TRABAJO PRODUCTIVO BLOQUE C

Routing protocols have a significant impact on energy efficiency and latency perfor- mances and choosing an efficient routing scheme is a multi-objective optimization prob- lem [43]. Long-hop routes demand substantial transmission power but minimize the energy cost for reception, computation and etc, meanwhile, decrease the number of hops, i.e, reduce the end to end delay. On the opposite, routes made of shorter hops use fewer transmission power but maximize the energy cost for reception since there is an increase in the number of hops which means more delay. M. Haenggi points out several advantages of using long-hop routing in [38,39], among which high energy ef- ficiency is one of the most important factors. These works reveal the importance of the transmission range and its impact on the energy conservation but don’t provide a theoretical analysis on the optimal hop length regarding various networking scenarios. Some works analyze the optimal transmission range from the viewpoint of physi- cal layer. [14] defines the optimal one-hop length for multi-hop communications that minimizes the total energy consumption and analyzes the influence of channel param- eters on this optimal transmission range in a linear network. The same issue is studied in [30] with a Bit-Meter-per-Joule metric where the authors study the effects of the network topology, the node density and the transceiver characteristics on the overall energy expenditure. This work is improved by [25] which showed the effects of network parameters such as node density, network radius on the optimal transmission range and the impacts of the path loss exponent in a 2-dimension Poisson network. [22] solve a cross-layer optimization problem to minimize the energy consumption and delay for a TDMA based small-scale sensor networks. However, all of the aforementioned works are based on the assumption of a disc link model as described in Chapter 1.

Recently, unreliable links are taken into account in the routing scheme design by introducing a link probability and the effect of link error rate, e.g., in [8, 46]. In [8], the authors derive the minimum energy paths for a given pair of source and destination nodes and propose the corresponding routing algorithm. However, the energy model used in this thesis includes the transmission power only and does not consider circuitry energy consumption at the transmitter and receiver side. In fact, such a model leads to an unrealistic conclusion which states that the smaller hop distance, the higher energy efficiency. As we show in this thesis, considering a constant circuitry power according to [47] results in completely different conclusions. In [46], a routing scheme is proposed whose metric for the relay selection is P RR× distance, where PRR is short for Packet Reception Ratio. This routing scheme makes best use of unreliable links to improve the energy efficiency.

These efforts are devoted to the various low-energy routing scheme design while keeping non-protocol system parameters fixed such as the transmission power, transceiver power characteristics, node density and etc. However, very few works address the re- lationship between the network performance and the network parameters, in other words, the best networks performance that could be obtained by setting all parameters of physical layer, MAC layer and routing layer in a network as a whole.

In this chapter, we will explore the Pareto front of energy-latency trade-off while adopting a very generic network layer/routing model for low-traffic applications. This Pareto front can serve as a benchmark for preliminary performance evaluation and is suitable in the early phases of network planning and design to optimize physical parameters. To find this bound, a comprehensive energy model is used which includes energy consumption for both data packet and control packet. Meanwhile a realistic unreliable link model is introduced into the energy model by the metric, mean energy distance ratio, EDRb. We focus on two factors which are tightly related energy efficient and latency performance: mean hop length and transmission power.

The contributions of this chapter are:

• The closed form expression of the lower bound of energy-delay trade-off for a

linear and a Poisson network is achieved in AWGN, Rayleigh flat fading and Rayleigh block fading channels employing both a comprehensive energy model and an unreliable link model.

• The close-form expressions of the optimal transmission range and for the corre-

sponding optimal transmission power are derived in three types of channel afore- mentioned .

• The closed form expression of the lower bound of energy efficiency of a multi-hop

communication and its corresponding maximum mean delay are obtained. The rest of this chapter is organized as follows: Section2.3concentrates on present- ing the models and metrics used in the chapter. Next, two scenarios are considered: minimizing the energy consumption with and without delay constraint. Section 2.4

focuses on the optimal trade-off between the energy consumption and the delay in lin- ear networks. we derive the lower bound of energy-delay tradeoff and a closed form expression of optimal transmission range and optimal transmission power with mean delay request. In Section 2.5 the close-form expression of the lower bound in three kinds of channel is provided. Finally, section 2.6concludes our work and explains the applications of the all theoretical analyses.

18 Models and metrics