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Material Type: Notes; Class: Topics/Computer Engineering; Subject: Electrical & Computer Engineer; University: University of California - San Diego; Term: Fall 2005;
Typology: Study notes
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Curt Schurgers
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Scheduling issue: in which order should transmissions take place?
● How is bandwidth allocated in a fair fashion? ● Can throughput and delay be guaranteed?
MH
MH
MH
MH
in fade
in fade
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Round robin (RR) scheduling: visit each active connection in turn
● Can lead to long periods of unfairness
w = 2
w = 1
w = 1
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GPS: similar to RR, but service infinitesimal fraction
● Different weightsw can provide different amount of service
● Proportionally shares resource ● Provides isolation between flows ● Non-implementable
w = 2
w = 1
w = 1
GPS
Figures from: http://www.comp.nus.edu.sg/~cs5229/
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The finish number of a packet arriving at time k can be calculated as:
● : Finish number of packet k of flow i ● : Packet length of packet k of flow i ● R : Current round number
0 1 2 3 4 5 6 7
time
1 Kbps Service rate 1000 bits 1000 bits 1000 bits
500 bits 500 bits
500 bits 500 bits 500 bits
1500 bits
S / 1000 = 1/3 1/2 1/3 1
0 1 2 3 4 5 6 7
time
Packet arrivals
1000 bits 2000 bits 2000 bits (^) 2000 bits
F (^) i( k ) L (^) i( k )
R ( t 2 )=R(t 1 )+S[t 1 ,t 2 ]⋅ (t 2 −t 1 )
t = 0 R = 0 FA (1) = 1000 FB (1) = 2000 FC (1) = 2000 t = 3 R = 1000
S = 1000/
S = 1000/ t = 4 R = 1500 S = 1000/3 FA (2) = 1500 + 2000 = 3500 t = 5.5 R = 2000 S = 1000 t = 7 R = 3500 S = 0
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WFQ serves connections in the order of smallest finish number
● Upon arrival of a new packet: calculate its finish number
● Keep track of the round number
● B is the set of active connections Active connection: finish number of packet in queue or last served packet is larger than the current round number
i
i i i w
L k F k F k R
( )=max ( − 1 ), +
R ( t 2 )= R(t 1 )+S[t 1 ,t 2 ]⋅(t 2 −t 1 ) ∑ ∈
= k B
wk
C S
Different weights
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Finish number is not related to the finish time of the actual transmission
Benefits of WFQ ● Connections are shielded from each other ● Delay guarantees under certain conditions ● Guaranteed service rate at each time for flowi is:
Drawbacks of WFQ
● State required per connection: expensive to implement
Other variants: WF 2 Q, self-clocked fair queuing, start-time fair queuing
A B (^) C A
0 1 2 3 4 5 6 7
time
WFQ packet transmission schedule
0 1 2 3 4 5 6 7
time
GPS service rate
w
w g (^) N
k
k
i i = ⋅
= 1
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Errors in wireless links are bursty and spatially uncorrelated
● Due to interference or fades ● Common model: 2-state Markov chain on packet level
FIFO (first in, first out) scheduling leads to head-of-line blocking
● Packets that are destined for the terminal with the bad channel are retransmitted over and over ● Bad resource utilization and negative effect on TCP ● Fairness problem: terminal with bad channel affects those with a good link
TCP
TCP
TCP
TCP
P1P4P2P3P1P
MH
MH
MH MH
in fade
WLAN Card Xmit
Recv
Source: http://nesl.ee.ucla.edu/courses/ee206a/2002s /
PER = 0 Good Bad PER = 1
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Goal: provide fairness despite temporary localized channel errors
● Channel errors should be almost transparent to the user
If a scheduled flow is experiences a bad channel, one with a good channel will be allowed to transmit instead to avoid wasting capacity
Flows most be compensated for capacity lost due to channel errors
Issues:
● Monitoring the channel state ● Separation between flows: flows that always perceive a good channel should not be impacted
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A variant of WFQ is used as the reference model
Properties
● Short-term and long-term fair ● Achieves delay and throughput bounds ● Delay and bandwidth decoupling ● Graceful relinquishing of slots ● Fair compensation of lagging flows
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Intrinsic variability ● Channel variability Dynamic channel conditions in space and time ● Traffic variability New streams, applications, users Non-constant data rate, e.g. mpeg video
