Dritan Nace

Max-min fairness and its applications to routing and load-balancing in communication networks: a tutorial

This tutorial is devoted to the notion of max-min fairness (MMF), associated optimization problems, and their applications to multi-commodity flow networks.We first introduce a theoretical background for a generic MMF optimization problem and discuss its relation to lexicographic optimization. We next present resolution algorithms for convex MMF optimization, and analyze their properties. In the second half of the tutorial we discuss its applications to communication networks, in particular to routing and load-balancing. We state several properties with respect to each of the studied problems and analyze the behavior of the algorithms.

A robust approach to the chance-constrained knapsack problem

In this paper, the chance-constrained knapsack problem (CKP) is addressed. Relying on robust optimization, a tractable combinatorial algorithm is proposed to solve approximately CKP. For two specific classes of uncertain knapsack problems, it is proved to solve CKP at optimality.

Max-min fairness in multi-commodity flows

In this paper, we provide a study of Max-Min Fair (MMF) multi-commodity flows and focus on some of their applications to multi-commodity networks. We first present the theoretical background for the problem of MMF and recall its relations with lexicographic optimization as well as a polynomial approach for achieving leximin maximization. We next describe two applications to telecommunication networks, one on routing and the second on load-balancing. We provide some deeper theoretical analysis of MMF multi-commodity flows, show how to solve the lexicographically minimum load network problem for the link load functions most frequently used in telecommunication networks. Some computational results illustrate the behavior of the obtained solutions and the required CPU time for a range of random and well-dimensioned networks.

Computing optimal max-min fair resource allocation for elastic flows

In this paper, we consider the max-min fair resource allocation problem as applied to elastic flows. We are interested in computing the optimal max-min fair rate allocation. The proposed approach is a linear programming based one and allows the computation of optimal routing paths with regard to max-min fairness, in stable and known traffic conditions. We consider nonbounded access rates, but we show how the proposed approach can handle the case of upper-bounded access rates. A proof of optimality and some computational results are also presented.

A linear programming based approach for computing optimal fair splittable routing

We consider the fair flow problem in a multiple source multiple sink network, as applied to telecommunication networks. We present an iterative algorithm for computing fair routing in networks where the available resources are shared among competing flows according to a max-min fair sharing criterion. Our main objective is computing optimal routing paths, with regard to max-min fairness, in stable and known traffic conditions. It is a linear programming based approach which permits a lexicographical maximization of the vector of fair-share attributed to the connections competing for network resources. An optimality proof and some computational results are also presented.

Fair Optimization and Networks: A Survey

Optimization models related to designing and operating complex systems are mainly focused on some efficiency metrics such as response time, queue length, throughput, and cost. However, in systems which serve many entities there is also a need for respecting fairness: each system entity ought to be provided with an adequate share of the systems services. Still, due to system operations-dependant constraints, fair treatment of the entities does not directly imply that each of them is assigned equal amount of the services. That leads to concepts of fair optimization expressed by the equitable models that represent inequality averse optimization rather than strict inequality minimization; a particular widely applied example of that concept is the so-called lexicographic maximin optimization (max-min fairness). The fair optimization methodology delivers a variety of techniques to generate fair and efficient solutions. This paper reviews fair optimization models and methods applied to systems that are based on some kind of network of connections and dependencies, especially, fair optimization methods for the location problems and for the resource allocation problems in communication networks.

On a resource-constrained scheduling problem with application to distributed systems reconfiguration

This paper is devoted to the study of a resource-constrained scheduling problem, the Process Move Programming problem, which arises in relation to the operability of certain high availability real-time distributed systems. Informally, this problem consists, starting from an arbitrary initial distribution of processes on the processors of a distributed system, in finding the least disruptive sequence of operations (non-impacting process migrations or temporary process interruptions) at the end of which the system ends up in another predefined arbitrary state. The main constraint is that the capacity of the processors must not be exceeded during the reconfiguration. After a brief survey of the literature, we prove the NP-hardness of the problem and exhibit a few polynomial special cases. We then present a branch-and-bound algorithm for the general case along with computational results demonstrating its practical relevance. The paper is concluded by a discussion on further research.

Optimization Problems in Wireless Sensor Networks

The Wireless Sensor Networks (WSNs) design related questions give rise to new complex and difficult theoretical problems and challenges in operations research and optimization areas. As WSNs become increasingly pervasive, a good understanding of these problems in terms of theoretical complexity is of great help in designing appropriate algorithms. In this paper, we examine some of the most fundamental optimization problems related to coverage, topology control, scheduling, routing and mobility in WSNs. Then we focus on their complexity and analyze the differences that exist with the counter part conventional theoretical problems or those already studied in traditional networks. We present as well some of the main methods proposed in the literature and report some open issues regarding these problems.

Review of Optimization Problems in Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are an interesting field of research because of their numerous applications and the possibility of integrating them into more complex network systems. The difficulties encountered in WSN design usually relate either to their stringent constraints, which include energy, bandwidth, memory and computational capabilities, or to the requirements of the particular application. As WSN design problems become more and more challenging, advances in the areas of Operations Research (OR) and Optimization are becoming increasingly useful in addressing them.

Two-stage hybrid flow shop with precedence constraints and parallel machines at second stage

This study deals with the two-stage hybrid flow shop (HFS) problem with precedence constraints. Two versions are examined, the classical HFS where idle time between the operations of the same job is allowed and the no-wait HFS where idle time is not permitted. For solving these problems an adaptive randomized list scheduling heuristic is proposed. Two global bounds are also introduced so as to conservatively estimate the distance to optimality of the proposed heuristic. The evaluation is done on a set of randomly generated instances. The heuristic solutions for the classical HFS in average are provably situated below 2% from the optimal ones, and on the other hand, in the case of the no-wait HFS the average deviation is below 5%. Highlights? We study the hybrid flow shop problem with precedence relations. ? An adaptive randomized list scheduling heuristic is proposed. ? Two global lower bounds are examined. ? Distance to the optimum, in average, is under 5% for randomly generated instances.