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QoS Topology Control and Energy Efficient Routing in Ad hoc Wireless Networks Prof. Xiaohua Jia Dept of Computer Science, City Univ of Hong Kong 1 Mobile Ad Hoc (Wireless) Networks What’s a mobile ad hoc network? 1) Mobility 2) No wired infrastructure S 2 Energy-efficiency in ad hoc networks Power function: p(u,v) = dα(u,v), 2 ≤ α ≤ 4 Two special features of radio transmission: 1) Broadcast in nature. 2) p(u,w) + p(w,v) < p(u,v), relaying messages by a third node may result in a smaller energy cost. 3 Topology Control Problem Given a set of wireless nodes V in a plane, for each node u, adjust its transmission power to p(u), such that the network is fully connected and is minimized. 4 R. Ramanathan, R. Rosales-Hain, “Topology control of multihop wireless networks using transmit power adjustment”, INFOCOM’00. Greedy algorithm (based on Kruskal’s MST algorithm) 4 5 3 C D 1 1 A B 3 Side-effect edge problem Distributed algorithms: LINT and LILT 5 R. Wattenhofer, L. Li, P. Bahl and Y.M. Wang, “Distributed topology control for power efficient operation in multihop wireless ad hoc networks”, INFOCOM’01. G: topology by max power; G’: topology by min power. Algorithm: 1) Divide uniformly a node’s region into cones with angle α; 2) Increase a node-power until there is a neighbor in each cone, or it reaches max power of the node. Theorem. Let α ≤ 2π/3. G’ is connected if G is connected. u α 6 N. Li, J. Hou and Lui Sha, “Design and Analysis of an MST-based Topology Control Algorithm”, IEEE INFOCOM’03. N. Li and J. Hou, “Topology control in heterogeneous wireless networks: problems and solutions”, IEEE INFOCOM’04. Algorithm: 1) Collect information about maximally reachable neighbors; 2) Construct a local MST (in terms of transmission power) among neighbors by each node; 3) Determine the actual power of each node (the neighbors of u in G’ are 1-hop nodes in u’s local MST). Theorem 1. G’ is connected if G is connected. Theorem 2. The degree of any node in G’ is bounded by 6. 7 QoS topology control Given a set of nodes in a plane: B, max bandwidth capacity at a node. λs,d, end-end traffic demand between s, d. Δs,d, maximal hop-count allowed between s, d. Problem. Find transmission power p(i) for 0 i n, such that λs,d, for all pairs (s,d), can be routed within Δs,d, and Pmax is minimized, where Pmax = max{p(i) | 0 i n}. 8 Traffic Non-splittable Formulations Variables: xi,j - boolean, xi,j = 1 if there is a link from node i to node j; otherwise, xi,j = 0. - boolean, = 1 if the route from s to d goes through the link (i,j); otherwise = 0. Pmax - the maximum transmitting power of nodes. 9 Traffic non-splittable Objective : Min Pmax Topology constraints: i j’ j Transmission power constraint: Delay constraint: i 10 Traffic non-splittable Bandwidth constraint: Flow constraints: Binary constraint: 11 Traffic non-splittable Topology of six nodes and six requests Non-splittable case Splittable case 12 Trarffic Splittable Formulation Variables: and Pmax remain the same. - amount of (s, d)’s traffics going through link (i, j). Objective : Min Pmax Topology constraints: i j’ j Transmission power constraint: 13 Formulation (cont’d) Bandwidth constraint: Flow constraints: Variable constraints: 14 Two steps of solution Step 1. QoS load-balanced routing Lmax: maximal node-load Problem. Given a network graph G and traffic demands between node pairs, route these traffics in this graph, such that Lmax minimized. 15 Formulation of QoS routing problem Objective : Min Lmax Constraints: 16 Step 2. QoS topology control Algorithm: 1) sort all node-pairs (i,j) in ascending order according to their distance d(i,j). 2) pick up the node-pair with closest distance but not yet connected and increase the power to make them connected. 3) run the QoS routing algorithm on G to obtain Lmax. If Lmax ≤ B, then stop; otherwise repeat (b) and (c). 17 Experimental results (a) λ = 0.02B (b) = 0.1B (c) λ = 0.2B (d) λ = 0.32B 18 Experimental results max avg min 14 node degree 12 10 8 6 4 2 0 0.025B 0.05B 0.075B 0.1B 0.125B 0.15B 0.175B 0.2B 0.225B λm Node-degrees versus λm X. Jia, D. Li, and D. Du, “QoS topology control in ad hoc wireless networks” , INFOCOM’04. 19 Routing Protocols in Ad Hoc Networks • Proactive protocols (routing table based), such as DSDV (Destination Sequenced Distance Vector), OLSR (Optimized Link State Routing), etc. • On-demand protocols (reactive protocols), such as DSR (Dynamic Source Routing), AODV (Ad- hoc On-demand Distance Vector), etc. • Virtual backbone based protocols, such as Spine-based method, clustering method, hierarchical protocols, etc. 20 D. B. Johnson, D. A. Maltz, Y.C. Hu, and J. G. Jetcheva, The Dynamic Source Routing Protocol for Mobile Ad Hoc Networks, http://www.ietf.org, draft-ietf-manet-dsr-05.txt, Mar 01. Dynamic Source Routing (DSR): 1. Source s finds a route to destination d by flooding a Rreq packet. 