1. On Maximizing Network Lifetime of Broadcast in WANETs under an Overhearing Cost Model Guofeng Deng, Sandeep K.S. Gupta IMPACT Lab (http://impact.asu.edu)http://impact.asu.edu Arizona State University, Tempe, AZ, USA

2. MPACT I Arizona State S.K.S Gupta, ICDCN'062 Outline Background and motivation Receiver Cost Models –Zero Receiver Cost (ZRC) model –Designated receiver cost (DRC) model –Overhearing Cost (OC) model NP-hardness and Approximation ratio Heuristic solutions Simulation results Conclusions

3. MPACT I Arizona State S.K.S Gupta, ICDCN'063 Wireless Broadcast Transmission Energy consumed for reliably transmitting to a node at distance d is proportional to d a where a >=2. Energy is also consumed for various tasks such as packet processing at the sender node and the receiver node. Local Broadcast –Wireless multicast advantage Assuming omnidirectional antenna, all the nodes in the transmission range of transmitting node recv the transmitted packet Energy consumption is equal to reach the farthest neighbor node – instead of sum of transmission power to reach each and every neighbor node. Network (Multihop) Broadcast –Flooding –Tree/Mesh based

4. MPACT I Arizona State S.K.S Gupta, ICDCN'064 Energy Efficient Broadcast in WANETs Minimum energy broadcast (minimizing total transmission power) –NP-hard –BIP [Wieselthier Infocom 2000], EWMA [Cagalj Mobicom 2002] Maximum lifetime broadcast (minimizing maximum transmission power) –Solvable in polynomial time –MST [Camerini IPL 1978][Kang ICC 2003], sub-network solution [Lloyd Mobihoc 2002][Floreen DIALM-POMC 2003], MDLT [Das Globecom 2003], Problem: Receiver cost was ignored. –Receiver cost matters. –TelosB mote: receiver power = peak transmission power

5. MPACT I Arizona State S.K.S Gupta, ICDCN'065 Maximizing Broadcast Tree Lifetime Broadcast tree lifetime: the period of time for the first node to die, i.e., the ratio of battery capacity (E u )to power consumption (p u ) i.e. E u /p u. Maximizing Broadcast Tree Lifetime (MaxBTL): Find a broadcast tree that maximizes the broadcast tree lifetime among all the broadcast trees rooted at the given source node. In the case of identical battery capacity, broadcast tree lifetime is decided by the maximum nodal power consumption. Here, we assume identical battery capacity for simplicity.

6. MPACT I Arizona State S.K.S Gupta, ICDCN'066 Receiver Power Models DRC † –The receiver power, which may vary from node to node, is fixed regardless of the signal strength at the receiver. –E.g., p a T = 16mW –If p a R = 5mW, then p a = 21mW TRC † [Cui ICC 2003][Vasudevan et al. Infocom’06] –The receiver power for decoding a signal is a function of the transmission power of the transmitter as well as the distance between them. –E.g., p a R = d 3 /p s T and d = 5m. p a R = 10.4mW when p s T = 12mW; when p s T increases to 20mW, p a R reduces to 6.25mW. † DRC and TRC are called CORP and TREPT in [Deng&Gupta Globecom’06] respectively.

7. MPACT I Arizona State S.K.S Gupta, ICDCN'067 OC Model A node – whether intended or unintended receiver - consumes energy for receiving packets transmitted by any neighboring nodes. Amount of power consumed for receiving a packet is constant – but can be node-dependent., –N is the set of nodes –X(u,v)=1 if v recv packets from u, otherwise X(u,v)=0. E.g., and.

8. MPACT I Arizona State S.K.S Gupta, ICDCN'068 OC - Example Assuming required transmission power is symmetric between each pair of neighboring nodes; an unitary receiver cost of s is mW. Then, p s R = 5mW because s overheard the transmission from a to b and c. p s R = 0 under any model that does not take into account overhearing cost.

9. MPACT I Arizona State S.K.S Gupta, ICDCN'069 Broadcast Lifetime Example s b a t t t+ε The broadcast tree lifetime is decided by the minimum node lifetime. In the case of identical battery capacity, it is determined by the maximum nodal power consumption. We will present the formal definition shortly. t - transmission power r - receiving power ε - a sufficiently small value We assume t=r s b a t t A maximum lifetime tree in the case of 0-receiving cost OC s b a t t t+r r MAX=t+r=2t s b a t t+ε OC An optimal solution MAX=tr s b a t t+ε t r Lifetime is half of the optimal!

