## 3 Adaptive Real-Time Routing Protocol
### Real-Time Model  
We aim to model the application of multimedia data traffic and a real-time routing protocol to deliver traffic timely. We assume the event happens continuously and is recognized by a node. We focus on traffic modeling and real-time delivery. The network architecture, including the nodes, is illustrated in Figure 1, which also shows that a sink node exists in the network. Traffic model and requirements are as follows.  
A node is capable of processing consecutive images and transmitting them to the sink node with the identity unique \(ObjID\). The application stream, \(T_{ObjID}\), is modeled by the (_m,k_)-firm model, that is, \(T_{ObjID}=\{\)\(m_{ObjID}\), \(k_{ObjID}\), \(D_{ObjID}\),\(DBP_{ObjID}\}\) where \(m_{ObjID}\) and \(k_{ObjID}\) represent the requirements of a multimedia application. In addition, if the packet is transmitted within the deadline, \(D_{ObjID}\), the corresponding packet is marked as Hit; otherwise, it is marked as Miss. Here, \(DBP_{ObjID}\) is prioritized value based on the distances of the stream requirement to recognize the current (_m,k_)-firm status. For example, with a (3,5)-firm real-time stream requirement, the traces of the reception status of the last 5 packets can be represented as HHMMM where H and M represent the Hit and Miss of status of an individual packet, respectively. Then, the DBP value becomes \(-1\) as the required number of Hit is 3 where the Hit status remains only 2 as explained in our previous paper [35].  
In addition to application stream, a real-time session flow between node \(i\) and the sink, denoted by \(S_{i}\), is defined as \(S_{i}=\{node_{i}\), \(m_{i}\), \(k_{i}\), \(D_{i}\), \(DBP_{i}\}\) like \(T_{ObjID}\). The different element between \(T_{ObjID}\) and \(S_{i}\) is node identifier, \(node_{i}\). Even though two model consists with the same parameters, the value for them is different according to requirements. \(T_{ObjID}\) represents the application requirement while \(S_{i}\) does requirement for routing protocol.  
Before an event end at node \(i\), \(S_{i}\) is maintained and packets are transmitted to the sink by filling \(T_{ObjID}\) with them through multiple paths as illustrated in dotted rectangle in Figure 1. According to current status of \(D_{ObjID}\) and \(DBP_{i}\), one of multiple paths are selected to transmit the packets. Each session is used to partially build \(T_{ObjID}\). Each session has the same (\(m_{i}\), \(k_{i}\)) requirements in the \(T_{ObjID}\). The same values for \(D_{i}\) are assumed for \(T_{ObjID}\) and \(S_{i}\). As illustrated in Figure 1, \(T_{ObjID}\) consists of each consecutive sessions, that is \(T_{ObjID}=\{\)\(S_{1}\cup S_{2}\cup\ldots\cup S_{n}\}\). Thus, \(DBP_{ObjID}\) is affected by \(DBP_{i}\) as well as (\(m_{ObjID}\), \(k_{ObjID}\)) value.  
To meet the requirements of the two (_m,k_)-firm models, the values are assigned to comply with the following conditions. These two conditions guarantee that the requirement of \(S_{i}\) cannot exceed that  
Figure 1: Overview of the proposed real-time model.  
of the \(T_{ObjID}\). This is because, occasionally, the network cannot ensure the time requirement because of severe constraints.  
\[\frac{m_{i}}{k_{i}}>\frac{m_{ObjID}}{k_{ObjID}} \tag{1}\]  
\[k_{i}\geq k_{ObjID} \tag{2}\]  
Upon detecting any event, a node \(i\) builds a multimedia stream by using consecutive packets with the (\(m\),\(k\))-firm model and delivers them to the sink. The sink checks whether a packet is lost or whether the packet has arrived after the deadline. These measurements are used to compute the values of \(DBP_{i}\) and \(DBP_{ObjID}\), which are then transmitted to the node \(i\).