## 4 Algorithm Description
### Calculation of Network Parameters  
The Logarithmic distance path loss model is as  
\[P_{L}=20\lg(\frac{4\pi d}{\lambda})+10n\lg d+X_{\sigma}, \tag{12}\]  
where \(d\) is the distance between two communication points, \(\lambda=c/f_{c}\), \(n\) is the path loss exponent, and \(X_{\sigma}\) represents a Gaussian random variable with a mean value of 0 and a standard deviation of \(\sigma\).  
The packet delivery ratio is an important indicator to evaluate whether a routing protocol is reliable, and it is the ratio between the number of packets that reach the destination and the number of packets generated by the source.  
When calculating the end-to-end delay, which is the average time to receive data from the source to the destination, this paper uses the M/M/1 model to analyze the queuing time. The probability distribution of the service time is exponential with a mean \(1/\mu\) sec. \(E[X]=1/\mu\) is the average service time, and the second-order moment is \(E[X^{2}]=2/\mu^{2}\). \(E[W]\) is the average latency of the packets in the queue, and \(E[Q]\) is the average queue length when the packets arrive. \(E[T]\) is the average latency of the data packets within the system. The calculation formula is as follows:  
\[E[W]=\frac{\lambda E[X^{2}]}{2(1-\rho)}=\frac{\rho}{\mu(1-\rho)}, \tag{13}\]  
\[E[Q]=\frac{\lambda^{2}E[X^{2}]}{2(1-\rho)}=\frac{\rho^{2}}{1-\rho}, \tag{14}\]  
\[E[T]=\frac{1}{\mu}+\frac{\rho}{\mu(1-\rho)}=\frac{1}{\mu-\lambda}, \tag{15}\]  
where \(\mu\) represents the service rate, which refers to the number of packets that a router can serve per unit of time. \(\lambda\) is the number of packets arriving at a router per unit of time, \(\rho=\lambda/\mu\).  
When calculating the end-to-end time delay, it is necessary to consider the queuing delay when packets are forwarded through each router. Therefore, \(\lambda\) is not a fixed value but is determined based on the arrival rate of the previous router and the average waiting time of the packets in the previous system. The arrival rate of the kth router \(\lambda_{k}\) is  
\[\lambda_{k}=\frac{1}{\frac{1}{\lambda_{k-1}}+E(T)_{k-1}}. \tag{16}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Schemes**} & **Path between** & **Path between** & \multirow{2}{*}{**Path between DE**} & \multirow{2}{*}{**New Path**} \\  & **AB** & **BC** & & \\ \hline Scheme 1 & (A,H,B) & (B,J,C) & (D,K,E) & (A,H,B,I,C,D,K,E,G) \\ Scheme 2 & (A,H,J,C) & (D,K,L,F) & (A,H,J,C,D,K,L,F) \\ Scheme 3 & (A,H,J,J,D) & (D,K,L,M,G) & (A,H,J,D,K,L,M,G) \\ Scheme 4 & (A,H,B) & (B,J,C  
The end-to-end delay of AODV consists of propagation delay, queuing delay, and route discovery delay. The delay of DASC consists of propagation delay and queuing delay, eliminating the delay of route discovery.  
Routing discovery overhead is the ratio between the number of control packets (RREQ and RREP) and the number of messages that are sent in the network:  
\[cost=\frac{num\_RREQ+num\_RREP}{num\_packet}, \tag{17}\]  
where \(cost\) is the routing discovery overhead; \(num\_RREQ\) is the valid RREQ packets for routing discovery broadcasts; \(num\_RREP\) is the number of packets sent during route discovery to establish a reverse path, which equals to the number of hops in the path discovered by the route; and \(num\_packet\) is the total number of data packets sent by the source node.