investigating wireless systems two case studies

Investigating Wireless SystemsTwo Case Studies

Roch Guerin

University of Pennsylvania

2

Starting Point

• Wireless means no wire…– Flexibility in using and allocating spectrum resources

• No wire means lots of unpredictable interactions– User interferences, fluctuations in channel quality, e.g.,

fading, etc.

• What is the trade-off between flexibility and predictability?– A common theme at the “physical layer” (MIMO,

OFDM, etc.)– But how does it play out at the link/network layer?

3

Broad Problem Setting

• Multiple distinct channels, e.g., different frequencies, spreading codes, etc.

• One or more user seeks to transmit data• How should data be transmitted to maximize “performance?”

– Which user transmits when on what channel– What definition for performance (system centric versus user centric)

• Performance factors– Channel quality– Channel access schemes– Channel allocation and packet transmission strategies– User traffic patterns– User level coding for resiliency

4

Not an Easy Problem in General…

• M users and C (slotted) channels– An idle user becomes active with probability p and

remains active for k1 slots– Users can direct any transmission to any channel (no

channel switching cost)– Basic slotted Aloha MAC and error-free channels

• What’s the best assignment of users to channels– If CM, then obviously one user per channel is best– If CM, the answer depends on p and k

– Analysis is possible based on standard Markov chain formulation

• Nothing sophisticated, but complex state enumeration and bookkeeping

5Load

Thr

ough

put

Impact of Channel Allocation (k=1)(M,C)

(2,1)

(4,2)

(6,3)

(8,4)

(16,8)

(32,16)

Sharing pays only at high loads

M M =2

M =32

6

Our Focus• Two case studies within the broad framework we just

outlined• Case study 1: Controlled diversity

– Channels: Variable quality with known open-loop “statistics”– Channel access: No interferences/collisions between users– Performance goals: Coding and transmission policies to improve

individual user throughput• Case study 2: Distributed diversity

– Channels: Variable quality with closed control loop to equalize channels across users

– Channel access: A CDMA setting with “controlled” interferences between users

– Performance goals: Transmission policies that optimize trade-off between system throughput and transmission flexibility of individual users

7

Generic Outline for Both Case Studies

• Problem justification– Why someone else should care about it…

• Problem formulation– What parameters

• Prior work– What others have done

• Problem solution– What analytical tools and techniques

• Solution evaluation– Methodology and scope

8








9

Case Study 1

• Should I do this? • Or that?

• And if that, how and when?

10

Why the Question?

• Mobile devices are increasingly powerful– They run pretty much the same range of applications as

wired devices– Many of these applications are performance sensitive

• Wireless resources are subjected to random fluctuations in quality that are outside the control of users and network providers alike

• So it’s worth exploring what we can do to make performance more predictable to users in spite of our limited control on the resources they access

11

Why the Approach?

• Spreading transmissions across multiple channels allows us to– Avoid being stuck with a really bad channel– Decrease the effective length of error bursts, which can

facilitate recovery (fewer consecutive lost packets)

• Potential for improvements, therefore, arises from– A higher probability of successful message transmission– The ability to lower coding overhead

• The questions are then how to realize the best possible improvement, and how big it is

12

System Overview• One user, C channels (remember perfect channel access…)

– User wants to transmit messages (data blocks) of size k packets

• Channel model is “known” – e.g., Gilbert-Elliot model– Independent channels with known statistics

• Reliable transmissions through packet-level code– Add redundant packets to achieve target probability of successful

message delivery Pmin

• Policy distributes packet transmissions across channels – Deterministic and probabilistic policies– No channel switching overhead

• Performance measure: Effective Rate (ER)– Number of messages successfully delivered per unit of time (unit

of time is packet transmission time)

13

Channel Model• Two-state Markov chain with Good and Bad states

– Packets are lost when channel is in bad state

– Long-term error rate

– Expected burst length

• More complex channel models can be constructed using higher order Markov chains– Increased computational complexity (of transmission policies)

G BPe

1-Pb

1-PePb

be

e

PP

PLTER

1

bPEBL

1

1

14

Transmission Model

• Fixed size message consisting of k packets

• Messages sent using (N,k) diversity code– Corrects all patterns of i N-k erasures

(erroneous or lost packets)

– N ≥ k is chosen to realize Pmin

• Policy A selects channel for each packet transmission

15

Transmission Policies

• Probabilistic policies– Before each packet transmission select channel

i, 1i C, with probability pi

– Policy specified by p = [p1 p2 … pC]

• Deterministic policies– For N-packet messages, pre-determine the

channel ci that packet i, 1i N, is to be sent on

– Schedule S=[c1, c2,…,cN] specifies policy

16

Performance Metric

• Identify policy A and code length N that maximize

where is the probability of successful message transmission given N and A, and N is the smallest value that satisfies Pmin

• For two policies A and B, the relative gain in ER of using B over A is given by

N

kNPkkNER

Asucc

A

),(),(

),(

),(),(),(

AAA

AAABBBER kNER

kNERkNERBAG

),( kNP Asucc

17

Related Works1. L. Golubchik, J. C. Lui, T. Tung, A.L. Chow, W.-J. Lee, G. Franceschinis,

and C.Anglano, “Multi-path continuous media streaming: What are the benefits?” Performance Evaluation, Vol. 39, Sept. 2002.

