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Register a new userTraffic dynamics in scale-free networks with limited packet-delivering capacity
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We propose a limited packet-delivering capacity model for traffic dynamics in scale-free networks. In this model, the total nodes packet-delivering capacity is fixed, and the allocation of packet-delivering capacity on node $i$ is proportional to $k_{i}^{phi}$, where $k_{i}$ is the degree of node $i$ and $phi$ is a adjustable parameter. We have applied this model on the shortest path routing strategy as well as the local routing strategy, and found that there exists an optimal value of parameter $phi$ leading to the maximal network capacity under both routing strategies. We provide some explanations for the emergence of optimal $phi$.
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Recently, Broido & Clauset (2019) mentioned that (strict) Scale-Free networks were rare, in real life. This might be related to the statement of Stumpf, Wiuf & May (2005), that sub-networks of scale-free networks are not scale-free. In the later, those sub-networks are asymptotically scale-free, but one should not forget about second-order deviation (possibly also third order actually). In this article, we introduce a concept of extended scale-free network, inspired by the extended Pareto distribution, that actually is maybe more realistic to describe real network than the strict scale free property. This property is consistent with Stumpf, Wiuf & May (2005): sub-network of scale-free larger networks are not strictly scale-free, but extended scale-free.
We consider the effects of network topology on the optimality of packet routing quantified by $gamma_c$, the rate of packet insertion beyond which congestion and queue growth occurs. The key result of this paper is to show that for any network, there exists an absolute upper bound, expressed in terms of vertex separators, for the scaling of $gamma_c$ with network size $N$, irrespective of the routing algorithm used. We then derive an estimate to this upper bound for scale-free networks, and introduce a novel static routing protocol which is superior to shortest path routing under intense packet insertion rates.
The study of complex networks sheds light on the relation between the structure and function of complex systems. One remarkable result is the absence of an epidemic threshold in infinite-size scale-free networks, which implies that any infection will perpetually propagate regardless of the spreading rate. The vast majority of current theoretical approaches assumes that infections are transmitted as a reaction process from nodes to all neighbors. Here we adopt a different perspective and show that the epidemic incidence is shaped by traffic flow conditions. Specifically, we consider the scenario in which epidemic pathways are defined and driven by flows. Through extensive numerical simulations and theoretical predictions, it is shown that the value of the epidemic threshold in scale-free networks depends directly on flow conditions, in particular on the first and second moments of the betweenness distribution given a routing protocol. We consider the scenarios in which the delivery capability of the nodes is bounded or unbounded. In both cases, the threshold values depend on the traffic and decrease as flow increases. Bounded delivery provokes the emergence of congestion, slowing down the spreading of the disease and setting a limit for the epidemic incidence. Our results provide a general conceptual framework to understand spreading processes on complex networks.
In this paper, we study traffic dynamics in scale-free networks in which packets are generated with non-homogeneously selected sources and destinations, and forwarded based on the local routing strategy. We consider two situations of packet generation: (i) packets are more likely generated at high-degree nodes; (ii) packets are more likely generated at low-degree nodes. Similarly, we consider two situations of packet destination: (a) packets are more likely to go to high-degree nodes; (b) packets are more likely to go to low-degree nodes. Our simulations show that the network capacity and the optimal value of $alpha$ corresponding to the maximum network capacity greatly depend on the configuration of packets sources and destinations. In particular, the capacity is greatly enhanced when most packets travel from low-degree nodes to high-degree nodes.
For many power-limited networks, such as wireless sensor networks and mobile ad hoc networks, maximizing the network lifetime is the first concern in the related designing and maintaining activities. We study the network lifetime from the perspective of network science. In our dynamic network, nodes are assigned a fixed amount of energy initially and consume the energy in the delivery of packets. We divided the network traffic flow into four states: no, slow, fast, and absolute congestion states. We derive the network lifetime by considering the state of the traffic flow. We find that the network lifetime is generally opposite to traffic congestion in that the more congested traffic, the less network lifetime. We also find the impacts of factors such as packet generation rate, communication radius, node moving speed, etc., on network lifetime and traffic congestion.
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