2. d replies a Rrep packet to s by reversing the route appended to the Rreq. 3. s includes the route to d in each data packet to d (called source routing). 21 Route Caching in DSR • Each node learns routing information from both Rreq and Rrep packets and caches the routes. • When a node receives a Rreq to d and it has a valid route in its cache, it replies the route to s. 22 Charles E. Perkins, E. M. Royer and Samir R. Das, “Ad-hoc On-Demand Distance Vector (AODV) Routing”, draft-ietf- manet-aodv-08.txt, http://www.ietf.org, Mar 2001. AODV (Ad-hoc On-demand Distance Vector) • It is similar to DSR in route discovery, but improves DSR by keeping routing tables (next-hop) at nodes (no route info in data packets). • When a node receives a Rreq, it sets up a reverse path to the source in its routing table. • Rrep travels along the reverse set-up path to s and the forward-path (i.e., the route from s to d) is set up as the Rrep travels to s. • Entries in routing table are purged after a timeout. 23 C. E. Perkins and Pravin Bhagwat, “Highly Dynamic Destination-Sequenced Distance-Vector Routing (DSDV) for Mobile Computers”, ACM SIGCOMM, Oct 1994, pp.234-244. Destination Sequence Distance Vector Routing: • It mimics the Distance Vector Routing. • Each node keeps a routing table: next-hop and distance to each destination, and dest-sequnce-no. • Each node periodically exchange the routing table with neighbors. • Data packets are forwarded towards destinations by using the next-hop info in routing tables on the way. 24 Power-Aware Routing • Define optimization goals on energy cost for routing, e.g., minimum energy cost per packet, maximum network lifetime, maximum minimum residual energy. • Assign a weight to each link according to optimization goal, e.g., energy cost over a link, residual energy at nodes. • Perform routing with minimum weight. 25 Energy Efficient Broadcasting Ts: broadcast tree rooted from source s; NL(Ts): set of non-leaf nodes of Ts. Problem. Given a set of nodes in a plane, for each node u, adjust its transmission power p(u), to form a Ts, such that: S To determine, for each node u: 1) Transmission power of u, and 2) The children of u. 26 J. Cartigny, D.Simplot, and I. Stojmenovic, “Localized minimum-energy broadcast in ad-hoc networks”, IEEE INFOCOM’03. Algorithm: 1) Construct a connected topology that has min total energy. 2) Derive the broadcast tree from the min-energy topology using neighbor elimination scheme. S 27 J.E. Wieselthier, G. D. Nguyen, and A. Ephremides, “On the Construction of Energy-Efficient Broadcast and Multicast Trees in Wireless Networks”, IEEE Infocom’00. BIP (broadcast incremental power): 1) It is based on Prim’s MST algorithm. 2) Starting from s, each time a new node that can be connected by a tree-node with least incremental power is added to the tree, until all nodes are in the tree. s 28 Energy Efficient Broadcast with Given Transmission Power p(v): transmission power of node v; Ts: broadcast tree rooted from source s; NL(Ts): set of non-leaf nodes of Ts. Problem. Given a set of nodes in a plane and p(v) for each node v, find a Ts that: 29 Transforming the problem to the Steiner tree problem The broadcast routing problem is transformed to: finding a directed tree Ts’ in G’ that spans all nodes in V’ and the total weights of Ts’ is minimized. 30 A Greedy Heuristic U: uncovered set; D: covered set; Vi: set of outgoing neighbors of node i; 1) D ←Vs; U ← V – Vs; 2) Pick from D a node i that has the largest value of: | Vi∩U|/p(i); D ← D + Vi; U ← U - Vi; 3) Repeat step 2 until D = V. 31 A Node-weighted Steiner Tree Based Heuristic Theorem 1. Given G(V, E) and s, this heuristic can output a broadcast tree in time O(n4). Theorem 2. The approximation ratio is at most 2ln(n-1)+1. 32 Experimental Results 4000 4000 NST-h NST-h 3750 Greedy-h 3750 Greedy-h SPT-h SPT-h 3500 3500 energy cost energy cost 3250 3250 3000 2750 3000 2500 2750 2250 2500 2000 2250 0 20 40 60 80 100 0 20 40 60 80 100 the num ber of nodes the num ber of nodes D. Li , Xiaohua Jia and H. Liu, "Energy efficient broadcast routing in ad hoc wireless networks", IEEE Trans on Mobile Computing, Vol. 3, No. 2, Apr - Jun, 2004, pp.144-151. 33 Energy-Balanced Multicast Routing Given a wireless network G(V,E): Ei – initial energy at node i. wi,j – power cost per time-unit on link li,j, wi,j = dαi,j. Problem. For a multicast request (s, D, t), find a routing tree, such that the minimal remaining energy of nodes is maximized after the multicast session. S. Cheng, X. Jia, F. Hung, and Y. Wang, “Energy efficient broadcasting and multicasting in static wireless ad hoc networks”, IEEE Trans on Wireless Communications. 34 Maximizing broadcast/multicast duration routing Given a wireless network G(V,E): Ei – initial energy at node i; wi,j – power cost per time-unit on link li,j. Problem. Find a set of broadcast / multicast trees, such that the duration of the broadcast / multicast session is maximized. 35 The End 36