2. A. Tsirigos and Z. Haas, “Analysis of multipath routing-Part I: The effect on the packet delivery ratio.” IEEE Trans. Wireless Commun., Vol. 3, No. 1, Jan. 2004.

3. B. Abdouni, W. Cheng, A. L. Chow, L. Golubchik, W.-J. Lee, and J. C. Lui, “Multi-path streaming: Optimization and evaluation.” Proc. MMCN'05, San Jose, CA, Jan. 2005.

4. E. Vergetis, R.Guerin, and S. Sarkar, “Improving performance through channel diversity in the presence of bursty losses.” Proc. ITC 19, Beijing, China, Aug. 2005.

5. E. Vergetis, R. Guerin, and S. Sarkar, “Realizing the benefits of user-level channel diversity.” ACM Computer Communication Review, Vol. 35, No. 5, Oct. 2005.

6. E. Vergetis, E. Pierce, M. Blanco, and R. Guerin, “Packet-Level Diversity: From Theory to Practice. An 802.11-based Experimental Investigation.” Proc. ACM MOBICOM 2006, Los Angeles, CA, Sept. 2006.

http://www.cse.cuhk.edu.hk/~cslui/PUBLICATION/pe_multi_path.pdf

http://www.cs.nyu.edu/~tsirigos/files/publications/tow2004a.pdf



http://www.cse.cuhk.edu.hk/~cslui/PUBLICATION/mmcn2005.pdf

http://repository.upenn.edu/ese_papers/111


http://repository.upenn.edu/ese_papers/138/



18

Identifying Optimal PoliciesProbabilistic Policies• Calculate PA

succ(N,k) given the channel characteristics– Recursive solution– 4-state Markov Chain for

two independent GE channels

– For C independent channels, you end-up with a Markov chain with 2C states

• Search through all policies to find optimal selection

Deterministic Policies• Deterministic schedule allows

each channel to be viewed independently– Compute statistics of the

associated embedded Markov chains (one for each channel)

• Total number of errors is sum of independent random variables (number of errors when using each channel)– Use convolution to compute

overall probability of success

• Search through all policies to find optimal selection

19

Probabilistic PoliciesTwo Independent GE Channels

• Two GE channels give rise to a 4-state Markov Chain– Denote the stationary

probability of state i as i

• Let be the conditional probability of m errors in n transmissions under policy A, given that the initial channel state was i and the ending state was j

• We then have

),( nmP Aij

kN

m i j

Aiji

Asucc NmPkNP

0

4

1

4

1

),(,

20

Recursive Computation Procedure

• For all n = 0,1,… and m = 0,1,…,n and for all i,j{1,2,3,4}, we have

where Pkj is the transition probability from state k to state j

• Initial conditions are defined as

4

1

4

1

}{)1,1(

}{)1,(),(

k

Akj

Aik

k

Akj

Aik

Aij

jPPnmP

jPPnmPnmP

, is stateerror

is stateerror no

. and all for

otherwise; 0 and if

00),(

,1)0,0(

mnmnmP

jiPA

ij

Aij

21

Deterministic Policies• For each of the N packets, specify the channel used

– There are CN such policies…

• Focus on round-robin policy– Maximizes return time to channel, i.e., every C slots.

Ceb

eb

bstepCb

Ceb

eb

estepCe

PPPP

PP

PPPP

PP

)(11

11

)(11

• Let vi be the number of errors when using channel i– Distribution of vi is easy to calculate via a recursion

• Use convolution to calculate the distribution of

V= v1 + v2 + …+ vC and the performance of any (N,k) code.

22

Computational Challenges

• We have computational procedures to explore the space of possible policies, but while identifying optimal policies is feasible, it can be complex

• No computationally tractable “closed-form” solutions– Caused in part by the discrete nature of the problem– No consistent behavior of optimal policy

• Identical channels need not be used equally• Bernoulli channels not always preferred over burstier channels• More channels does not always improve performance

• What do we do next?– Look for “heuristics” to identify what policies are good, when

23

Methodology and Results Summary

• Step 1: Initial information gathering– Evaluate a broad range of channel combinations

• When does using multiple channels help?• Common characteristics of the optimum policy?

