i) RTS-RTS collision
Figure 4 shows an example of an RTS-RTS collision. In Fig. 4, x indicates the airtime of each node. Here, we consider a link between Node 10 and Node 11. In Fig. 4, RTS-RTS collisions occur when Node 10 starts to transmit an RTS frame during the RTS transmission of Node 12. Similarly, RTS-RTS collisions also occur when Node 12 starts to transmit an RTS frame during the RTS transmission of Node 10.
Now, Node 11 uses the airtime during the interval [0, Time]. While Node 11 transmits an RTS frame, neither Node 10 nor Node 12 can transmit a frame because of the carrier-sensing mechanism and the reception of the frame, respectively. Then, we consider the following four situations.
1. The situation in which both Node 10 and Node 12 receive an RTS frame of Node 11 successfully. Node 10 sets the NAV until the data transmission of Node 11 finishes, i.e., Node 10 cannot transmit a frame. Similarly, Node 12 cannot transmit a frame during the reception of Node 11’s frame or the transmission of Node 12’s frame.
2. The situation in which Node 12 receives an RTS frame of Node 11 successfully, but Node 10 does not receive an RTS frame of Node 11. Node 10 does not set the NAV. However, because of the carrier-sensing mechanism, Node 10 cannot transmit a
frame until the data transmission of Node 11 finishes.
3. The situation in which Node 10 receives an RTS frame of Node 11 successfully, but Node 12 does not receive an RTS frame of Node 11. The transmission of Node 11 is not successful. However, Node 10 sets the NAV during the normalized time expended from data transmission until ACK reception.
4. The situation in which neigher Node 10 nor Node 12 receive an RTS frame of Node 11. This situation occurs when both Node 9 and Node 13 start to transmit a frame during the RTS transmission of Node 11. Such network situations rarely occur.
In the above cases, if Node 11 uses x, then transmission failures between Node 10 and Node 11 do not occur during (x + y). This is because transmissions of Node 10 and Node 12 do not overlap during this period. Thus, for Node 10 and Node 12, the remaining time is1−(x+y), during which both transmissions may overlap. The probability that Node 10 starts to transmit an RTS frame during the RTS transmission of Node 12 is ax. Furthermore, the probability that Node 12 starts to transmit an RTS frame during the RTS transmission of Node 10 is ax.
i) RTS-RTS collisionFigure 4 shows an example of an RTS-RTS collision. In Fig. 4, x indicates the airtime of each node. Here, we consider a link between Node 10 and Node 11. In Fig. 4, RTS-RTS collisions occur when Node 10 starts to transmit an RTS frame during the RTS transmission of Node 12. Similarly, RTS-RTS collisions also occur when Node 12 starts to transmit an RTS frame during the RTS transmission of Node 10. Now, Node 11 uses the airtime during the interval [0, Time]. While Node 11 transmits an RTS frame, neither Node 10 nor Node 12 can transmit a frame because of the carrier-sensing mechanism and the reception of the frame, respectively. Then, we consider the following four situations.1. The situation in which both Node 10 and Node 12 receive an RTS frame of Node 11 successfully. Node 10 sets the NAV until the data transmission of Node 11 finishes, i.e., Node 10 cannot transmit a frame. Similarly, Node 12 cannot transmit a frame during the reception of Node 11’s frame or the transmission of Node 12’s frame.2. The situation in which Node 12 receives an RTS frame of Node 11 successfully, but Node 10 does not receive an RTS frame of Node 11. Node 10 does not set the NAV. However, because of the carrier-sensing mechanism, Node 10 cannot transmit aframe until the data transmission of Node 11 finishes.3. The situation in which Node 10 receives an RTS frame of Node 11 successfully, but Node 12 does not receive an RTS frame of Node 11. The transmission of Node 11 is not successful. However, Node 10 sets the NAV during the normalized time expended from data transmission until ACK reception.4. The situation in which neigher Node 10 nor Node 12 receive an RTS frame of Node 11. This situation occurs when both Node 9 and Node 13 start to transmit a frame during the RTS transmission of Node 11. Such network situations rarely occur.In the above cases, if Node 11 uses x, then transmission failures between Node 10 and Node 11 do not occur during (x + y). This is because transmissions of Node 10 and Node 12 do not overlap during this period. Thus, for Node 10 and Node 12, the remaining time is1−(x+y), during which both transmissions may overlap. The probability that Node 10 starts to transmit an RTS frame during the RTS transmission of Node 12 is ax. Furthermore, the probability that Node 12 starts to transmit an RTS frame during the RTS transmission of Node 10 is ax.
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