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 system’s 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.

The recent problem of network resource allocation is studied where pairs of users could be in a favourable situation, given that the allocation scheme is refined by some add-on technology. The general question here is whether the additional effort can be effective with regard to the user’s experience of fairness. The computational approach proposed in this paper to handle this question is based on the framework of relational optimization. For representing different weightings for different pairs of users, the use of a fuzzy measure appears to be reasonable. The generalized Choquet integrals are discussed from the viewpoint of representing fairness and it is concluded that the asymmetric Choquet integral is the most suitable approach. A binary relation using the asymmetric Choquet integral is proposed. In case of a supermodular fuzzy measure, this is a transitive and cycle-free relation. The price of fairness with regard to a wireless channel allocation problem taking channel interference into account is experimentally studied and it can be seen that the asymmetric on relation actually selects allocations that perform on average between maxmin fairness and proportional fairness, and being more close to maxmin fairness as long as channel interference is not high.

We consider an auction design problem under network flow constraints. We focus on pricing mechanisms that provide fair solutions, where fairness is defined in absolute and relative terms. The absolute fairness is equivalent to “no individual losses” assumption. The relative fairness can be verbalized as follows: no agent can be treated worse than any other in similar circumstances. Ensuring the fairness conditions makes only part of the social welfare available in the auction to be distributed on pure market rules. The rest of welfare must be distributed without market rules and constitutes the so-called price of fairness. We prove that there exists the minimum of price of fairness and that it is achieved when uniform unconstrained market price is used as the base price. The price of fairness takes into account costs of forced offers and compensations for lost profits. The final payments can be different than locational marginal pricing. That means that the widely applied locational marginal pricing mechanism does not in general minimize the price of fairness.

The paper presents a method for optimising the wireless optical network that carries elastic packet traffic. The particular focus is on modelling the effect of elastic traffic flows slowing down in response to the decrease of the optical transmission systems’ capacity at bad weather conditions. A mathematical programming model of the network design problem is presented that assumes that the packet rates of elastic traffic flows decrease fairly. While practically any subset of network links can be simultaneously affected by unfavourable transmission conditions, a particular challenge of solving the problem results from a huge number of network states considered in the model. Therefore, how the problem can be solved by generating the most unfavourable network states is presented. Moreover, it is proved that it is entirely sufficient to consider only the states that correspond to the decrease of capacity on a single link. Finally, as the general problem is nonlinear, it is shown that the problem can be transformed to a linear MIP problem and solved effectively when single-path routing of traffic flows is assumed.

This paper addresses first the problem of max-min fair (MMF) link transmissions in wireless sensor networks (WSNs) and in a second stage studies the joint link scheduling and transmission power assignment problem. Given a set of concurrently transmitting links, the MMF link transmission problem looks for transmission powers of nodes such that the signal-to-interference and noise ratio (SINR) values of active links satisfy max-min fairness property. By guaranteeing a “fair” transmission medium (in terms of SINR), other network requirements may be directly affected, such as the schedule length, the throughput (number of concurrent links in a time slot), and energy savings. Hence, the whole problem seeks to find a feasible schedule and a power assignment scheme such that the schedule length is minimized and the concurrent transmissions have a fair quality in terms of SINR. The focus of this study falls on the transmission power control strategy, which ensures that every node that is transmitting in the network chooses a transmission power that will minimally affect the other concurrent transmissions and, even more, achieves MMF SINR values of concurrent link transmissions. We show that this strategy may have an impact on reducing the network time schedule.

We present a new approximation algorithm to the discrete facility location problem providing solutions that are close to the lexicographic minimax optimum. The lexicographic minimax optimum is a concept that allows to find equitable location of facilities serving a large number of customers. The algorithm is independent of general purpose solvers and instead uses algorithms originally designed to solve the $p$-median problem. By numerical experiments, we demonstrate that our algorithm allows increasing the size of solvable problems and provides high-quality solutions. The algorithm found an optimal solution for all tested instances where we could compare the results with the exact algorithm.

Network quality of experience (QoE) metrics are proposed in order to capture the overall performance of radio resource management (RRM) algorithms in terms of video quality perceived by the end users. Metrics corresponding to average, geometric mean, and minimum QoE in the network are measured when Max C/I, proportional fair, and Max-Min RRM algorithms are implemented in the network. The objective is to ensure a fair QoE for all users in the network. In our study, we investigate both the uplink (UL) and downlink (DL) directions, and we consider the use of distributed antenna systems (DASs) to enhance the performance. The performance of the various RRM methods in terms of the proposed network QoE metrics is studied in scenarios with and without DAS deployments. Results show that a combination of DAS and fair RRM algorithms can lead to significant and fair QoE enhancements for all the users in the network.

Developing effective, fairness-preserving optimization algorithms is of considerable importance in systems which serve many users. In this paper we show the results of the threshold accepting procedure applied to extremely difficult problem of fair resource allocation in wireless mesh networks (WMN). The fairness is modeled by allowing preferences with regard to distribution of Internet traffic between network participants. As aggregation operator we utilize weighted ordered weighted averaging (WOWA). In the underlaying optimization problem, the physical medium properties cause strong interference among simultaneously operating node devices, leading to nonlinearities in the mixed-integer pricing subproblem. That is where the threshold accepting procedure is applied. We show that, the threshold accepting heuristic performs much better than the widely utilized simulated annealing algorithm.

We show an impact of using interference cancelation mechanisms for signals that have been overheard in the past on performance of fair wireless mesh networks. In our research we show that even in those very restricted conditions and max-min cost function, the idea of interference cancelation can significantly increase the capacity of such networks. In order to approximate possible advantages of using interference cancelation in the considered conditions, we propose a novel MIP model that allows for calculating perfect scheduling and maximal throughput in a network. We compare the results with cases when the interference cancelation mechanisms are disabled. Our results show that using interference cancelation mechanisms for signals that have been overheard in the past increases a network throughput by 40% on average in approximately 20% of test cases.

Extensive research in the field of telecommunications has been done on the techniques of multipath routing, as they offer many advantages over conventional single-path routing methods. Some of these techniques make use of the so-called Destination-Oriented Directed Acyclic Graphs (DODAGs) which are constructed on the networks, usually in a distributed way. However, while defining methods of forming DODAGs, the authors of multipath algorithms tend to overlook a possibly significant issue which could, in a way, define the quality of a given DODAG in the context of multipath routing, namely, providing an equitable distribution of the paths between the nodes in the newly created DODAG. In this paper, a few requirements for constructing a “fair” DODAG are identified in the context of multipath routing. An optimization algorithm that tries to find an equitable solution according to these requirements is also presented. Three DODAG-creation algorithms that appear in the literature are simulated and compared against this equitable solution, and none of them is getting close to it in terms of fairness in the distribution of the paths. Moreover, two interesting properties of equitable solutions are revealed in the simulations.

In multibeam satellite communication systems it is important to improve the utilization efficiency of the power resources, due to the scarcity of satellite power resources. The interbeam interference between the beams must be considered in the power allocation; therefore, it is important to optimize the power allocated to each beam in order to improve the total system performance. Initially the power allocation problem is formulated as a nonlinear optimization, considering a compromise between the maximization of total system capacity and the fairness of the power allocation amongst the beams. A dynamic power allocation algorithm based on duality theory is then proposed to obtain a locally optimal solution for the optimization problem. Compared with traditional power allocation algorithms, this proposed dynamic power allocation algorithm improves the fairness of the power allocation amongst the beams, and, in addition, the proposed algorithm also increases the total system capacity in certain scenarios.