# A Novel Opportunistic Network Routing Method on Campus Based on the Improved Markov Model
## 3 Materials and Methods  
### Markov-Based Next Destination Prediction  
The storage-forward model of messages in opportunity networks relies on human contact, and the potential for message delivery arises as people move around. There are more options for message delivery when nodes are on their way to the same location as the destination node of a message. This is so that these nodes can send the message to the intended node faster. Some of the symbols used in the text and what they represent are listed in Table 2.  
According to the way people move in the campus opportunity network, we make the following provisions:  
The number of times a node chooses a location as its next destination in time period, 0 to \(t\) is denoted as \(X(t)\), which is a stochastic process with \(X(0)=0\). Assume:  
* Within mutually exclusive time intervals, the number of times that nodes choose the place as a destination point is independent of one another;
* The probability distribution of the number of times \(X(s+t)-X(s)\) that a node chooses this location in period \((s,s+t]\) is independent of s, where \(s\geq 0\);
* \(o(\Delta t)\) is the likelihood that a node will choose the same place more than once in a sufficiently little period of time. According to the above rules, the number of times \(X(t)\) for a node to select the location before time t is a stochastic process, and the number of times to select the location before \(t_{y}(t_{y}>t)\) in the future only depends on the number of times to select the location at time t. The overall number the location is selected in period \([0,t]\) and \((t,t_{v}]\) is equal to the number of times the location is selected in \([0,t_{v}]\). From the assumption (1) that the number of times the location is selected in period \([0,t]\) and period \((t,t_{v}]\) are independent of each other, it is known that \(X(t)\) has no posteriority and belongs to the Markov process. The parameter set for the number of choices \(X(t)\) in the above Markov process is \(T=[0,\infty)\) and the state space is \(E=\{0,1,2,\ldots\}\). Therefore, \(X(t)\) is a Markov process with continuous time and discrete states. \begin{table}
\begin{tabular}{c c} \hline \hline
**Limitations of Existing Works** & **Novelties of This Paper** \\ \hline The previous section describes how nodes & In this paper, we transmit messages based on the \\ can reduce network resource usage by & probability that the nodes will meet at the next \\ providing a restricted number of copies, & location which can guarantee the successful \\ but messages with a short survival time & transmission of messages in a short time. \\ may not be delivered. & We consider the probability that nodes will meet \\ \hline The prediction-based routing presented & We consider the probability that nodes will meet \\ above takes into account the encounter & one another at various places and the number of \\ interval of the nodes. & contacts between nodes. \\ \hline FCIM considers the caching of networks. & Description of the message’s energy consumption \\ and the network’s degree of message spread was & added to the node. \\ \hline They encourage selfish nodes to engage & Skip selfish nodes to avoid being impacted \\ in collaboration. & by them. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Novelties of this paper. \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Description** \\ \hline \(N_{a},N_{b}\) & Node \(N_{a}\) and node \(N_{b}\) \\ \(f\epsilon(N_{a},N_{b})\) & Probability \(N_{a}\) and \(N_{b}\) meet \\ \(m\) & Message \\ \(DC\) & Centrality degree of node \\ \(D_{m}\) & Destination node of message m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Lists of the notations used in this paper to represent variables.