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Let us now include the energy consumed by circuitry other than the RF amplifier at node u in this analysis, and let us consider the power measurements performed on a real wireless card, such as those referring to a CISCO Aironet PC4800 card reported in (Ebert et al.
2002). With this energy model, a node consumes 1.9 W when transmitting at maximum power (corresponding to a nominal transmit power of 50 mW), and 1.48 W when transmitting at minimum power (nominal transmit power 1 mW). So, under the assumption that v is within uís maximum transmitting range (otherwise the direct communication between u and v would be impossible), we have that sending the packet directly has a power cost of at most 1.9 W. On the other hand, relaying the packet through w would require two transmissions, each consuming at least 1.48 W. Since 1.9 < 2 ? 1.48 = 2.96, we can conclude that with this more-realistic energy model sending the packet directly to node v is always the best solution! Note that in this analysis we have not considered the power consumed at the receiver end of the communication, which would also play in favor of the single-hop transmission.
The example above has clearly shown that the energy model has a strong influence on the choice of the energy-efficient links and that accounting for only the radiated power is likely to lead to incorrect conclusions about what an energy-efficient topology is. Thus, further research along this line is urgently needed.
15.3 Mobility and Topology Control
In Chapter 13, we have discussed the effects of node mobility on the design and implementation of TC protocols and on the setting of important parameters such as the critical neighbor number in neighbor-based TC. However, fundamental questions concerning the application of TC techniques in mobile networks still have to be answered. In particular, we cite the following:
1. Is mobility beneficial or detrimental? On one hand, we have seen that mobility results in an increased message overhead for maintaining the desired topology (see Chapter 13). This has a negative effect on both network capacity (because a portion of the available bandwidth is used for control messages) and node energy consumption (because nodes send/receive more control messages). On the other hand, mobility has also positive effects on both capacity and energy consumption. In fact, it is known that node mobility can be seen as a means to increase network capacity, provided the delay in packet delivery is not a primary concern (Grossglauser and Tse 2001). As for energy, mobility has the positive effect of balancing the node power consumption: in stationary networks, if a node u uses twice the transmit power of another node v, it is likely to deplete its battery much faster than node v. In presence of mobility, nodes change the transmit power dynamically, and a more balanced energy consumption (with positive effects on network lifetime) is likely to occur. Given this picture, it is still not clear what the overall effect of node mobility is on the network capacity increase and lifetime extension potentially achieved by TC mechanisms.
2. Determination of the optimal frequency for reconfiguration: As discussed in Section 13.2, in presence of node mobility, there is a clear trade-off between the message overhead generated by the repeated execution of a TC protocol and the quality of the constructed topology: the more frequently the protocol is reexecuted (i.e. the higher the message overhead), the higher the quality of the constructed topology (e.g. a topology that preserves connectivity). A careful investigation of this trade-off, which would help in answering the issue (1), is still lacking in the literature.
15.4 Considering MultiHop Data Traffic
As witnessed by the considerable body of research reported in this book, a great deal of attention has been devoted to the identification of efficient network topologies, with a particular emphasis on energy efficiency. However, a common approach in the literature is to consider the TC problem as a stand-alone problem, which is analyzed and solved under a graph-theoretic perspective. This type of approach has resulted in the message conveyed by current TC literature: the sparser the network topology, the better (provided certain spanning properties of the graph are satisfied).
Indeed, we believe that the problem of determining the Ďoptimalí network topology cannot be solved by assigning a weight to the links and building a spanner graph, as it is commonly done in current TC literature: in fact, what is an optimal topology depends on several factors, such as the expected network traffic, the desired level of QoS that the network should provide, and so on, which are disregarded by the current approaches to the TC problem. In the following, we clarify this point with some examples.
Figure 15.4 Example showing that a topology with optimal power spanning factor might not be optimal for extending network lifetime.