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March 7 2006
Rice UniversitySlide 1
doc.: IEEE 802.11-06/0466r0
Submission
Modeling Imperfect Clock Synchronization in CSMA Wireless Networks
Date: 2006-03-07
Notice: This document has been prepared to assist IEEE 802.11. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein.
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Authors:Name Address Company Phone Email
Theodoros Salonidis 6100 Main St. #366
Houston, TX 77005Rice University
Jingpu Shi 6100 Main St. #366
Houston, TX 77005Rice University
Edward Knightly 6100 Main St. #380
Houston, TX 77005Rice University
Joseph Camp 6100 Main St. #366
Houston, TX 77005Rice University
March 7 2006
Rice UniversitySlide 2
doc.: IEEE 802.11-06/0466r0
Submission
Motivation• Several CSMA MAC protocols use frame-based
synchronization– Increase aggregate throughput
• MMAC– Save Power
• SMAC– However: assume perfect synchronization
• Impact of imperfect synchronization not known• Our contribution
– Formally analyze performance under clock drift differences, carrier sense and topology asymmetries
– Consider fairness and starvation issues.
March 7 2006
Rice UniversitySlide 3
doc.: IEEE 802.11-06/0466r0
Submission
Synchronized CSMA Protocol
• Periodic transmission frames with fixed size, split in a contention phase and a data phase.
• Contend at the beginning of frame using CSMA + REQ/GRANT handshake
• If win contention, transmit until the end of frame
March 7 2006
Rice UniversitySlide 4
doc.: IEEE 802.11-06/0466r0
Submission
Imperfect Synchronization
• Factors affecting performance– Clock drifts– Carrier Sense tx of previous cycle– REQUEST packet size
March 7 2006
Rice UniversitySlide 5
doc.: IEEE 802.11-06/0466r0
Submission
Guard Time (GT) System
• Insert Guard Time at end of data phase• GT size > max clock drift in the network
– Carrier Sense tx of previous cycle is disabled– Clock drifts and REQ packet size still affect
performance
• Is a GT system better than a no GT system?
March 7 2006
Rice UniversitySlide 6
doc.: IEEE 802.11-06/0466r0
Submission
Starvation
• Starvation for slower flow 2– If clock drift > contention window of flow 1
• Persists whether GT is used or not
March 7 2006
Rice UniversitySlide 7
doc.: IEEE 802.11-06/0466r0
Submission
Single Cell Analysis Markov Chain Model
• Capture impact of clock drift differences• State x means node x transmits (# states = # nodes)• Memoryless property (chance of a flow winning
cycle k+1 depends on which flow transmits on cycle k)
• Stationary probabilities of MC = flow throughputs
2-node example
March 7 2006
Rice UniversitySlide 8
doc.: IEEE 802.11-06/0466r0
Submission
Single Cell Analysis Results (Fixed drifts)
• 10 flows, • W=32 minislots• Clock drifts spaced 10 mini-
slots apart
• Later flows get lower throughput
• Exponential decrease as clock drift increases
• Flows 32 mini-slots late from earliest flow starve
• Guard Time less fair
March 7 2006
Rice UniversitySlide 9
doc.: IEEE 802.11-06/0466r0
Submission
Example Analysis (GT system)
p12= p22 = P(x1 > + x2) p11=1 - p12*where x is chosen backoff and is drift p21=1 - p22
• Guard Times exacerbate the unfairness• Earlier Flow 1 always has the advantage
March 7 2006
Rice UniversitySlide 10
doc.: IEEE 802.11-06/0466r0
Submission
Single Cell Analysis Results (Random drifts)
• 10 flows, W=32 mini-slots• Clock drifts drawn from
uniform distribution [0 to max clock drift]
• Measure lowest throughput as a function of max clock drift / W
• Even if clock drift less than contention window, exponential decrease of lowest throughput
March 7 2006
Rice UniversitySlide 11
doc.: IEEE 802.11-06/0466r0
Submission
Multi-hop Topologies
• More issues in addition to clock drift– Carrier sense (not all nodes sense the same thing)
– High collision due to hidden terminals from transmitter (gets worse as REQ packet size increases).
