Exploring the impact of node mobility on cascading failures in spatial networks

doi:10.1016/j.ins.2021.06.067

Information Sciences

Volume 576, October 2021, Pages 140-156

https://doi.org/10.1016/j.ins.2021.06.067 Get rights and content

Abstract

Existing researches on cascading failures mainly focus on static spatial networks, but rarely consider network scenarios where mobile nodes and static nodes coexist. Therefore, in this work, we explore the impact of node mobility on cascading failures in spatial networks. We first develop a cascading model for static-mobile spatial network systems. In this model, we use the general betweenness to characterize the load of static nodes in the network, and adopt the Gauss–Markov mobility model to generate the movement trajectory of mobile nodes. On this basis, we develop three node interaction modes (i.e., all-connection mode, high-load priority mode and low-load priority mode) to characterize the interaction between static nodes and mobile nodes. Experimental results have shown that 1) unlike the traditional cascading process that is a continuous process, the cascading process of static-mobile spatial networks consists of multiple cascading processes that occur at different times; 2) expanding the network size and reducing the number of mobile nodes can help the network resist cascading failures; 3) there is a tolerance space for network configuration parameters. When the configuration parameters fall into this space, the network can avoid cascading failures; 4) among the three interaction modes, the network robustness in all-connection mode is the worst, followed by low-load priority mode, and finally high-load priority mode. The obtained results can provide theoretical guidance for users to establish a more robust static-mobile spatial network.

Introduction

In many actual network systems, the failure of network components (i.e., nodes and links) will cause the network load to be redistributed, which may cause some nodes and links to fail due to overload. These failures will lead to a new round of network load redistribution, which may cause more nodes or links to fail. This dynamic failure process is called cascading failures, which is one of the hot issues in the field of network robustness [1], [2], [3].

Most of the existing researches on cascading failures focus on the cascading robustness of topological networks (e.g., random graph, scale-free network and small-world network) [4], [5], [6], [7]. Topological networks mainly consider the connection state between nodes, but rarely consider the spatial attributes of network components (i.e., location of nodes and length of links) on the cascading failure process of the network. However, for most actual networks, the spatial attributes of nodes and links are important factors affecting network characteristics. For this reason, spatial networks have gradually become a hot spot in the field of cascading failures. Compared with topological networks, spatial networks consider spatial attributes of nodes and links in the topology construction, which are closer to the actual networks.

Some promising progress has been made regarding the cascading failures in spatial networks, but these studies all assumed that nodes in spatial networks are static. In a static spatial network, if external interference is not applied, the topology and load distribution of the network will not change, and the network will not experience cascading failures. However, many actual network systems are composed of static nodes and mobile nodes. For example, in Wireless Sensor Networks (WSNs), mobile sensor nodes collect environmental data and send the data to the static sensor nodes encountered, and the static sensor nodes spread the data to the entire network in a multi-hop manner. The similar static-mobile network compositions also widely exist in robot-assisted Internet of Things (IoTs), Internet of vehicles, and mobile ad hoc networks [8], [9], [10], [11], [12]. In these static-mobile spatial networks, when the location of a mobile node changes, the network topology will also change accordingly. This may cause the network load to be redistributed locally or globally. During this load redistribution process, some nodes may overload, which may lead to a new round of load redistribution. This cascading process can continue until no new nodes fall into overload. Compared with static spatial networks relying on external attacks to trigger cascading failures, static-mobile spatial networks use the mobility of internal nodes as the triggering condition for cascading failures, which is more common in practice.

Although many actual network systems exhibit obvious static-mobile spatial characteristics, there are relatively few studies on the cascading failures of such networks. To this end, in this work, we explore the impact of node mobility on cascading failures in spatial networks. The main contributions of this work are summarized as follows:

•
A cascading model for static-mobile spatial networks is proposed. In this model, we use the general betweenness to characterize the load of static nodes in the network, and adopt the Gauss–Markov mobility model to generate the movement trajectory of mobile nodes;
•
We define three interaction modes between static nodes and mobile nodes (i.e., all connection mode, high-load priority mode and low-load priority mode);
•
Extensive experiments have been done to observe the cascading failure process of the network and investigate the impact of network configurations on network robustness.

