There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalisations to large-scale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum characterised by a proportional fairness criterion. Stability is established by showing that, with an appropriate formulation of the overall optimisation problem, the network's implicit objective function provides a Lyapunov function for the dynamical system defined by the rate control algorithm. The network's optimisation problem may be cast in primal or dual form: this leads naturally to two classes of algorithm, which may be interpreted in terms of either congestion indication feedback signals or explicit rates based on shadow prices. Both classes of algorithm may be generalised to include routing control, and provide natural implementations of proportionally fair pricing.

https://link.springer.com/content/pdf/10.1057%2Fpalgrave.jors.2600523.pdf

Rate control for communication networks: shadow prices, proportional fairness and stability

A survey of current continuous nonlinear multi-objective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user’s preferences, the solution requirements, and the availability of software.

Survey of multi-objective optimization methods for engineering

Human beings are described by many spiritual traditions as ‘blind’ or ‘asleep’ or ‘in a dream.’ These terms refers to the limited attenuated state of consciousness of most human beings caught up in patterns of conditioned thought, feeling and perception, which prevent the development of our latent, higher spiritual possibilities. In the words of Idries Shah: “Man, like a sleepwalker who suddenly ‘comes to’ on some lonely road has in general no correct idea as to his origins or his destiny.” In some religious traditions, such as Christianity and Islam, the myth of the ‘Fall from the Garden of Eden’ symbolizes the loss of the primordial state through the veiling of higher consciousness. Other traditions use similar metaphors to describe the spiritual condition of humanity:

The Human Condition.

In this paper, we demonstrate the existence of fair end-to-end window-based congestion control protocols for packet-switched networks with first come-first served routers. Our definition of fairness generalizes proportional fairness and includes arbitrarily close approximations of max-min fairness. The protocols use only information that is available to end hosts and are designed to converge reasonably fast. Our study is based on a multiclass fluid model of the network. The convergence of the protocols is proved using a Lyapunov function. The technical challenge is in the practical implementation of the protocols.

https://www-inst.eecs.berkeley.edu/~ee228a/fa03/228A03/papers/Mo.pdf

Fair end-to-end window-based congestion control

DDoS attacks and defense mechanisms: classification and state-of-the-art

Consideration is given to the problem of optimal flow control in a multiclass telecommunications environment where each user (or class) desires to optimize its performance while being fair to the other users (classes). The Nash (1950) arbitration scheme from game theory is shown to be a suitable candidate for a fair, optimal operation point in the sense that it satisfies certain axioms of fairness and is pareto optimal. This strategy can be realized by defining the product of individuals user performance objectives as the network optimization criterion. This provides the rationale for considering the product of user powers, as has been suggested in the literature. For delay constrained traffic, the constrained optimization problem of maximizing the product of user throughputs subject to the constraints leads to a Nash arbitration point. It is shown that these points are unique in throughput space, and the authors also obtain some convexity properties for power and delays with respect to throughputs in a Jackson network. >

Fairness in network optimal flow control: optimality of product forms

The wide utilization of Wireless Sensor Networks (WSNs) is obstructed by the severely limited energy constraints of the individual sensor nodes. This is the reason why a large part of the research in WSNs focuses on the development of energy efficient routing protocols. In this paper, a new protocol called Equalized Cluster Head Election Routing Protocol (ECHERP), which pursues energy conservation through balanced clustering, is proposed. ECHERP models the network as a linear system and, using the Gaussian elimination algorithm, calculates the combinations of nodes that can be chosen as cluster heads in order to extend the network lifetime. The performance evaluation of ECHERP is carried out through simulation tests, which evince the effectiveness of this protocol in terms of network energy efficiency when compared against other well-known protocols.

https://www.mdpi.com/1999-4893/6/1/29/pdf

Energy Efficient Routing in Wireless Sensor Networks Through Balanced Clustering

Energy efficient automated control of irrigation in agriculture by using wireless sensor networks

Power saving is a very critical issue in energy-constrained wireless sensor networks. Many schemes can be found in the literature, which have significant contributions in energy conservation. However, these schemes do not concentrate on reducing the end-to-end packet delay while at the same time retaining the energy-saving capability. Since a long delay can be harmful for either large or small wireless sensor networks, this paper proposes a TDMA-based scheduling scheme that balances energy-saving and end-to-end delay. This balance is achieved by an appropriate scheduling of the wakeup intervals, to allow data packets to be delayed by only one sleep interval for the end-to-end transmission from the sensors to the gateway. The proposed scheme achieves the reduction of the end-to-end delay caused by the sleep mode operation while at the same time it maximizes the energy savings.

Christos Douligeris

Papers

DDoS attacks and defense mechanisms: classification and state-of-the-art

Fairness in network optimal flow control: optimality of product forms

Energy Efficient Routing in Wireless Sensor Networks Through Balanced Clustering

Energy efficient automated control of irrigation in agriculture by using wireless sensor networks

Energy efficiency in wireless sensor networks using sleep mode TDMA scheduling