10. MPACT I Arizona State S.K.S Gupta, ICDCN'0610 MaxBTL under ORC: A Difficult Problem NP-hardness: by reducing set cover to MaxBTL Approximation ratio of ZRP and DRP, which are optimal solutions under the ZRC and DRC models respectively, can be as bad as n/2-1. Let t=r. MAX(b)=5r; MAX(c)=3r; MAX(d)=2r. Then put more nodes on the border…

11. MPACT I Arizona State S.K.S Gupta, ICDCN'0611 Prim-Like Greedy Algorithms Prim-Like Greedy Algorithms: –Starts from a single node tree consisting of the source node –Grows the tree iteratively: choosing the best link that connects an on-tree to a non-on-tree node until all the nodes in the network are included in the tree For example, ZRP weights each link in the network graph in terms of transmission power threshold. Proposed heuristic solutions, CRP & PRP, are Prim-like greedy algorithms. We will discuss the link selection criteria in terms of power consumption by assuming identical battery capacity, but the algorithm can be easily modified to accommodate non-identical capacity case. Notice: Prim’s algorithm is used to generate a Minimum- weight Spanning Tree (MST) in an undirected graph; the resulting tree may not be a MST in a directed graph.

12. MPACT I Arizona State S.K.S Gupta, ICDCN'0612 CRP: Cumulative Receiver Power Weight of a link (u,v) is defined as the larger of the following values: –Transmission power over link (u,v), denoted by p(u,v), plus the overall cost of u for receiving/overhearing at the time of being selected. –Unitary receiver cost of v The best link is the one with the lowest weight. s a b c d An on-tree link An overhearing link The theoretic worst case of CRP is also n/2-1 as shown in the aforementioned network graph.

13. MPACT I Arizona State S.K.S Gupta, ICDCN'0613 PRP: Proximity Receiver Power Weight of a link (u,v) is defined as the largest of the following values: –Transmission power over link (u,v) plus the overall cost of u for receiving/overhearing at the time of being selected. –The power consumption of a nearby node that is going to be affected by the added link (increased transmission power) –Unitary receiver cost of v The best link is the one with the lowest weight. s a b c d An on-tree link An overhearing link A potential overhearing link

14. MPACT I Arizona State S.K.S Gupta, ICDCN'0614 Algorithms Summary

15. MPACT I Arizona State S.K.S Gupta, ICDCN'0615 Simulation Results Note: Each caption includes battery capacity, peak transmission power and unitary receiving power.

16. MPACT I Arizona State S.K.S Gupta, ICDCN'0616 Simulation Results (Cont’d) (a)The 4 curves perfectly overlap in the case of 0-receiver cost. (c) Results in asymmetric wireless medium (asymmetric transmission power threshold) (l) Results of non-identical battery capacity.

17. MPACT I Arizona State S.K.S Gupta, ICDCN'0617 Conclusion TDMA based MAC layer (Designated Receiver Cost) DRC: Proposed an optimal solution [Deng & Gupta Globecom 2006] (Was named CORP) DRA: Proposed a binary search algorithm (optimal) when the tree is given [Deng & Gupta Globecom 2006] (Was named TREPT) Random access MAC layer (Overhearing Cost) ORC (OC): NP-hard problem. Proposed two heuristics solutions [This paper] ORA: NP-hard problem. Future work. Constant Receiver CostAdaptive Receiver Cost Receiver power matters Future directions: distributed solutions and more results on adaptive receiver cost

18. MPACT I Arizona State S.K.S Gupta, ICDCN'0618 Thank You!

19. MPACT I Arizona State S.K.S Gupta, ICDCN'0619 Maximizing Broadcast Tree Lifetime Network model –Power consumption is the sum of transmission and receiving power consumption –Transmission power control –Wireless multicast advantage (WMA) –Receiving power will be discussed shortly –Finite battery power capacity and linear battery power model, i.e., the lifetime of a node is the ratio between the amount of battery energy and power consumption. Problem statement –Broadcast tree lifetime: the period of time for the first node to die –MaxBTL: find a broadcast tree that maximizes the broadcast tree lifetime among all the broadcast trees rooted at the given source node.