1. NCKU CSIE CIAL1 How Optimal are Wireless Scheduling Protocols? Authors: Thomas Moscibroda, Yvonne Anne Oswald and Roger Wattenhofer Publisher: IEEE INFOCOM 2007 Present: Shih-Chin Chang ( 張士晉 ) Date: Friday, June 12, 2015

2. NCKU CSIE CIAL2 Outline Introduction Related Work and Existing Protocols Model Proposed Protocol Conclusions

3. NCKU CSIE CIAL3 Introduction Simulation is problematic, as one can never cover all possible scenarios. Analytic worst-case analysis has the advantage to include all possible cases, and offers strict performance guarantees. Scheduling problem: Given a set of transmission requests, how do we do not cause a level of interference preventing the correct reception of messages and that the total time needed to successfully schedule all requests is minimized. LDS schedules n transmission requests in Ο (log 2 n) time whereas previous heuristics require Ω(n) time.

4. NCKU CSIE CIAL4 Related Work Graph-based scheduling algorithms usually neglects the aggregated interference of nodes located further away. Existing scheduling algorithms and protocols for the SINR model can be classified into three classes: –Uniform power assignment: the transmission power of all nodes is the same. –Linear power assignment: the transmission power for link of length d i is set to a value proportional to d i α. Protocols analyzed using the so-called “energy-metric” belong to this category. –Link removal heuristics: SRA, SMIRA, WCRP, LISRA Protocols with uniform or linear power assignment can result in long schedules. [13]

5. NCKU CSIE CIAL5 Model The network consist of a set of n nodes X = {x 1,…, x n } located in the Euclidean plane. The Euclidean distance between two node x i, x j, is donated by d (x i, x j ), w.l.o.g., the minimal distance is 1. A communication request λ i from a sender s i to a receiver r i is represented as a directed link (s i, r i ) with length d i = d(s i, r i ).

6. NCKU CSIE CIAL6 The Physical SINR Model In the Physical Signal-to-Interference-plus-Noise-Ratio ( SINR ) model, the successful reception of a transmission depends on the received signal strength, the interference caused by nodes transmitting simultaneously, and the ambient noise level. The received power P r (s i ) of a signal transmitted by sender s i at an intended receiver r i is where P(s i ) is the transmission power of s i and g (s i, r i ) is the propagation attenuation (link gain) modeled as g (s i, r i ) = d(s i, r i ) － α. α is the path-loss exponent.

7. NCKU CSIE CIAL7 The Physical SINR Model Given a request λ i = (s i, r i ), I r (s j ) = P r (s j ) for any other sender s j concurrent to s i. The total interference r i receiver s i ’s transmission iff where β is the minimum SINR required for a successful message reception.

8. NCKU CSIE CIAL8 Problem Formulation The aim of scheduling and power control algorithm is to generate a sequence of power assignment vectors, such that the SINR level is above a threshold β at every intended receiver and all links are scheduled successfully at least once. The scheduling complexity defined in [13] is a measure that captures the amount of time required by a scheduling protocol to schedule requests in the Physical SINR model.

9. NCKU CSIE CIAL9 The Disturbance For a given set of communication requests Λ and some constant ρ ≧ 1, we define the ρ-disturbance as the maximal number of senders (receivers) that are in close physical proximity of any sender (receiver). Consider disks S i and R i of radius d i /ρ around sender s i and receiver r i, respectively. Formally, the ρ-disturbance of a link λ i is the larger of either the number of senders in S i or the number of receivers in R i.

10. NCKU CSIE CIAL10 Low-Disturbance Scheduling Protocol Consist of three parts: –A pre-processing step: to assign two values τ(i) and γ(i) to every request λ i. –The main scheduling-loop –A test-subroutine: to determines whether a link is to be scheduled in a given time slot. The value γ(i) is an integer values between 1 and The idea is that only requests with the same γ(i) values are considered for scheduling in the same iteration of the main scheduling-loop.

11. NCKU CSIE CIAL11 LDS Protocol (cont.) The second assigned value, τ(i), further partitions the requests. In particular, it holds that the length of all requests that have the same γ(i) and τ(i) differ by at most a factor two. The smaller the value τ(i) assigned to a requests λ i, the longer the corresponding communication link.

12. NCKU CSIE CIAL12 LDS Protocol (cont.)

13. NCKU CSIE CIAL13 LDS Protocol (cont.)

14. NCKU CSIE CIAL14 LDS Protocol (cont.)

15. NCKU CSIE CIAL15 The Analysis of LDS Protocol

16. NCKU CSIE CIAL16 The Analysis of LDS Protocol

17. NCKU CSIE CIAL17 The Analysis of LDS Protocol

18. NCKU CSIE CIAL18 The Analysis of LDS Protocol

19. NCKU CSIE CIAL19 The Analysis of LDS Protocol

20. NCKU CSIE CIAL20 The Analysis of LDS Protocol

21. NCKU CSIE CIAL21 Conclusions By employing a novel power assignment scheme and reuse distance criterion, our algorithm achieves a provably efficient performance in any network and request setting that features low disturbance. The LDS protocol is centralized and hence suited to be employed in static networks with known traffic patterns only. Finding a distributed algorithm in a manner similar to the LDS protocol is an exciting open problem.