Maximizing the Lifetime of Wireless Sensor Networks through Optimal Single-Session Flow Routing Y.Thomas Hou, Yi Shi, Jianping Pan, Scott F.Midkiff Mobile computing September 2006

2 Outline  Introduction  Network Reference Model  Optimal Single-Session Flow Routing  Extension to Variable Bit-Rate  Conclusion

3 Introduction  Consider a two-tier wireless sensor network and address the network lifetime for upper- tier aggregation and forwarding node.  Existing flow routing solutions proposed for maximizing network lifetime require AFNs to split flows to different path during transmission, which we called multi-session flow routing.

4 Network model considered here

5 Introduction  Owing to the transmission bottleneck of AFN, the lifetime of whole sensor network here is the lifetime of AFN.  The majority of power consumption at an AFN is due to its radio communication, it is essential to devise strategies that can minimize radio-related power consumption at AFN.  One promising approach to maximizing network lifetime is to dynamically control the output power level of radio transmitters.

6 Introduction  Existing solutions to this problem, obtained under linear programming, require each AFN to split data flows to multiple path during transmission, which we call multi-session flow routing solutions.

7 Introduction  Multi-session flow routing solutions has some problems here: Necessary for the AFN to perform power control at packet-level to conserve energy. To guarantee packet-level power control between a transmitter and a receiver, the synchronization requirement is stringent and will bring in considerable overhead.

8 Introduction  Our goal is to develop single-session flow routing solutions, where routing topologies are relatively static and are adjusted (via power control) on large timescale.  To achieve this objective, we first show that an optimal multi-session can be transformed into an equivalent single-session flow routing solution.

9 Network Reference Model Deployed densely Within one hop Constituted by MSN Energy unconstrained Aggregation & Relay Constituted by AFN && BS

10 Network Reference Model- power consumption model  When AFN i transmits data to AFN k, the power consumption at transmitter can be modeled as is the power consumption cost of link ( i, k) is the bit-rate of flow sent by AFN i to AFN k

11 Network Reference Model- power consumption model  Where is a distance-independent term is a coefficient associated with the distance-dependent term is the distance between these two nodes n is the path loss exponent and  In this paper we adopt n = 4

12 Network Reference Model- power consumption model  The power consumption at receiver of AFN j can be modeled as: is the incoming bit-rate of composite flow received by AFN j from AFN k is the coefficient of receiver, there is a detailed discussed in other paper

13 Optimal Single-Session Flow Routing-LP method  Variable used introduction Data flow ’ s bit-rate generated by AFN i is Initial energy at AFN i is The lifetime of AFN is T  We then have the following equations for each AFN i AFN generated bit + received bit = outgoing bit The energy required to received and transmit all these flows, cannot exceed it total energy

14 Optimal Single-Session Flow Routing-LP method  We then derive the following LP formulation Where Our object is to maximizing T

15 Optimal Single-Session Flow Routing-Single flow method  Advantages of single flow routing Power control and topology change are only done on a much larger time scale instead of on the per-packet basis Synchronization requirement compared to multi-session is quite low and its overhead is negligible when compared to multi-session flow routing

16 Optimal Single-Session Flow Routing-Single flow method   Theorem 1 can be proved by constructing a single-session flow routing solution (denoted as ) for a given multi-session flow routing solution, and showing that is equivalent to

17 Optimal Single-Session Flow Routing-Single flow method

18 Optimal Single-Session Flow Routing-Single flow method

19 Optimal Single-Session Flow Routing-Single flow method

20 Optimal Single-Session Flow Routing-Single flow method

21 Optimal Single-Session Flow Routing-Single flow method

22 Optimal Single-Session Flow Routing-Single flow method

23 Optimal Single-Session Flow Routing-Numerical Example  Consider the following network

24 Optimal Single-Session Flow Routing-Numerical Example  With the LP approach, we obtain a static multi-session flow routing solution.  For given initial energy at each AFN, the maximum network lifetime obtained by solving the corresponding LP problem is T = days

25 Optimal Single-Session Flow Routing-Numerical Example  According to algorithm 1, since nodes 2, 4, 5 are already in single-session mode, there is no need to perform transformation on them.( except the flow rate of 4 and 5 need to be recomputed )  We then transform AFN 1 to a single- session routing schedule. Since and only is unknown, we obtain = [0,37.79) Similarly, It is easy to verify that the flow balance equation at each AFN is satisfied throughout[0,302.88).

26 Optimal Single-Session Flow Routing-Numerical Example

27 Optimal Single-Session Flow Routing-Numerical Example

28 Extension to Variable Bit-Rate  We relax the constant bit-rate constraint for at each AFN i  We show that as long as the average bit-rate( denoted by ) for can be estimated, the optimal single- session flow routing solution is also obtainable

29 Extension to Variable Bit-Rate- Perfect knowledge of average bit-rate  As above, this theorem can be proved by constructing a single session flow routing solution for P with the same network lifetime as that obtained for

30 Extension to Variable Bit-Rate- Perfect knowledge of average bit-rate

31 Extension to Variable Bit-Rate- Perfect knowledge of average bit-rate

32 Extension to Variable Bit-Rate- Perfect knowledge of average bit-rate  We proof theorem 3 by showing that the maximum network lifetime for problem is indeed greater than or equal to maximum network lifetime for problem P.( vice versa )

33 Extension to Variable Bit-Rate- Proof  For any given network flow routing solution under P with network lifetime, we can find an equivalent flow routing solution under with the same network lifetime

34 Extension to Variable Bit-Rate- Proof

35 Extension to Variable Bit-Rate- Proof

36 Extension to Variable Bit-Rate- Perfect knowledge of average bit-rate  The significance of theorem 2 and 3 is that they enable us to obtain an optimal single- session flow routing solution for a general sensor network of variable bit-rate AFNs.  In a nutshell, this approach takes the following two steps Find an optimal multi-session flow routing solution for Apply algorithm 2 to get an optimal single- session flow routing solution for p

37  For a node with single transceiver, this would require a packet-level power control to conserve energy, which calls for considerable overhead in synchronization among the AFNs.  We show that the packet-level power control is not necessary.  Instead, it is possible to achieve the same maximum network lifetime by employing power control in a much larger timescale with so-called single-session flow routing method.  In practice, the estimated average bit-rate for g could deviate from actual value.  As long as this discrepancy is not substantial, the procedure developed previously can still yield near- optimal single-session flow routing solution. Conclusion