• Step 2: Data analysis and further evaluation– Most scenarios that yield “meaningful” (≥ 30%)

improvements use all channels roughly equally– What channel combinations give rise to such behavior?

• Concept of equivalent channels

• Step 3: Distilling a simple heuristic to quickly– Identify when and how using multiple channels helps

24

Step 1• All possible 1540

channel pairs between 55 different channels– LTER [1%, 9%]– EBL [1.01, 20] pkts

• Different combinations of values for k and Pmin

• Initial findings– Max. benefits when

channels are used roughly equally

– Necessary but not sufficient

25

The Cost of Using Channels Equally

• Define the loss in performance gain as

L = Gopt – Gequal

Average 1.28%

Std. Deviation 2.71%

Minimum 0.00%

Maximum 15.72%

Median 0.03%

L 5% 81.62% of cases

L 10% 98.77% of cases

L 15% 99.04% of cases

L 20% 100% of cases

26

A Different Look at the Data

27

Equal Channel Use Focus on Deterministic Policies

Easier and better

28

Step 2

• Understanding when channels are used equally– Holds for identical channels in most settings– Any other scenarios?

• Classifying channel combinations– Channels are used equally under the optimal policy– Channels have identical individual performance (ER)– Channels yield the highest gain when used together

• Simple test to identify “good” combinations – All three above perspectives give similar answers Look for combinations of channels with similar

performance

29

“Equivalent” Channels – (1)

30

“Equivalent” Channels – (2)

• Optimal policy remains close to 0.5 for “equivalent” channels

31

Step 3 - Simple HeuristicGiven C channels• Identify subsets of ~ equivalent channels

– Compute ERi, for each channel i, 1 i C– Group channels into |E| “equivalence classes”

• For each equivalence class eE with ne channels– Compute achieved by cycling through all channels

– If , use all channels

– Else use channel

– Set

• Pick equivalence class

)(max

)(max

1

1

)(equal

ini

ini

e

ER

ERER

e

e

)(equal

eER

)(argmax1

)(i

ni

e ERe

),max( )()(

equal)(

eERERER ee

)(argmaxˆ )(e

eERe

32

Exploring Further When Using Multiple Channels Helps

• Three parameters of interest:

1. Channel characteristics, i.e., EBL and LTER

2. Performance target Pmin

3. Number of channels available

• Focus on the case of two identical channels

33

Impact of Channel• The gain is biggest for bad channels

34

Impact of Pmin

• The more stringent the performance, the greater the gains

• Relative burstiness of channel plays a major role

No gain

Rapid transition to 50/50 policy

Large gains until relative burst size decreases N

35

Impact of Number of Channels

Biggest bang for the buck with just a few channels

36

Shifting Focus• Better performance is great, but

– How robust are the improvements?• Sensitivity to measurement inaccuracies, non-stationary

channels, etc.– Are we optimizing ourselves into a corner?

• Explore sensitivity to errors in channel estimates– Different channel statistics

• EBL and LTER• Distribution of duration of error bursts (not a GE channel!)

• Can we trade-off optimality for robustness of solution

– Already do this to some extend with round-robin policy

37

Sensitivity to Channel Quality

• Three users, three channels– Two scenarios: (1) each user is assigned one channel; (2) all three users

share the three channels– Both EBL and LTER are progressively made worse

• First on only one channel (left), then on all three channels (right)

• Better performance also comes with mostly greater robustness!– Exception in the single bad channel case, when both EBL and LTER are

over 40% worse

38

Performance vs. Robustness (1)

• Explore trade-off by varying the code length N – Bigger N greater robustness, but lower performance gain– Initial focus on basic channel statistics (LTER and EBL)

System Performance gain over the one channel system

Increase in both LTER and EBL before target Pmin is violated

One channel (N=19) 0% 2%

Three channels (N=15) 27.6% 16%




Three channels (N=19) 2.7% > 100%

39

Performance vs. Robustness (2)

• This time we vary the channel model (target Pmin=0.97)– Ever burstier channel (variance of error burst )

Variance Multiplier

One channel Three channels

N = 19 N = 15 N = 16 N = 19

ER Psucc ER Psucc ER Psucc ER Psucc

Original 1.534 0.971 1.956 0.978 1.850 0.987 1.574 0.997

x 0.25 1.555 0.985 1.947 0.973 1.840 0.982 1.574 0.997

x 0.5 1.547 0.980 1.942 0.971 1.837 0.980 1.568 0.993

x 1 1.538 0.974 0 0.968 1.83 0.976 1.562 0.989

x 2 0 0.963 0 0.962 0 0.968 1.552 0.986

x 4 0 0.961 0 0.949 0 0.957 1.538 0.974

x 8 0 0.953 0 0.941 0 0.949 0 0.966

40

Resting on our Laurels – Or Not?

