The reliability of swarm systems needs to be investigated because of their self-adaption and self-organized features. Previous studies mainly focused on the reliability of a single agent, whereas for swarm systems, the ability to maintain their overall connection and function under adverse conditions is more important. It remains challenging on how to evaluate the reliability of swarm systems at the system level. In this paper, we present a reliability evaluation method for swarm systems by characterizing the behavior of the whole system using the method of temporal network analysis. A novel comprehensive reliability metric, i.e. cooperation reliability (CR), is proposed, considering both system integrity and motion consensus. Meanwhile, by identifying critical individuals in swarm systems, we design different malicious attack strategies. It is found that the malicious attacks perform much more harmfully to the reliability of swarm systems than noise and random attack. Moreover, we find that the reliability of a swarm system is sensitive to the swarm density in our framework due to the dynamical interaction of the system. Our findings may shed light on understanding the complicated behaviors of swarm systems under attack and designing a more robust swarm system.

For the edge computing network, whether the end-to-end delay satisfies the delay constraint of the task is critical, especially for delay-sensitive tasks. Virtual machine (VM) migration improves the robustness of the network, whereas it also causes service downtime and increases the end-to-end delay. To study the influence of failure, migration, and recovery of VMs, we define three states for the VMs in an edge server and build a continuous-time Markov chain (CTMC). Then, we develop a matrix-geometric method and a first passage time method to obtain the VMs timely reliability (VTR) and the end-to-end timely reliability (ETR). The numerical results are verified by simulation based on OMNeT++. Results show that VTR is a monotonic function of the migration rate and the number of VMs. However, in some cases, the increase in task VMs (TVMs) may conversely decrease VTR, since more TVMs also brings about more failures in a given time. Moreover, we find that there is a trade-off between TVMs and backup VMs (BVMs) when the total number of VMs is limited. Our findings may shed light on understanding the impact of VM migration on end-to-end delay and designing a more reliable edge computing network for delay-sensitive applications.