## 3 Network Model and Problem Definition  
In this section, first, the network model is described. Then, the problem definition is presented.  
Figure 1 shows the network model that consists of four entities as follows:  
* Mobile nodes (mobile users): Mobile nodes collect data, such as temperature, images of traffic conditions, and videos of accidents, using the sensors embedded in their smart devices (e.g., camera, microphone, positioning sensor, temperature sensor), and send to edge nodes. They can walk or be in a vehicle to move around the area. When mobile users are in contact with other people or sensors, they can exchange data between them and transmit data to the destination.
* Sensors: Sensors are deployed in specific locations to collect data, such as air quality, radioactivity, noise levels, and humidity levels. When sensors and destinations (edge nodes) are not directly connected, the sensors must relay packets to mobile users to transfer them to the destinations.
* Edge nodes: Edge nodes are located in particular locations to gather and preprocess collected data from sensors and mobile users. Then, edge nodes send processed data to the server center.
* The server center: The server center receives data from edge nodes and uses the received data for urban-sensine applications.  
Messages in this network can be of different data types, such as text, images, and video. This model could be used in various applications, such as environmental monitoring [4, 5], smart traffic light systems [6], and waste management [31]. For example, in monitoring environmental conditions [4, 5], the data from sensors, such as air quality, noise, and radiation sensors, and the data from sensors embedded in smart devices for temperature measurement, are collected and sent to edge nodes. Then, edge nodes preprocess the collected data and send it to the server center.  
In this system, edge nodes connect with the server center via an infrastructure network, whereas edge nodes, sensors, and mobile nodes exchange messages with each other using wireless communications such as Bluetooth 5.0. Therefore, this work addresses the problem of how to effectively route data from sensors and mobile nodes to edge nodes. Data collection at edge nodes in this system relies on mobile nodes that move around the city. The selection of nodes for forwarding messages is an important issue. Our work considers network performance in terms of \(DC\), \(PDL\), and \(PDR\). The \(DC\) is calculated by dividing the total number of replications by the total number of messages generated. The \(PDL\)  
Figure 1: The network model.  
is the time it takes for messages to be delivered from sources to destinations. The \(PDR\) measures the number of messages delivered to their intended destinations divided by the total number of messages.  
We assume that the movement histories of a number of mobile nodes are observed, and each node knows its encounter history with other nodes. The information from observed movement history is denoted as \(M\). Let \(\mathbb{S}_{u}^{NB}\) denote the set of neighboring nodes of node \(u\). The information on the encounter history of nodes in \(\mathbb{S}_{u}^{NB}\) is denoted \(E\). Node \(u\) wants to send a message to edge node \(v\). The objective is to choose relay nodes in \(\mathbb{S}_{u}^{NB}\) to maximize the \(PDR\) and minimize the \(PDL\) and the \(DC\), given the information on movement history \(M\) and information on encounter history \(E\).