Low Latency Broadcast in Multi-Rate Wireless Mesh Networks

1. Low Latency Broadcast in Multi-Rate Wireless Mesh Networks LUO Hongbo CS Dept, City Univ.

2. Outline • Introduction • Heuristic Algorithms • Discussion CS Dept, City Univ.

3. Introduction- Wireless Mesh Networks • Mesh routers & mesh clients • Mesh routers have minimal mobility • No strict constraint on power consumption CS Dept, City Univ.

4. Introduction- Low Latency Broadcast • Energy-efficient broadcast • Broadcast advantage is exploited • Broadcast latency: computed as the maximum delay between the transmission of a packet by a source node and its eventual reception by all the intended receivers. • Multi-rate natures in WMNs CS Dept, City Univ.

5. Introduction- Transmission and Interference Model • Transmission model: Pr =Pt • The transmission range is a decreasing function of transmission rate • Interference Model: • The distance between the transmitter and receiver dijRi; • No transmitter nk within a finite distance Rk’ (such that dkj <=Rk’) is transmitting concurrently. CS Dept, City Univ.

6. Introduction- Impact of Multi-rate Links (Interference range is 520m) CS Dept, City Univ.

7. Introduction- The Model Assumptions • Single radio & single channel • Fixed transmission power and multi-rate broadcast by adjusting the modulation scheme • Receiver based interference model CS Dept, City Univ.

8. Problem: Minimize the broadcast latency with possibly multiple number of transmissions per node in a multi-rate wireless mesh network This problem is NP-Hard Key Issues: Whether a node should broadcast and if so, to which of its neighbors; The timing of these broadcasts. Introduction- Optimization Problem CS Dept, City Univ.

9. Topology Construction SPT CDS BIB WCDS Downstream Multicast Grouping Multiple transmission per node is allowed Transmission Scheduling Heuristic Algorithm - Problem Decomposition CS Dept, City Univ.

10. Heuristic Algorithm - Broadcast Incremental Bandwidth (BIB) • Mathematical notations The mesh network can be represented as a graph G=(V,E). denotes the direct unicast link between nodes i and j, which is associated with a transmission rate Rij. • Basic Idea (from BIP) • Initially, every node except the root node will be set to a cost with 1/Rij • In each iteration, the node with the minimum of incremental cost will be added to the tree CS Dept, City Univ.

11. Heuristic Algorithm – An Example with BIB 1 2 8 8 CS Dept, City Univ.

12. Heuristic Algorithm – An Example with BIB 1 1 2 8 8 CS Dept, City Univ.

13. Heuristic Algorithm – An Example with BIB 1 8 1 1 2 8 8 CS Dept, City Univ.

14. Heuristic Algorithm – Weighted Connected Dominating Set (WCDS) • MCDS performs poorly in multi-rate case • Minimum WCDS problem For a given graph G= (V,E), we suppose there are k different rates given by r1,r2,…,rk, Let N(x,ri) denote the nodes that are reachable from node using rate ri. The aim is to find a subset Y = {y1,y2,…} in V and the broadcast rate wi for node yi such that: • Every element of V\Y is in • The set Y is connected • The weighted sum is minimal CS Dept, City Univ.

15. Heuristic Algorithm – Weighted Connected Dominating Set (WCDS) • The basic idea of the algorithm We suppose the set C including the nodes which have received the message and are eligible to transmit. • Initially, we make the source node s eligible to transmit, C={s} • In each iteration, for every eligible node c and rate r, we choose the (c, r) combination that maximizes the rate of increase of not-yet-covered nodes, as measured by f(c,r) = |N(c,r)\C| * r. CS Dept, City Univ.

16. Heuristic Algorithm – An Example with WCDS 1 f(c,r) =1 CS Dept, City Univ.

17. Heuristic Algorithm – An Example with BIB 1 f(c,r) =2*1/2 =1 2 CS Dept, City Univ.

18. Heuristic Algorithm – An Example with BIB 1 f(c,r) =4*1/8 =1/2 2 8 8 CS Dept, City Univ.

19. Heuristic Algorithm – An Example with WCDS 8 2 1 1 2 8 8 CS Dept, City Univ.

20. Heuristic Algorithm – Transmission Scheduling • Some Notations • Vb : Let Vb={b1,b2,…,bk} V be the set of the branch points in the broadcast tree T • b1: Source node • Gb: A directed graph(tree) Gb=(Vb, Eb) such that (bi, bj) Eb if and only if it is an edge in the tree T • t(bi): For every node bi Vb, we assign a cost t(bi) which is the minimum multicast transmission time it takes the node bi to transmit a fixed-size packet to all its children. • Gc: An undirected conflict graph Gc = (Vc, Ec) such tat Vc = Vb and (bi, bj) Ec if and only if the multicast of bi interferes with the reception of the children of bj in T. CS Dept, City Univ.

21. Heuristic Algorithm – Transmission Scheduling • Problem Formulation Formally, a schedule can be defined as a mapping which gives the transmission time of node biVb. Given Gb, t(bi) and Gc, a valid schedule is one which meets the following constraints: • The source multicasts at time zero: =0. • . • For any edge , we have The objective is to find a valid schedule which minimizes the broadcast latency CS Dept, City Univ.

22. Heuristic Algorithm – Transmission Scheduling • Basic idea of the greedy algorithm In each iteration, for each qualified node in Q ={q1,q2,…,qm}, we select the the node qi with the largest value of f(qi). The metric f(qi) is defined as follows: Where e(qi) is the earliest possible multicast time for the node qi, and w(bi) is the time needed to reach all the descendants of bi in T in the absence of interference and can be written: Where D(bi) denote the set of all descendants of bi in Gb. For any x in D(bi), let P(bi,x) denote the set of nodes on the path from bi to x. CS Dept, City Univ.

23. Heuristic Algorithm – Transmission Scheduling CS Dept, City Univ.

24. Discussion • Lack of quantitative analysis • Is the joint optimization via combing the routing and scheduling possible? • Should mesh clients be considered? CS Dept, City Univ.

25. Thanks! CS Dept, City Univ.