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continue their study of heterogeneous WSNs in reference 15 They consider a WSN with nodes of two types distributed over a sensor eld using twodimensional homogeneous Poisson point processes: (a) type 0 nodes with intensity (average number per unit area) 0 and battery energy E0 and (b) type 1 nodes with intensity 1 and battery energy E1 The type 0 nodes do the sensing while the type 1 nodes act as the cluster heads Nodes use multihop paths to communicate with their closest cluster head The optimum node intensities ( 0 , 1 ) and node energies (E0 , E1 ) that guarantee a lifetime of at least T units, while ensuring both connectivity and coverage of the surveillance area with high probability, are determined The overall cost of the network is minimized under these constraints.

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Rate control for communication networks: Shadow prices, proportional fairness and stability Journal of Operations Research Society, 49(3):237 252, 1998 50 S Boyd and L Vandenberghe Convex Optimization, Cambridge University Press, 2004 51 M Chiang To layer or not to layer: Balancing transport and physical layers in wireless multihop networks In Proceedings of IEEE INFOCOM, 2004, pp 2525 2536 52 L S Brakmo and L L Peterson TCP Vegas: End to end congestion avoidence on a global internet IEEE Journal on Selected Areas in Communications, 13(8):1465 1480, 1995 53 E-S Jung and N H Vaidya Power aware routing using power control in ad hoc networks Department of Computer Science, Texas A&M University, College Station, TX, Technical Report, February 2005 54 T Nandagopal, T Kim, X Gao, and V Bharghavan Achieving MAC layer fairness in wireless packet networks In Proceeding of ACM MobiCom, 2000 55 B Radunovic and J-Y.

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Limit orders have specific price instructions, requiring them to be filled at the designated price or better. For example, if you enter a buy limit order, it needs to be filled at or below that price and cannot be filled at a higher price. In effect, you are saying you will pay x price but no more. If you enter a sell limit order, it needs to be filled at the specific price you designate or higher. The fill cannot be at a lower price, but it could be higher than you specified, depending on price action at the time. These orders set specific prices where you want to enter or exit the market. Generally, the market needs to trade through your price area to ensure a fill. If you absolutely must have a fill, you may want another type of order as there is no guarantee that a limit order will be filled, even if your designated price is touched. You should also be aware of the fact that floor brokers are typically not held to execute these limit orders during the opening and closing ranges. For example, if you placed a limit order before the open to buy 10 contracts of March Corn at 2.18 and the low of the day was 2.17, you could expect to be filled on your order unless it was in the opening or closing range or in a fast market condition.

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Here, the network lifetime is de ned as the number of successful data gathering trips (or cycles) that are possible until connectivity and/or coverage are lost Conditions for a sharp cutoff are taken into account This means that it is ensured that almost all the nodes run out of energy at about the same time so that there is very little energy lost due to residual energy The results comparing a random deployment of nodes with a deployment in which nodes are placed deterministically along grid points show that 1 scales approximately as 0 The results can be extended to take into account unreliable nodes Duarte-Melo and Liu [25] examine the performance and the energy consumption of a heterogeneous WSN providing periodic data from a sensor eld to a remote receiver.

Le Boudec Optimal power control, scheduling and routing in UWB networks IEEE Journal on Selected Areas in Communications, 22(7):1252 1270, 2004 56 Y Nesterov and A Nemirovskii Inter-point polynomial algorithms in convex programming In SIAM Studies in Applied Mathematics, 1994 57 M Minoux Mathematical Programming: Theory and Algorithms, John Wiley & Sons, New York, 1986..

A at homogeneous WSN is compared to one in which an overlay of fewer more powerful sensor nodes is added The energy consumption is formulated and the estimated lifetime based on a clustering mechanism with varying parameters related to the sensor eld, such as size and distance, is studied The optimal number of clusters is quanti ed based on the model Also, an allocation of energy between the two levels of the architecture is discussed Li and Mohapatra [26] develop an analytical model for the problem of nonuniform energy drainage It is found that density does not affect the energy consumption rate of a node This con rms the fact that simply deploying more nodes in a network cannot prolong its lifetime Using the model, they investigate the effectiveness of some existing approaches toward mitigating the nonuniform energy drainage problem in a.

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