# On Edge Pruning of Communication Networks under an Age-of-Information Framework
###### Abstract  
Effective non-repetitive routing among nodes in a network is an essential function in communication networks. To achieve that, pruning the links of the network is helpful with the trade-off of making the network less robust in transmitting messages while reducing redundancy to increase flow with limited network bandwidth, so we enhance the quality of service (QoS). In our paper, we study the case that if a link removal has either no effect or an insignificant effect on the Age of Information (AoI) of the messages delivered in the communication network. The pruning of such links can be applied to the \(k\) least significant links in terms of their impact on the AoI of the messages transmitted in the system. The objective of our work is to study the effect of pruning a number of links in a network on the AoI, in order to reduce the redundancy of the messages that may be received at the destination many times while transmitted only once. In our context, the objective of the communication system would be to maintain the information from the source as fresh as possible when it arrives at the destination while reducing the redundancy of messages. In this work, we introduce an efficient reduction method designed for series-parallel networks with links of exponentially distributed wait times. In addition, we consider the deterministic case and present the pruning technique when link removal would not affect the AoI. Lastly, we present a comprehensive simulation to study the effect of pruning the links on the AoI of the network and the redundancy of messages received by the destination.  
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transmitted through the network. The new metric of AoI, which has spawned relevant performance metrics, has opened new research fields. In the context of timely updates, it is widely considered that those relevant performance metrics are desired to have values that guarantee some kind of high freshness of the information of the message when they arrive at the destination [15; 16; 17; 18].  
We investigate the two cases when a link removal either has no effect or insignificantly affects the AoI of the messages delivered in the network; we consider that link an insignificant link which we may prune. The pruning can be applied on the least \(k\) significant links in terms of their impact on the AoI of the messages transmitted in the system. In our model, we consider that each node forwards the messages toward the direction of the destination node once it receives the message.  
The objective of our work is to study the effect of pruning a number of links in a network on the AoI in order to reduce the redundancy of the messages that may be received at the destination many times while transmitted only once. Thus, improving the quality of service (QoS). This duplicate of receiving the same messages would happen, for example, in general gossip networks [19].  
Our results are summarized as follows:  
* An efficient reduction method designed for series-parallel networks with links of exponentially distributed wait times or with links of deterministic periodic wait time.
* A pruning algorithm that determines the least significant link in the network, in terms of its effect on the AoI, and prunes it.
* A comprehensive simulation to study the effect of pruning the links on the AoI of the network and the redundancy of messages received by the destination.  
The remainder of the paper is organized as follows. In Section 2, related work is reviewed. In Section 3, the general model of the problem is proposed. In Section 4, the network reduction method for our model is introduced. Section 5 discusses the characterization of the AoI under our model. Section 6 briefly visits the periodic case. Section 7 shows the simple pruning techniques. Section 8 presents the simulation results. Section 9 gives the conclusion.