## 4 Pheromone Termite Analytical Routing Model  
Pheromones are the chemicals used for communication. Pheromone communication is conceivably the most ancient means of communication in the animal realm. The animals transmit the chemical messages that include information regarding food location, territory, threats, and companions. The chemical messages are private, potent in darkness, and long-term, and they may function over long distances. Here, we specifically consider pheromones as used by termites. Termites use pheromones for communication purposes. When termites search for food, they use a pheromone to mark the track from the food to their shell. The termites deposit the pheromone from a gland on the bottom of their stomachs. When termites are back at the nest, they recruit other termites to follow the trail of the pheromone back to the food. Based on the idea of termites' use of pheromones, we introduce the pheromone termite model with new features added for routing purposes. Our pheromone termite model adds two additional new features into the existing working process of the pheromone termite model: the packet generation rate and pheromone sensitivity. The packet generation rate helps avoid congestion, and the pheromone sensitivity helps determine the link capacity prior to sending the packets on each link. These two additional features provide a tradeoff between fault tolerance and QoS provisioning. Here, we use the PT model with O-MAC to obtain cross-layering support. The model with two additional new features connects the MAC sub-layer with the network layer to find the optimal path to transmit the data packets through one-hop neighbor nodes. We achieve the following goals using the PT model. * Low latency,
* Higher throughput,
* No-overlapping,
* Collision/congestion handling,
* Fault-tolerance, and
* Use of the shortest paths. The working process of the PT model starts once a carrier is accessed to forward the data packets using the optimal path. We use an analytical mathematical computation to determine the effectiveness of the PT model with the two additional features. Let us assume that \"\(C_{R}\)\" is the communication range and that the distance between the two nodes is \"r\" in meters. The force is inversely proportional to the distance [24]. Therefore, we can apply the free space propagation model to measure \"\(C_{R}\)\", as shown in Equation (18):  
\[C_{R}=\frac{T_{X}\,R_{X}P_{t}\lambda^{2}}{(4\pi^{2})r^{2}N_{l}} \tag{18}\]  
where \"\(R_{X}\)\" and \"\(T_{X}\)\" are the energy gains of the receiver and transmitter, respectively, in watts, \(N_{l}\) (\(N_{l}\geq 1\)) is the network loss, and \"\(\lambda\)\" is the wavelength in meters/second. It is typical to set \(R_{X}=T_{X}=1\) and \(N_{l}=1\). The distance between the two sensors, \"r\", is periodically calculated after a time interval to generate new entries in the table. This process removes the old entries and calculates \"r\", which is used to update the trajectory pheromone in the sensor nodes. The trajectory pheromone is the group of termitesextending from the source to the destination (\(l,s\)). We deploy the features of the trail pheromone and ant control algorithm [25]:  
\[P_{l,s}^{(N)}=\left\{P_{l,s}^{(N)}\times e^{-(rc-rsn)^{\beta})+}\ p^{a}\ ;\ l=\ h^{p}\right. \tag{19}\]  
where \(P_{l,s}^{(N)}\) is the number of pheromones (total number of packets transmitted over the network). from the source sensor node \"s\" that are forwarded onto the link to the one-hop neighbor \"\(l\)\" for node \"n\", h\({}^{p}\) is the previously determined hop of the packet, \"Pa\" is the amount of pheromone that each packet carries, \"r\({}_{c}\)\" is the current distance to the neighbor node \"n\" at link \"l\", \"e\" is the distance from the same neighbor node at link \"l\" to the destination node where the last packet was delivered, and \"\(\beta\)\" is the packet generation rate.