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section. In the simulations, no retransmission is allowed and the available next-hop node set size is 6.7 on average. The reception power consumption is varied from 10−3 to 10 mw, so the corresponding RTER is in range [3_{× 10}−4_,0.75].

Fig. 3.6 shows the energy efficiency of EGOR is always the best of the three pro- tocols and the RTER is a crucial parameter affecting the energy efficiency of the opportunistic routing. There is a watershed on RTER, smaller than which the energy efficiency of the opportunistic routing is better than the geographic routing, while

10−4 10−3 10−2 10−1 100 0 1 2 3 4 5 6x 10 7 Erx/Etx Energy efficiency (bmpJ) Geographic Opportunistic EGOR

10−4 10−3 10−2 10−1 100 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Erx/Etx

Packet delivery ratio

Geographic Opportunistic EGOR

Figure 3.7: Packet delivery ratio vs reception to transmission power ratio greater than which the geographic routing surpasses the opportunistic routing. The reason is that when the energy consumption of reception is negligible to the trans- mission, the opportunistic routing achieves larger EPA than the geographic routing while consumes nearly the same energy as the geographic routing. So opportunistic routing is more energy efficient. However, when the energy consumption of recep- tion is comparable to transmission, involving all the available next-hop nodes in the opportunistic routing consumes much more energy than the geographic routing, and the cost of the increased energy consumption overwhelms the benefit of the increased EPA. Thus, the energy efficiency of the opportunistic routing is less than the geo- graphic routing when RTER is greater than the watershed. For these two protocols, RTER does not affect the forwarding candidate(s) selecting criteria, so it does not affect the PDR.

Fig. 3.7 shows the results that the PDR of the geographic routing and opportunis- tic routing does not change according to the RTER. For EGOR, the PDR decreases when RTER increases, because EGOR takes the energy consumption into account. When the reception energy cost increases, fewer nodes are selected as forwarding candidates, then the packet is more likely to be lost without retransmission. An interesting observation here is that, even when RTER is very small, EGOR only se- lects a very small number of nodes as the forwarding candidate, but achieves nearly the same energy efficiency as opportunistic routing. For example, when RTER = 0.03%, EGOR only selects 2.2 forwarding candidates on average, while has the same energy efficiency and PDR as the opportunistic routing which selects 6.7 candidates on average. This result again suggests that only a small number of nodes need to be involved in opportunistic routing to achieve a good balance between energy efficiency and routing efficiency.

The hop count performance shown in Fig. 3.8 indicates that the RTER does not affect the hop count of the opportunistic routing and geographic routing, the reason is as the same as the PDR performance of these two protocols. For EGOR, the hop count increases after the RTER is larger than 10% because fewer forwarding candidates are selected and the EPA is decreased.

3.4.2.3 Impact of retransmission limit

In this section we study how the retransmission limit affects the performance of the three protocols. The reception power consumption is fixed on 2mw and the the available next-hop node set size is also 6.7 on average .

Intuitively, increasing retransmission limit will increase the reliability, say PDR. Fig. 3.9 exactly shows this trend for all the three protocols. It is worthy to mention that the benefit of increasing retransmission limit (can be seen as the slopes of the curves) for the opportunistic routing is trivial but for the geographic routing is ob-

10−4 10−3 10−2 10−1 100 7.6 7.7 7.8 7.9 8 8.1 8.2 Erx/Etx Hop count Geographic Opportunistic EGOR

0 1 2 3 4 5 6 7 8 9 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Retransmission limit

Packet delivery ratio

Geographic Opportunistic EGOR

0 1 2 3 4 5 6 7 8 9 0.4 0.6 0.8 1 1.2 1.4 1.6x 10 4 Retransmission limit Energy efficiency (bmpJ) Geographic Opportunistic EGOR

Figure 3.10: Energy efficiency vs retransmission limit

vious (especially when retransmission limit is less than 4). The reason is that the opportunistic routing has already achieves high PDR (nearly 1) by involving all the available next-hop nodes in forwarding even when there is no retransmissions allowed. For the geographic routing, however, there is only one next-hop node involving in the forwarding, then the packet is more likely to be lost in one transmission than the opportunistic routing. For EGOR, the PDR increasing rate is less than that of the geographic routing because EGOR already achieves higher PDR than the geographic routing when there is no retransmissions allowed. When retransmission limit is larger than 1, the PDR gains become less and less for both EGOR and the geographic routing, and when the limit is larger than 3, the PDRs of both are approaching to 1. Fig. 3.10 shows that for opportunistic routing, the energy efficiency is not changed much according to the change of retransmission limit. The reason is that the retrans-

0 1 2 3 4 5 6 7 8 9 7.6 7.7 7.8 7.9 8 8.1 8.2 8.3 Retransmission limit Hop count Geographic Opportunistic EGOR

Figure 3.11: Hop count vs retransmission limit

mission does not play a role for the PDR in opportunistic routing, and almost the same packets can be delivered to the destination whether retransmission is allowed or not. For geographic routing and EGOR, the retransmission does play a role for the energy efficiency when retransmission limit is less than 3. As we have analyzed retransmission affects the PDR, especially from allowing no retransmission to one and from one to two. When retransmission limit is larger than 3, the energy efficiency of these two protocols does not change much as the PDRs are already approaching to 1. As retransmission does not affect EPA much, Fig. 3.11 shows that the hop count remains almost the same when the retransmission limit varies for each of the three protocols.

4 5 6 7 8 9 10 11 −4 −3 −2 −1 0 0 2 4 6 8 10 12

Number of available next−hop neighbors log(Erx/Etx)

Number of forwarding candidates involved

Opportunistic EGOR

Figure 3.12: Number of forwarding candidates involved under different node densities and RTERs