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

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

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

4. 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

5. CS Dept, City Univ.5 Introduction - Transmission and Interference Model Transmission model: P r =P t The transmission range is a decreasing function of transmission rate Interference Model:  The distance between the transmitter and receiver d ij R i ;  No transmitter n k within a finite distance R k ’ (such that d kj <=R k ’) is transmitting concurrently.

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

7. 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

8. CS Dept, City Univ.8 Introduction - Optimization Problem 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.

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

10. CS Dept, City Univ.10 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 R ij. Basic Idea (from BIP)  Initially, every node except the root node will be set to a cost with 1/R ij  In each iteration, the node with the minimum of incremental cost will be added to the tree Heuristic Algorithm - Broadcast Incremental Bandwidth (BIB)

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

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

13. CS Dept, City Univ.13 Heuristic Algorithm – An Example with BIB 1 1 1 2 88 8

14. 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 r 1, r2,…,r k, Let N(x,r i ) denote the nodes that are reachable from node using rate r i. The aim is to find a subset Y = {y 1,y 2,…} in V and the broadcast rate w i for node y i such that:  Every element of V\Y is in  The set Y is connected  The weighted sum is minimal

15. 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.

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

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

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

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

20. CS Dept, City Univ.20 Heuristic Algorithm – Transmission Scheduling Some Notations  V b : Let V b ={b 1,b 2,…,b k } V be the set of the branch points in the broadcast tree T  b 1 : Source node  G b : A directed graph(tree) G b =(V b, E b ) such that (b i, b j ) E b if and only if it is an edge in the tree T  t(b i ): For every node b i V b, we assign a cost t(b i ) which is the minimum multicast transmission time it takes the node b i to transmit a fixed-size packet to all its children.  G c : An undirected conflict graph G c = (V c, E c ) such tat V c = V b and (b i, b j ) E c if and only if the multicast of b i interferes with the reception of the children of b j in T.

21. 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 b i V b. Given G b, t(b i ) and G c, 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

22. CS Dept, City Univ.22 Heuristic Algorithm – Transmission Scheduling Basic idea of the greedy algorithm In each iteration, for each qualified node in Q ={q 1,q 2,…,q m }, we select the the node q i with the largest value of f(q i ). The metric f(q i ) is defined as follows: Where e(q i ) is the earliest possible multicast time for the node q i, and w(b i ) is the time needed to reach all the descendants of b i in T in the absence of interference and can be written: Where D(b i ) denote the set of all descendants of b i in G b. For any x in D(b i ), let P(b i,x) denote the set of nodes on the path from b i to x.

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

24. 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?

25. CS Dept, City Univ.25 Thanks!