Alexander Stepanenko

Network visualisation and analysis tool based on logical network abridgment

A novel procedure of summarizing and abstracting the topology and distributed statistical measures of routing performance for communication networks is presented. This procedure, called logical network abridgment (LNA), forms the basis of a novel resilient recursive routing (R3) protocol. In this paper, we investigate the usefulness of LNA in visualizing and defining the state of health of a communication network. Traditionally, connectivity and metrics (such as link utilization, end-to-end delay, etc.) are used to provide indications of the state of health of a network. However, connectivity alone tells us little about the intrinsic diversity of the network and therefore its resiliency to attacks or attrition. Similarly, individual localized or path specific metrics tell us little about the overall intrinsic capability of the network. The LNA procedure summarizes the metric of choice over the total network and is thus capable of describing the intrinsic state of its health. In the context of military command and control, as well as commercial network management, scenarios, operators wish to easily create well-designed networks, in terms of resiliency and performance. Furthermore, operators need to identify, in an intuitive manner, the vulnerabilities that exist in a network. In addition, the consequences of actions taken to remedy failures or strengthen resiliency are often time consuming to understand in a large distributed system. The LNA procedure offers a quick and reliable algorithmic visual tool to achieve these. The paper presents work funded by the US Air-Force Research Laboratory (AFRL-EOARD) that demonstrates the potential of network visualization and analysis through the proposed LNA procedure

The internet's unexploited path diversity

The connectivity of the Internet at the Autonomous System level is influenced by the network operator policies implemented. These in turn impose a direction to the announcement of address advertisements and, consequently, to the paths that can be used to reach back such destinations. We propose to use directed graphs to properly represent how destinations propagate through the Internet and the number of arc-disjoint paths to quantify this network¿s path diversity. Moreover, in order to understand the effects that policies have on the connectivity of the Internet, numerical analyses of the resulting directed graphs were conducted. Results demonstrate that, even after policies have been applied, there is still path diversity which the Border Gateway Protocol cannot currently exploit.

Chain routing:a new routing framework for the Internet based on complete orders

A new framework to perform routing at the autonomous system (AS) level is proposed here. This mechanism, called chain routing framework (CRF), uses complete orders as its main topological unit. Since complete orders are acyclic digraphs that possess a known topology, it is possible to use these acyclic structures to route consistently packets between a group of ASs. The adoption of complete orders also allows easy identification and avoidance of persistent route oscillations, eliminates the possibility of developing transient loops in paths and provides a structure that facilitates the implementation of traffic engineering. Moreover, by combining CRF with other mechanisms that implement complete orders in time, the authors propose that it is possible to design a new routing protocol, which can be more reliable and stable than the border gateway protocol.

Novel Topological Framework for Adaptive Routing

We identify that a major contributing factor to the shortcomings of current routing protocols is their mathematical treatment of graphs used to represent networks. Typically, routing protocols decimate the rich connectivity present in a network into a small number of distinct trees for every source, which are then translated into routing table entries. We propose a new routing paradigm that introduces a novel concept of neighbourhood, embodying path diversity. This framework summarises rather than decimates paths throughout the network, preserving and exploiting all of the networks potentially rich intrinsic path diversity. Central to our abstraction are two intimately connected and complementary path diversity units: simple cycles, and cycle adjacencies. A recursive network abstraction procedure is presented, together with an associated generic recursive routing protocol family that offers many desirable features. A simple instance of such a protocol is compared against existing wired and wireless routing protocols through simulations for a highly-stressed network with unstable links, illustrating the potential advantages of the proposed approach.

Temporal correlations of local network losses

We introduce a continuum model describing data losses in a single node of a packet-switched network (like the Internet) which preserves the discrete nature of the data loss process. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that such a model exhibits strong fluctuations in the loss rate at the critical point and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process. The continuum model allows for rather general incoming data packet distributions and can be naturally generalized to consider the buffer server idleness statistics.

Random walks in local dynamics of network losses

We suggest a model for data losses in a single node (memory buffer) of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that for a finite-capacity buffer at the critical point the loss rate exhibits strong fluctuations and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process.

Fluctuation-driven traffic congestion in a scale-free model of the Internet

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analysing network failures caused by hardware faults or overload. There network reaction was modelled as rerouting of traffic away from failed or congested elements. Here we model network reaction to congestion on much shorter time scales when the input traffic rate through congested routes is reduced. As an example we consider the Internet where local mismatch between demand and capacity results in traffic losses. We describe the onset of congestion as a phase transition characterised by strong, albeit relatively short-lived, fluctuations of losses caused by noise in input traffic and exacerbated by the heterogeneous nature of the network manifested in a power-law load distribution. The fluctuations may result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible.

Fluctuation-induced traffic congestion in heterogeneous networks

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analyzing network failures caused by hardware faults or overload, where the network reaction was modeled as rerouting of traffic away from failed or congested elements. Here we model another type of the network reaction to congestion - a sharp reduction of the input traffic rate through congested routes which occurs on much shorter time scales. We consider the onset of congestion in the Internet where local mismatch between demand and capacity results in traffic losses and show that it can be described as a phase transition characterized by strong non-Gaussian loss fluctuations at a mesoscopic time scale. The fluctuations, caused by noise in input traffic, are exacerbated by the heterogeneous nature of the network manifested in a scale-free load distribution. They result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible.

Large-scale behaviour of packet-switched networks: theoretical analysis framework

We present a possible way to study large-size packet-switched networks capable of accounting for interactions between adjacent queues. The interaction between queues arises, because of the influence of the routing protocol on each switching decision, and the stochastic nature of packet lengths and inter-arrival times.Both the methodology and the analysis tools are adaptations of methods of statistical mechanics. The justification for their use lies in recent experimental evidence indicating that aggregate, core-network IP traffic, exhibits quasi-Markovian properties when the network is heavily loaded.In this paper, we present a general methodology and introduce approximations that greatly simplify the analysis. These approximations, are owing to the quasi-Markovian nature of the traffic and the large size of the network.

On a Theory of Interacting Queues

We present a possible way to extend queuing theory to account for interactions between adjacent queues in a packet-switched network. The interaction between queues arises because of the influence of the routing protocol on each switching decision and the stochastic nature of packet lengths and inter-arrival times.Both the methodology and the analysis tools are adaptations of methods of statistical mechanics and are presented in outline here. The justification for their use lies in experimental evidence given in [1,2,3] that aggregate, core-network IP traffic exhibits quasi-Markovian properties. In this paper, we focus on the interaction between pairs of queues, either in a cascaded arrangement, or connected to the same switching fabric, in the presence of an idealised routing protocol.