On Maximizing Network Lifetime of Broadcast in WANETs under an Overhearing Cost Model

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) Arizona State University, Tempe, AZ, USA

2. 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 S.K.S Gupta, ICDCN'06

3. Wireless Broadcast • Transmission Energy consumed for reliably transmitting to a node at distance d is proportional to da 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 S.K.S Gupta, ICDCN'06

4. 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 S.K.S Gupta, ICDCN'06

5. Maximizing Broadcast Tree Lifetime • Broadcast tree lifetime: the period of time for the first node to die, i.e., the ratio of battery capacity (Eu)to power consumption (pu) i.e. Eu/pu. • 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. S.K.S Gupta, ICDCN'06

6. 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., paT = 16mW • If paR = 5mW, then pa = 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., paR = d3/psT and d = 5m. paR = 10.4mW when psT = 12mW; when psT increases to 20mW, paR reduces to 6.25mW. † DRC and TRC are called CORP and TREPT in [Deng&Gupta Globecom’06] respectively. S.K.S Gupta, ICDCN'06

7. 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 . S.K.S Gupta, ICDCN'06

8. OC - Example • Assuming required transmission power is symmetric between each pair of neighboring nodes; • an unitary receiver cost of s is mW. Then, psR = 5mW because s overheard the transmission from a to b and c. psR = 0 under any model that does not take into account overhearing cost. S.K.S Gupta, ICDCN'06

9. t+r OC b b s b a s s a b a s s b a a t t+ε t t t t r t+r A maximum lifetime tree in the case of 0-receiving cost MAX=t+r=2t t t t+ε t+ε t t OC r r MAX=t An optimal solution Broadcast Lifetime Example Lifetime is half of the optimal! t - transmission power r - receiving power ε - a sufficiently small value We assume t=r 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. S.K.S Gupta, ICDCN'06

10. 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… S.K.S Gupta, ICDCN'06

11. 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. S.K.S Gupta, ICDCN'06

12. 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 d b c The theoretic worst case of CRP is also n/2-1 as shown in the aforementioned network graph. An on-tree link An overhearing link S.K.S Gupta, ICDCN'06

13. 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 d b c An on-tree link An overhearing link A potential overhearing link S.K.S Gupta, ICDCN'06

14. Algorithms Summary S.K.S Gupta, ICDCN'06

15. Simulation Results Note: Each caption includes battery capacity, peak transmission power and unitary receiving power. S.K.S Gupta, ICDCN'06

16. Simulation Results (Cont’d) • 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. S.K.S Gupta, ICDCN'06

17. Conclusion • Receiver power matters • Future directions: distributed solutions and more results on adaptive receiver cost S.K.S Gupta, ICDCN'06

18. Thank You! S.K.S Gupta, ICDCN'06

19. 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. S.K.S Gupta, ICDCN'06