The rest of this paper is organized as follows: Section 2 reviews the related work; Section 3 elaborates the cascading model in detail; Section 4 presents the experimental results; in Section 5, the discussion and lessons learnt are given; finally, the paper is concluded and the future work is discussed.

Section snippets

Related work

There have been some studies on cascading failures of spatial networks. In [13], Aslami et al. studied the network robustness under dish attacks, and proposed a method for users to configure node capacity to avoid cascading failures. In [14], Li et al. developed a similar attack mode called regional attacks. In this attack mode, the shape of the attack range can be round or square. More importantly, they found that by strengthening the connectivity among high-degree nodes, the robustness of

Network description

In this work, a static-mobile network system can be modeled by an undirected and unweighted graph G =  $(V, E)$ , where V =  $V_{S} \cup V_{M}$ is the node collection consisting of static nodes and mobile nodes. $V_{S} = {1, 2, \dots, N_{S}}$ and $V_{M} = {1, 2, \dots, N_{M}}$ are the collections of static nodes and mobile nodes, respectively. N =  $N_{S} + N_{M}$ is the total number of nodes in the network. The N  $\times$  N adjacency matrix $[a_{i, j}]$ has $a_{i, j} = 1$ if there is a link between node i and node j. We use the $N_{S} \times N_{S}$ adjacency matrix $[b_{i, j}]$ to represent the

Experimental setup

The simulations are based on Matlab, and we use the optimizer GUROBI [33] to speed up the simulation process. In the experiments, different numbers of static nodes and mobile nodes are deployed in a square area of 200 $\times$ 200 m. The interaction radius R of static nodes and mobile nodes is set to 50 m. The scheduled movement duration T of mobile nodes is set to 20 unit time steps. The maximum moving distance of mobile nodes at each time step is set to 80 m. We use the recommended parameters in [29]

Discussion and lessons learnt

The obtained experimental results can provide theoretical support for studying the cascading failure characteristics of static-mobile spatial networks in three aspects: (i) the impact of node mobility on network load redistribution; (ii) network cascading process; (iii) the impact of network configuration on network cascading robustness;

(i) The impact of node mobility on network load redistribution

•
Different from the traditional static spatial network which relies on external attacks to

Conclusions and future work

Static-mobile spatial network systems are very common in practice. Compared with static spatial networks relying on external attacks to trigger cascading failures, static-mobile spatial networks use the mobility of internal nodes as the triggering condition for cascading failures. Unfortunately, the existing research on cascading failures mainly focuses on the cascading characteristics of static spatial networks, and rarely involves static-mobile spatial networks. Therefore, in this work, in

CRediT authorship contribution statement

Xiuwen Fu: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Visualization, Investigation. Wenfeng Li: Writing - review & editing, Supervision. Yongsheng Yang: Writing - review & editing, Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This work is supported in part by the National Natural Science Foundation of China (NSFC) under Grant No. 61902238, the China Postdoctoral Science Foundation under Grant No.2021M692493, and the Research Project of Shanghai Science and Technology Commission under Grant No.20dz1203006.

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Exploring the impact of node mobility on cascading failures in spatial networks

Abstract

Introduction

Section snippets

Related work

Network description

Experimental setup

Discussion and lessons learnt

Conclusions and future work

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgment

Information Sciences

Reliability Engineering & System Safety

Reliability Engineering & System Safety

Physica A: Statistical Mechanics and its Applications

Journal of Network and Computer Applications

Information Sciences

Information Sciences

Information Sciences

Physica A: Statistical Mechanics and its Applications

Physica A: Statistical Mechanics and its Applications

Physica A: Statistical Mechanics and its Applications

Reliability Engineering & System Safety

Information Sciences

Structural Safety

Physica A: Statistical Mechanics and its Applications

Physica A: Statistical Mechanics and its Applications

Reliability Engineering & System Safety

Computer Networks

Future Generation Computer Systems