Traditional approach: design system for worst case operating conditions ● E.g. certain outage probability ● Wasteful in terms of resources
Adaptation ● Adjust the system settings to the best operating point for the current channel/traffic conditions and constraints
Static snapshot of signal intensity map
Source:[IEEE99]
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Channel varies in time and space Different models at different levels of detail
Severe channel degradation ● ‘Deep’ fades: e.g. 5 ms average BAD state duration in 2-state model, with ρ = -20 dB and speed of 10 km/h ● Heavy shadowing Additional quality variations when the channel is good enough to support communication
GOOD BAD
~ speed
~ speed
BERgood
BERbad
channel gain
time (s)
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Variability ● Channel quality varies (BER or distance varies)
Control knobs ● Adjust the packet length ● Fixed transmit power and raw data rate ● Erroneous packets are retransmitted
Maximize the goodputG (useful bit rate as seen by the higher layers)
G R
L L H O BER b
= L^ H
⋅ ( 1 − )+
L packet payload H packet MAC header O PHY overhead
L (bytes)
Adaptation problem 2
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Variability ● Channel fading rate varies: two-state Markov chain for different speeds (~transition prob) and same BER (^) good Control knobs ● Adjust the packet length ● Fixed transmit power and raw data rate ● TCP traffic source ● Erroneous packets are retransmitted at the MAC level ● Include error coding Minimize the energy
Sampling effect: fit more packets in the ‘good’ state
Adaptation problem 3
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SNR (dB)
BER
4-QAM16-QAM64-QAM256-QAM
Adaptation problem 4
Variability ● Channel quality varies: varying SNR Control knobs ● Adjust the constellation size ● Fixed transmit power and symbol rate ● Fixed target BER Maximize the throughput
Strategy ● Estimate SNR ● Look up highest constellation size that can be supported with target BER Side issue ● In a shared medium, slower nodes require more time to transmit the same amount of information. Fairness?
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Adaptation problem 5
Variability ● Traffic requirements: data rate Control knobs ● Adjust the constellation size and the transmit power ● Fixed symbol rate ● Fixed target BER ● Fixed channel Minimize the energy per bit Extension ● Include channel variations ● Vary FEC instead of, or together with, constellation size
Challenge ● Does transmit power relate to energy? ● Previous adaptations reduced number of packets to save energy
SNR (dB)
BER
4-QAM16-QAM64-QAM 256-QAM
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Power of interest,P, depends on the communication setup
● Transmitter constrained
● Receiver constrained ● Transmitter and receiver constrained:
Power components depend on the baseline
● With shutdown ● Without shutdown
P =P Tx
P =P Rx
P =PTx +P Rx
Time
Power Idle
Time
Power
Sleep
PTx =PTx−P sleep
PTx =PTx−P idle
PRx =PRx−P sleep
PRx =PRx−P idle
PTx = PS+P ETx PRx = PERx+PDEC
Source: [Sch02b]
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Adaptation variesR, the ‘raw’ number of bits/symbol ● Headers and useful user data are both part of the ‘raw’ number of bits
The total energy consumption per packet is then
Scaling optimizes the ‘raw energy per bit’
● Other techniques: minimize headers, packet length adaptation, minimize overhead, …
MAC headers FEC^ modulation
R bits/symbol
R ⋅ RS bits/s^ RS symbols/s
S
bit RR
Epacket =P⋅Tbit⋅ ( L+H) +Eoverhead
( ) L
E (^) usefulbit packet bit + overhead
Ebit =P⋅T bit
L packet payload H all packet headers Eoverhead energy of PHY overhead
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For a system with a variable symbol rate, some parts of the electronics operate at the maximum symbol rate, while others operate at the instantaneous symbol rate
The FEC decoder energy is expressed as a function of the decode energy per bit before encoding,E (^) DEC ● The decoding energy depends on the complexity of the code, which is related toR
● Example
max
2
1 DEC
DEC DEC C R
(^01) 1.2 1.4 1.6 1.8 2
100
200
300
S
bit c R
T R = 1
RS (n = 15)
RS (n = 63)
RS (n = 255)
MIPS
P E I proc DEC = bit⋅
Reed-Solomon decoding on a StrongARM microprocessor [Let99]
