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

Igor Konnov,Aleksey Kashuba,Erkki Laitinen

doi:10.3390/mca23020031

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.

Highlights

Efficient allocation of limited resources in communication networks require flexible mechanisms, which are based on proper mathematical models, since the conventional fixed allocation rules may lead to congestion effects and additional expenses from the inefficient utilization of network resources; see e.g., [1,2,3]
The general problem of the network manager is to find an optimal allocation of the limited homogeneous resource among the users in order to maximize the total payment received from the users and minimize the total network implementation expenses
We considered a general problem of optimal allocation of a homogeneous resource in a wireless telecommunication network with several levels of service

Summary

Introduction

Efficient allocation of limited resources in communication networks require flexible mechanisms, which are based on proper mathematical models, since the conventional fixed allocation rules may lead to congestion effects and additional expenses from the inefficient utilization of network resources; see e.g., [1,2,3]. In [10,11,12,13,14,15], several optimal resource allocation problems in telecommunication networks and proper zonal decomposition-based methods were suggested. They assumed that the network manager can satisfy all the varying user requirements or can buy additional volumes of the resource. This approach leads to constrained convex optimization problem for some selected time period. The comparison shows the advantage of proposed methods over the conventional ones

Problem Formulation

Solution Methods

Numerical Experiments

Conclusions