1. 1 Delay Aware Link Scheduling for Multi- Hop TDMA Wireless Networks Petar Djukic * and Shahrokh Valaee + *University of California +University of Toronto, Toronto, ON, Canada IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 17, NO. 3, JUNE 2009

2. 2 Outline  Introduction  Network and transmission model  TDMA scheduling  Minimum length TDMA scheduling  TDMA delay aware scheduling  Simulation  Conclusion

3. 3 Introduction  An important goal for TDMA scheduling algorithms is to find the minimum number of slots required to schedule requested end-to-end rates.  Although previous TDMA scheduling approaches can find minimum length schedules, they do not account for TDMA scheduling delay.

4. 4 Introduction  Scheduling delay occurs when packets arriving on an inbound link must wait for the subsequent frame to be transmitted on the outbound link.  Scheduling delay accumulates at every hop in the network, so end-to-end delay experienced on a path can be large.

5. 5 Introduction_ goal  Given an assignment of link bandwidths, what is the minimum length TDMA schedule that also minimizes end-to-end scheduling delay?

6. 6 Network and transmission model  TDMA network can be represented with a directed connectivity graph  is the set of nodes  is the set of directed links

7. Network and transmission model Notation: T s is the duration of each slot. N c slots reserved for the control traffic. N d slots reserved for data traffic.

8. 8 Network and transmission model Notation: r j is link rate P is the set of all paths found by the routing algorithm I(.) is the indicator function gl is the requested end-to-end rate of connection Notation: c j is capacity. h is the spacing between transmissions of different links.

9. 9 Network and transmission model Notation: n j is the number of times the link transmits in the frame. The actual rate The request rate

10. 10 Wireless interfere model Appear in 802.11

11. 11 Introduction

12. 12 Collision-free scheduling over N slots

14. Collision-free scheduling

15. 15 TDMA SCHEDULING

16. Conflict-Free Scheduling for Fixed Transmission Orders Even though the general scheduling problem is NP-complete, if the transmission order is fixed, the scheduling problem has polynomial complexity.

17. Conflict-Free Scheduling for Fixed Transmission Orders

18. eiei ejej 4 9 4 -2 9 – 4 = 5 9 2 2

19. Bellman-Ford Algorithm 19

20. Multiple Link Transmissions in a Frame 1 1 4 2 9 4 2 9 1 1 1 1 eiei ejej 8 1 ekek 4 2 1

21. MINIMUM LENGTH TDMA SCHEDULING The request rate

22. MINIMUM LENGTH TDMA SCHEDULING_ Linear Search Algorithm Input : the number of slots in the data sub-frame topology information, link durations, slot duration

23. MINIMUM LENGTH TDMA SCHEDULING_ Linear Search Algorithm [e 1,e 2,e 3,…,e m ]

24. TDMA DELAY AWARE SCHEDULING _ End-to-End Scheduling Delay if the conflict is traversed in the opposite direction

26. TDMA DELAY AWARE SCHEDULING _ End-to-End Scheduling Delay

27. TDMA DELAY AWARE SCHEDULING _ Min-Max TDMA Delay Scheduling

28. TDMA DELAY AWARE SCHEDULING _ Algorithm TH

29. 29 Simulation  802.16 frame duration is 10ms  giving a total of 800 Orthogonal Frequency Division Multiplexing(OFDM) symbols in each frame.  70 OFDM symbols are for the control sub-frame, 730 symbols for the data sub-frame.  Each link transmission has an overhead of h=3 slots.  the percentage of the frame used for centralized scheduling to

30. 30 Simulation

31. 31 Algorithm-MM Algorithm-TH

32. 32 802.16 Graph coloring

33. 33 Simulation

34. 34 Simulation

35. 35 Simulation

36. 36 Simulation

37. 37 Conclusions  This paper introduces TDMA delay aware scheduling for multi-hop wireless networks.  The proposed polynomial time algorithm that finds one-frame scheduling delay transmission orders on overlay tree topologies.

38. 38 Thank you~

39. TDMA DELAY AWARE SCHEDULING _ Modulo Operation Preserves Delay Properties is the final transmission order