• Two simple scenarios to isolate and study in detail using our model– Flow in the Middle
– Information Asymmetry
March 7 2006
Rice UniversitySlide 12
doc.: IEEE 802.11-06/0466r0
Submission
Flow in the Middle Scenario
• Middle flow senses both outer flows but outer flows sense only the middle flow
• Middle flow can starve sensing misaligned transmissions of outer flows
• Model applies: use one state for outer flows and another state for middle flow
March 7 2006
Rice UniversitySlide 13
doc.: IEEE 802.11-06/0466r0
Submission
Flow in the Middle scenario
• Early outer flow and middle flow drifts = 0, W=32
• Throughputs as drift of late outer flow increases
No GT: Middle flow starves if outer flows relative drift > W
GT: Throughput of middle flow increases
No GTGT
March 7 2006
Rice UniversitySlide 14
doc.: IEEE 802.11-06/0466r0
Submission
Flow in the Middle scenario
• Relative drift of outer flows =16, W=32 mini-slots
• Throughputs as drift of middle flow increases
No GT
No GT: Middle flow: Steep decrease with a stable region C
A B C D
16
16a
GT
GT: Middle flow: Smoother decrease but no stable region
March 7 2006
Rice UniversitySlide 15
doc.: IEEE 802.11-06/0466r0
Submission
Information Asymmetry Scenario
• tx1 unable to sense flow 2• tx2 senses flow 1 (through GNT of rx1)• Flow 1:disadvantage even under perfect synchronization
– Can succeed only if its backoff + REQ packet < backoff of flow 2
• Disadvantage of flow 1 aggravated as REQ packet size increases
March 7 2006
Rice UniversitySlide 16
doc.: IEEE 802.11-06/0466r0
Submission
Information Asymmetry Scenario
• Fix drift of flow 1 to 0, REQ packet size = 16 mini-slots• Throughputs as drift of advantaged flow 2 increases
GBNo GB
No GT and GT: perform similarly (carrier sense no effect)
Cross-over point: when drift difference = REQ packet size
March 7 2006
Rice UniversitySlide 17
doc.: IEEE 802.11-06/0466r0
Submission
To GT or not to GT?
• Pros– Better fairness in single-hop
systems– Protection regions for clock
phase jitter
• Cons (multi-hop systems)– Flows may starve irrespective of
their own contention windows due to high clock drift difference of their outer flows
– Hard to exploit protection regions
– Two-hop max drift bound
No GT• Pros
– Easier to extend MC model to arbitrary topologies
– Allow for simpler solutions• Only address clock drift differences
and REQ packet size.
– One-hop max drift bound
• Cons– Guard Time overhead– Less fairness in single-hop
networks– No inherent protection against
clock phase jitter
GT
March 7 2006
Rice UniversitySlide 18
doc.: IEEE 802.11-06/0466r0
Submission
Counter-starvation algorithm for GT systems
• Goal– Achieve per-flow throughputs above a set of reference
slotted aloha rates
• Operation– Utilize a model for arbitrary topologies for GT systems to
adjust contention windows.– Rule: ask neighbors with higher throughput to increase their
contention windows by a certain factor
• Outcome– Proportionally fair minimum throughput guarantees.– Throughputs greater than the reference rates.
March 7 2006
Rice UniversitySlide 19
doc.: IEEE 802.11-06/0466r0
Submission
Counter-starvation Algorithm
March 7 2006
Rice UniversitySlide 20
doc.: IEEE 802.11-06/0466r0
Submission
Conclusions
• Single-hop networks– Starvation: if W < max clock drift– Min throughput: exponential decrease with max clock drift– GT system less fair than no GT system
• Multi-hop networks– No GT systems
• Offer protection regions against clock phase jitter, yet solutions harder to implement
• Starvation sensitive to clock drifts of two-hop neighborhood
– GT systems allow for simpler solutions with predictable performance at the expense of GT overhead.
• Distributed CW adjustment mechanism to counter starvation in a GT system
March 7 2006
Rice UniversitySlide 21
doc.: IEEE 802.11-06/0466r0
Submission
Backup Slides
March 7 2006
Rice UniversitySlide 22
doc.: IEEE 802.11-06/0466r0
Submission
Example Analysis(no GB system)
p12=P(x1 > + x2) p11=1 - p12p22=P(x1 > x2) p21=1 - p22Access Probability 2 = p12/(1 + p12 - p22 )
1 = 1 - 2 *where x is chosen backoff interval and is the clock drift
March 7 2006
Rice UniversitySlide 23
doc.: IEEE 802.11-06/0466r0
Submission
Counter Starvation Algorithm, Results (1)
• Only counter size of REQUEST packet
March 7 2006
Rice UniversitySlide 24
doc.: IEEE 802.11-06/0466r0
Submission
Counter Starvation Algorithm, Results (2)
• Counter everything
March 7 2006
Rice UniversitySlide 25
doc.: IEEE 802.11-06/0466r0
Submission
Single Cell Analysis Results (3)
• Random clock phases, Fairness index
March 7 2006
Rice UniversitySlide 26
doc.: IEEE 802.11-06/0466r0
Submission
General Topology, Analysis on Size of REQ Packet
• Compute lowerbound instead, which is tight• Open form and closed form expression
March 7 2006
Rice UniversitySlide 27
doc.: IEEE 802.11-06/0466r0
Submission
Multihop Analysis Lower Bound Validation
• 15 flows randomly placed in 1000x1000 region
March 7 2006
Rice UniversitySlide 28
doc.: IEEE 802.11-06/0466r0
Submission
Multihop Analysis Model Decoupling
• When flow i is contending with three different flows separately, the lowerbound (in this case the throughput ) is given by,
March 7 2006
Rice UniversitySlide 29
doc.: IEEE 802.11-06/0466r0
Submission
General Topology, Analysis on Clock Drift