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The performance of the communication system depends onE (^) b /N 0 , which is a function of the received electro-magnetic powerPR
The received power is a function of the transmitted powerPT and the channel gain ● A: constant large scale channel gain ● α: fading (normalized to 1) – note that this is apower factor here
How the PA power,PS , relates to the transmitted power depends on the efficiency of the power amplifier
0 0
PR SNRN W b⎟⎟⋅ ⋅ S⋅ ⎠
S
b R
0
PT PR
PETx PS PERx
A ⋅α
2 0
2
0 0
PS b S S S b A
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R
1 R
1
Dynamic Modulation Scaling (DMS)
Dynamic Code Scaling (DCS)
PSK
QAM
RS (n = 15)
RS (n = 63) RS (n = 255) RCPC
b ↓ RC ↓
N 0
E (^) b N 0
E (^) b
Two examples ● Modulation scaling: vary the constellation size ● Code scaling: vary the redundancy of the code (code rateR (^) c = number of bits before coding/number of bits after coding)
Rc = (^1) b = 1 (BPSK)
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SendNtot bits within delay boundT (^) A (symbol rate is fixed)
Special case of a time-invariant channel in [0,T (^) A]: α = 1
Due to the convexity of , the optimum strategy is to use the same rate on all information carrying symbols
Ebit CS b⎟⎟+ E ⎠
0
E bit
S
bit RR
PA dominates
Electronics dominate
Etot = T ⋅N tot
Ttot = T ⋅N tot
(^0) T A
Ttot = T⋅N tot
(^0) T A
Etot = T⋅N tot Etot =Ebit⋅Ntot *
Ttot =Tbit⋅N tot
TA < T⋅N tot 0 *
tot
tot N
tot
A N
Region of scaling
Region of shutdown 1 2 3
1 2 3
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normalized Ebit
= 104 S
E C
C
= 3 ⋅ 102 S
E C
C
= 10 S
E C
C
R ↓
Shorter transmit range
(^1) R =Tbit ⋅R S
QAM-scaling
Shutdown-based system: Transmit as fast as possible and shut down the radio afterwards
Scaling-based system: Transmit as slow as possible and use all time available
0
2000
4000
6000
8000
0
100
200
300
0
200
400
600
nJ/bit (^) GSM
Medusa sensor node
WLAN
PA
TransmitelectronicsReceiveelectronics
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When multiple packets need to be transmitted, the problem becomes one of scheduling ● Different traffic conditions and constraints lead to different scheduling problems ● E.g. Scheduling for random packet arrivals under a global deadline constraint [Pra01]
Channel variations also result in scheduling issues ● Important when the optimization criterion is a long-term effect, e.g. long-term average throughput ● Intuitive explanation: it is better to transmit when the channel is good, but the future is unknown
Arrival 1 Deadline 1
Arrival 2 Deadline 2
Arrival 1 Deadline 1
Arrival 2 Deadline 2
time
Channel gain
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Adaptation improves the way energy scales with distance ● Impact of electronics on energy consumption ● Graceful degradation
Implementation dependent ● These tradeoffs depend on the hardware platform that is chosen (e.g. Viterbi decoding on the StrongARM is costly) ● Accurate hardware models are essential
Adaptation impacts other system tradeoffs ● Data aggregation ● Single hop versus multi-hop routing
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[Nan99] Nandagopal, T., Lu, S., Bharghavan, V., “A unified architecture for the design and evaluation of wireless fair queueing algorithms,” Mobicom’99, Seattle, WA, pp.132-142, 1999. [Sch03] Schurgers, C., Raghunathan, V., Srivastava, M., "Power Management for Energy-Aware Communication Systems," ACM Transactions on Embedded Computing Systems, Vol.2, No.3, pp. 431-447, 2003. [Par94] Parekh, A., Gallager, R., “A generalized processor sharing approach to flow control in integrated services networks: The multiple node case,” Transactions on Networking, Vol.2, No.2, pp.137–150, 1994. [IEEE99] IEEE 802.11, 1999 Edition (ISO/IEC 8802-11: 1999),Local and Metropolitan Area Network -- Specific Requirements -- Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, http://standards.ieee.org/getieee802/802.11.html. [Let99] Lettieri, P., Schurgers, C., Srivastava, M., “Adaptive Link Layer Strategies for Energy Efficient Wireless Networking,” Wireless Networks, Vol.5, No.5, ACM/Baltzer, pp. 339-335, 1999. [Let98] Lettieri, P., Srivastava, M., “Adaptive frame length control for improving wireless link throughput, range, and energy efficiency,” Infocom'98, San Francisco, CA, pp.564-571, 1998. [Web95] Webb, W., Steele, R., “Variable rate QAM for mobile radio,” IEEE Transactions on Communications, Vol.43, No.7, pp.2223–2230, 1995.
