# On the Potential of Enhancing Delay-Tolerant Routing Protocols via Age of Information
## 2 Related Work  
### Age of Information  
The concept of Age of Information (AoI) [17] was introduced in the early 2010s, in order to quantify the freshness of the knowledge that exists about a process observed from distance. More specifically, let a system consist of two nodes, namely a source and a destination node. For ease of tracking the mathematical symbols used in the following, Table 1 summarizes the symbols used in the paper. Assume a stochastic process \(X(t)\) is observed by the source node, extracting samples, which carry information about the state of the stochastic process at the source node. Each one of them must be transmitted via a communication channel to the destination node. In the transmitter of the source node, there is a buffer that stores the samples in the form of packets. Each packet contains not only the value of the stochastic process \(X(t_{i})\) at time \(t_{i}\) where the sample was extracted, but also the timestamp \(t_{i}\) itself. The transmission of status updates can be studied according to the model shown in Figure 1. Suppose that the creation of a status update is modeled as a stochastic process with average rate \(\lambda\) and packets are transmitted at an average service rate \(\mu\) to the destination. The concept of AoI refers to the freshness of the knowledge possessed by the destination about the status of the source node. This freshness measurement is quantified as the time elapsed since the last status update received from the destination. A typical definition of _Age of Information_ is as follows:  
**Definition 1** (Age of Information). : _Suppose a system consists of a source-destination communication pair. Let \(t^{\prime}_{k}\) be the times at which status updates are received from the destination. At the current time \(\zeta\), the index of the most recent update is:_  
\[N(\xi)=max\{k|t^{\prime}_{k}\leq\xi\}, \tag{1}\]_where the timestamp of the most recent update is:_  
\[u(\xi)=t_{N(\xi)}. \tag{2}\]  
_The Age of Information (AoI) of some information of the source, e.g., a packet carrying a value update, at destination is defined as the random process:_  
\[\Delta(t)=t-u(t). \tag{3}\]  
A sample path of the random process defined in Equation (3) exhibits a typical sawtooth form, illustrated in Figure 2. In our case, the AoI is a parameter defined for each separate packet and it describes the elapsed time, from the generation of the packet at the packet source until the current time instance Equation (3), wherever it is measured (the term destination actually refers to the point where AoI is measured). It shows the freshness of the packet from the same source at a point received in the network. AoI can be computed by inserting a timestamp when the packet is generated at the source, and each node holding the packet can compute the time difference between the current time and the packet's timestamp (in DTN implementations such as DTN2, only one node holds a packet copy--such node is denoted as custodian). Figure 2 provides an indicative sample of such quantity for a single packet, measured at the destination. The term destination here denotes any destination computing the difference between the current time and the packet's timestamp, namely AoI. Thus, each node computes the AoI of each packet in custody (received packets). Based on this, it will make a routing decision, as to whether it will further forward the packet or drop it because it is no longer considered as \"fresh\" enough. The intuition behind this is that if AoI grows too much, it might be more convenient to drop the packet for the sake of another fresher \"packet\" from the same source transferred in the network, thus saving resources, here saving on end-to-end delay, but also other metrics can be positively impacted, such as energy consumption.