An Algorithm for Incremental Joint Routing and Scheduling in Wireless Mesh Networks

1. An Algorithm for Incremental Joint Routing and Scheduling in Wireless Mesh Networks Abdullah-Al Mahmood and Ehab S. Elmallah Department of Computing Science University of Alberta, Canada IEEE WCNC 2010

2. Outline • Introduction • System Model • Problem Formulation • The Main Algorithm • Experimental Results • Conclusion

3. Introduction • Multi-hop wireless mesh networks (WMNs) offer a cost effective alternative to wired networks for deployment in both urban and remote areas • WMN aspects defined in the IEEE 802.16 Family of standards • Broadband Wireless Access (BWA) • Quality of service (QoS)

4. Introduction • Effective dynamic allocation of bandwidth to • Mesh routers • Motivated by the above objectives • TDMA-based WMNs • Providing throughput • Delay guarantees

5. Introduction • Goal • A joint routing and scheduling problem in TDMA-base wireless mesh networks(WMNs) • All flows contend for using one of the available wireless channel • A new flowdemand that needs to be routed along with the ongoing flows • Minimum cost single flow routing and scheduling(MC-SFRS)problem

6. System Model • Multi-hop WMNs with fixed mesh routers • One or more mesh router act as a gateway • Using one channel • TDMA • RI ≧ RT Frame i+1 Frame i RT RI

7. System Model • Assume that the mesh routers periodically forward bandwidth requests to a designated node that computes routes • The computed results are conveyed back to the mesh routers

8. Problem Formulation • Assumption • A WMN G = (V, ET, EI) • V：a set of nodes • ET：a set of transmission links • EI：a set of interference edges between pairs of transmission links • π：a total order relation over a subset of nodes in the give WMN G • Ex.π = (π1, π2…. πn), π1= u and πn = v • E′T：be selected to be any set of links between the nodes in π • R(π, E′T)：a Routing set(shortest length routes) • Table T ： at most Nframe slot • cost(e, c)：using slot con link e a b c

9. Problem Formulation • Thecost of a route is the sum of the costs of slots assigned to each of its links • A solution to the problem is a minimum costfeasible route • A route that serves a flow between nodes u and v is feasible • Assigned a time slot that no two interfering transmissions

10. Example • The network G = (V, ET, EI) on 11 nodes and 15 links h f’ d’ (g, h) does not interfere with any of the links (a, b), (b, c), (a, c), (a, c′),(c′, c′). g e a b f Neither link (f, g)nor(f ′, g) interfere with links (a, c), (a, c′)and(c, c′). d c c’ RT RI =2RT

11. Problem Formulation • List coloring problem • The available time slots (colors) that do not conflict with any time slot (colors) in the existing schedule T • Maximum Interference Distance(MID) • Given a route R = (e1, e2,…,em) • Define the MID of R to be the largest integerk • |i - j|≦k, eiand ej∈R

12. Example • The MID of route R = ((a, b), (b, e), (e, f ), (f, g) , (g, h)) is 3 • Since links (a, b) and (f, g) interfere with each other h f’ d’ g e a b f d c c’ RT RI =2RT

13. Problem Formulation • Performance benefit • Solving the MC-SFRS problem in maximizing network throughput RI =1.5RT link A only interferes with linksB, C, a and b

14. The Main Algorithm • Node Ordering • Maximum Interference Distance • The Main Algorithm

15. The Main Algorithm • Node Ordering • π = (π1, π2, π3… πn′), n′≧2 π = (a, (c, b, c′), (d, d′, e,),( f′, f), g, h ) h f’ • R(π, E′T)={(a, c′), (a, c), (a, b), (b, d), • (b, e), (b, d′), (e, f′), (e, f), • (f′, c′), (a, c′), (a, c′)} d’ g e a b f d c c’ RT RI =2RT

16. The Main Algorithm • Maximum Interference Distance • E′I：the set of possible interference edges in E′T • dI(eI, π)：the maximum number of links separating ei and ej on any such valid route R • dmax(x) = the maximum number of links in any valid route between nodes 1 and x. • dmin(x) = the minimum number of links in any valid route between nodes 1 and x. h f’ d’ g e a b f d c c’

17. The Main Algorithm • Example • suppose we want to route a flow f(a, h), and we choose π = (a, (c, b, c′), (d, d′,e),( f′, f ), g, h) dmax(h)：a→c →b →d →e →f →g →h h f’ dmin(h)：a→b →e →f →g →h d’ g e a b f d c c’ RT RI =2RT

18. The Main Algorithm • dmax(x) = 1 + max{dmax(w) : w < x, and (w, x) ∈ ET} • dmin(x) = 1+min{dmin(w) : w < x, and (w, x) ∈ ET} • Observe that the following inequality for eI=((i, i), (j, j)) gives an upper bound on dI(eI, π) • dI(eI, π)≦ dmax(j)- dmin(i′)

19. dmax(x) = 1 + max{dmax(w) : w < x, and (w, x) ∈ ET} dmax(f) = 1+dmax(e) h f’ d’ g e a b f d c c’ RT RI =2RT

20. dmin(x) = 1+min{dmin(w) : w < x, and (w, x) ∈ ET} dmin(f) = 1+dmax(e) h f’ d’ g e a b f d c c’ RT RI =2RT

21. dmax(x) = 1 + max{dmax(w) : w < x, and (w, x) ∈ ET} dmin(x) = 1+min{dmin(w) : w < x, and (w, x) ∈ ET} • Observe that the following inequality for eI=((i, i), (j, j)) gives an upper bound on dI(eI, π) • dI(eI, π)≦ dmax(j)- dmin(i′) eI=((a, b), (f, g)) h f’ d’ g e dI(eI, π) = 3 ≤ dmax(f)−dmin(b) = 5−1 = 4 a b f d c c’ RT RI =2RT

22. The Main Algorithm • Ongoing flow f(a, h) • New flow flow(e, g ) Ongoing：a→b →e →f→g →h h f’ d’ g new flow：d→e→f →f′ e a b f d→e e→f f →f′ d c c’ RT RI =2RT

23. Experimental Results • Topology

24. Experimental Results • Traffic to Gateway

25. Experimental Results • Additional Traffic over Tree-based Routing

26. Conclusion • This paper deals with the MC-SFRS problem that asks for finding a minimum cost schedulable route for serving a given flow in a multi-hop TDMA wireless mesh network.