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

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

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

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 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 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 Wireless interfere model Appear in

11 Introduction

12 Collision-free scheduling over N slots

Collision-free scheduling

15 TDMA SCHEDULING

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.

Conflict-Free Scheduling for Fixed Transmission Orders

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Bellman-Ford Algorithm 19

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

MINIMUM LENGTH TDMA SCHEDULING The request rate

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

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

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

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

TDMA DELAY AWARE SCHEDULING _ Min-Max TDMA Delay Scheduling

TDMA DELAY AWARE SCHEDULING _ Algorithm TH

29 Simulation  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 Simulation

31 Algorithm-MM Algorithm-TH

Graph coloring

33 Simulation

34 Simulation

35 Simulation

36 Simulation

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 Thank you~

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