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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Tensor Analysis of Networks. By Gabriel Kron. Pp. xxix, 635. 70s. 1965. (Macdonald)

Performance Modeling and Design of Computer Systems: The M/G/1 Queue and the Inspection Paradox

Abstract A two-level method of fast re-routing with load balancing in a software-defined network (SDN) is proposed. The novelty of the method consists, firstly, in the introduction of a two-level hierarchy of calculating the routing variables responsible for the formation of the primary and backup paths, and secondly, in ensuring a balanced load of the communication links of the network, which meets the requirements of the traffic engineering concept. The method provides implementation of link, node, path, and bandwidth protection schemes for fast re-routing in SDN. The separation in accordance with the interaction prediction principle along two hierarchical levels of the calculation functions of the primary (lower level) and backup (upper level) routes allowed to abandon the initial sufficiently large and nonlinear optimization problem by transiting to the iterative solution of linear optimization problems of half the dimension. The analysis of the proposed method confirmed its efficiency and effectiveness in terms of obtaining optimal solutions for ensuring balanced load of communication links and implementing the required network element protection schemes for fast re-routing in SDN.

/pdf/enhanced-method-of-fast-re-routing-with-load-balancing-in-4o8plytesz.pdf

Enhanced method of fast re-routing with load balancing in software-defined networks

The dynamics analysis of multipath QoS-routing tensor model with support of different flows classes is presented. The novelty of the tensor model is a representation of its covariant and contravariant components and metric of the introduced geometrical space as a function of time. The QoS-routing guarantees for different flows classes with different metrics such as average packet rate and average end-to-end delay were proposed. The research results demonstrated that it is especially important to take into account the dynamics of network state changes in the conditions of high utilization of its interfaces, when the average packet end-to-end delay along the network paths behaves nonstationary, changing quite widely during the router update timer.

Dynamics analysis of multipath QoS-routing tensor model with support of different flows classes

In this paper, the approach to providing a given level of information security for multipath routing of confidential messages in a network is considered. A method for providing secure routing over overlapping paths is developed and belongs to the class of proactive solutions for ensuring a given level of information security. The analysis has shown that using the proposed method within the presented calculated examples can improve the probability of compromising transmitted messages at average from 5–10% to 25–50% due to the possibility of using composite paths that are one of the subclasses of overlapping paths. A method of Secure Fast ReRouting (S-FRR) of messages in the network has been synthesized, the novelty of which lies in the fact that it focuses on the implementation of both proactive and reactive secure routing confidential messages. In this case, the proactive nature of the solutions is conditioned by the calculation of the set of primary composite paths forming the primary multipath, along which parts of the confidential message are transmitted. However, in the case of violation of the information security requirements in the network caused by the increased probability of compromising one or multiple composite paths constituent the primary multipath, the messages will be transmitted over the calculated set of the backup composite paths determining the backup multipath. Within the framework of the proposed S-FRR method, it is possible to protect both the primary multipath as a whole and one or several precomputed composite paths included in this primary multipath. The developed methods of secure routing can be used as the basis for new network protocols for routing and fast rerouting for multipath transmission of parts of a confidential message with specified requirements regarding the probability of its compromise in the network.

Secure Routing in Reliable Networks: Proactive and Reactive Approach

In this paper, the consistent solution for default gateway protection within fault-tolerant routing in an IP network is presented, and it is based on development of the appropriate flow-based mathematical model. Within the framework of the proposed model, a fault-tolerant routing problem has been reduced to the solution of the optimization problem of nonlinear programming. Fault-tolerance functions are implemented by introducing additional routing variables responsible for the calculation of a backup default gateway and the corresponding path (multipath) in the transport network. Several examples have demonstrated features of the application of the proposed model in solving default gateway protection within fault-tolerant routing for the case of realization of single path and multipath routing. The results have confirmed the efficiency of the proposed model and adequacy of the calculation results obtained.

/pdf/solution-for-the-default-gateway-protection-within-fault-2hvqe8rgqv.pdf

Solution for the Default Gateway Protection within Fault-Tolerant Routing in an IP Network

Effective solution for scalability and productivity improvement in fault-tolerant routing using the flow-based model was proposed. In practice, the fault-tolerant routing based on reservation of network resources is usually associated with decrease in overall performance and scalability of protocol solutions. In this regard, in structure of the model introduced conditions that are responsible for the fact that the primary and backup routes differed only by network elements for which redundancy provided. This was reflected in modification of objective function within the formulation and solution of optimization problem of the fault-tolerant routing. Numerical examples showed efficiency of the proposed solution.

http://ieeexplore.ieee.org/iel7/7347238/7357246/07357274.pdf

Oleksandr Lemeshko

Papers

Enhanced method of fast re-routing with load balancing in software-defined networks

Dynamics analysis of multipath QoS-routing tensor model with support of different flows classes

Secure Routing in Reliable Networks: Proactive and Reactive Approach

Solution for the Default Gateway Protection within Fault-Tolerant Routing in an IP Network

Effective solution for scalability and productivity improvement in fault-tolerant routing