (Academy of Finland Funding decision)
315366 (Academy of Finland Funding decision)
Copyright information: © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (