NCKU CSIE CIAL1 How Optimal are Wireless Scheduling Protocols? Authors: Thomas Moscibroda, Yvonne Anne Oswald and Roger Wattenhofer Publisher: IEEE INFOCOM.

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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: Tuesday, April 18, 2023

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Outline

• Introduction• Related Work and Existing Protocols• Model• Proposed Protocol• Conclusions

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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 (log2n) time whereas previous heuristics require Ω(n) time.

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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 di is set to

a value proportional to diα. Protocols analyzed using the so-called “energy-m

etric” belong to this category.– Link removal heuristics: SRA, SMIRA, WCRP, LISRA

• Protocols with uniform or linear power assignment can result in long schedules. [13]

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Model

• The network consist of a set of n nodes X = {x1,…, xn} located in the Euclidean plane.

• The Euclidean distance between two node xi, xj, is donated byd (xi , xj), w.l.o.g., the minimal distance is 1.

• A communication request λi from a sender si to a receiver ri is represented as a directed link (si, ri) with length di = d(si , ri).

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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 Pr(si) of a signal transmitted by sender si at an intended receiver ri is

where P(si) is the transmission power of si and g(si, ri) is the propagation attenuation (link gain) modeled as g(si, ri) = d(si , ri) － α. αis the path-loss exponent.

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The Physical SINR Model

• Given a request λi = (si, ri), Ir(sj) = Pr(sj) for any other sender sj concurrent to si. The total interference

• ri receiver si’s transmission iff

where β is the minimum SINR required for a successful message reception.

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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.

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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 Si and Ri of radius di/ρ around sender si and receiver ri, respectively.

• Formally, the ρ-disturbance of a link λi is the larger of either the number of senders in Si or the number of receivers in Ri.

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Low-Disturbance Scheduling Protocol

• Consist of three parts:– A pre-processing step: to assign two values τ(i) and γ(i) to ever

y request λi.– The main scheduling-loop– A test-subroutine: to determines whether a link is to be sched

uled in a given time slot.

• The value γ(i) is an integer values between1 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.

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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 λi, the longer the corresponding communication link.

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LDS Protocol (cont.)

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LDS Protocol (cont.)

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LDS Protocol (cont.)

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The Analysis of LDS Protocol

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The Analysis of LDS Protocol

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The Analysis of LDS Protocol

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The Analysis of LDS Protocol

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The Analysis of LDS Protocol

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The Analysis of LDS Protocol

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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.