• Theory tells us that we can have our cake and eat it!– Both better and more robust performance

• But the theory is rife with holes and assumptions– Independent, stationary channels, with known statistics– No impact of user transmissions on channel statistics– No channel switching overhead

• Putting it all to the harsh test of reality– 802.11b environment– Standard end-systems (PCs) without precise control of

transmission timings

– If it survives “that” then maybe there is some hope…

41

Surviving 802.11

• Performance is all over the place…

• There is no “average” 802.11 channel– Stationary GE model not particularly accurate– Significant time-of-day and location dependent variations

• Wild fluctuation across 10 minute intervals– LTER can range from 0.01% to 70%– EBL varies between 1 and 40 packets

• Actual error bursts between 1 and several hundred packets

• Similar observations made by others

• Does not bode too well for the “survival” of our theory– Nevertheless

42

Experimental Setup• Two 802.11b Access Points (APs)

– Intel StarEast board, with one miniPCI NIC each– External omni-directional antennas– Assigned “non-overlapping” frequency bands– Located ~1m from each other– Transparent logging of all incoming packets on both systems– Within reach of other APs interfering in all 11 frequency bands

• Sender– Standard laptop with two NICs

• One external PCMCIA NIC, and one internal miniPCI NIC• Linux operating system• Transmission speed set at 2Mbps

– Located between 2m and 10m away from the two APs• Maintains association with both APs• Line-of-sight (LoS) as well as non-LoS (indoor wall) transmissions

43

Some Other Implementation Issues

• Impact of 802.11 operation– RTS/CTS handshake before transmissions

[Disabled - Large RTSThreshold value]– “Feedback” mechanism: ACK packets

[Disabled - Broadcast packets ]– Channel access control (untouched)

• Sensing and exponential backoff• Inter-frame spaces (SIFS, DIFS, etc.)

• Processor and OS overhead vs. transmission speed of the NICs– Where is the bottleneck and how does it affect

transmission timings?

44

Transmission Timing Scenarios

• Single channel

• Interleaving on one channel

• Perfect timing on two channels

• Bandwidth limited on two channels

• Processor limited on two channels

• Interleaving on two bandwidth limited channels

NIC1

NIC1

NIC1

1 2 3 4 5 6 7 8

1 2 3 41’ 2’ 3’ 4’

NIC2

1

2

3

4

5

6

7

8

NIC1

NIC2

1

2

3

4

5

6

7

8

NIC1

NIC2

1

2

3

4

5

6

NIC1

NIC2

1

2

3

4

5

6

7

81’ 5’

2’

3’

4’ 6’

7’

8’

(S0)

(S1)

(S2)

(S3)

(S4)

(S5)

45

Experimental Evaluation

• Generate extensive sets of traces– “Continuous” transmissions on both NICs

• Traces of received packets (1,000 bytes) recorded at each AP

– Different configurations• Sender location, time-of-day, selection of frequency bands

– With and without interferer in “intermediate” band• Test for channel correlation

• Post-process traces to emulate different settings– Different combinations of system parameters: N, k, Pmin – Various packet inter-leaving strategies, transmission

timing policies, channel switching overhead, etc.

46

The Net of It(see MOBICOM Paper for Details)

• Generic findings– Channel correlation was not found to be a major issue, at least

when using non-overlapping channels– Precise timing of transmissions does not appear to have a major

impact on performance– With current technology, dynamic channel switching mandates the

use of multiple radio cards• Cannot compensate for it through smart scheduling

• Performance/robustness findings – Some benefits remain in spite of 802.11 channel “characteristics”

IF channel characteristics are known• Unlikely to be of much use in practice given the erratic nature of the

802.11channel– For unknown channels, meaningful benefits remain ONLY when

some of the channels are really bad• Benefits are more as a performance stabilizer than an enhancer

47

Stabilizing Performance

• Two channels:– LTER1 ~ 11.4%

– EBL1 ~ 10 pkts

– LTER2 ~ 29.2%

– EBL2 ~ 11 pkts

• Measure ER over a 200 messages sliding window– Mean value improves

by 6%/30%

– Variance decreases by 60%/90%

Channels 1+2

48

Wrapping Up Case Study 1• When and how can using multiple wireless channels be of

benefit?– Assumed no user interference (centralized control) and no channel

feedback (open-loop)– Relied on packet-level diversity coding– Ignored overhead in changing channel

• Analytical tools– Basic Markov chain analysis (stationary probabilities, recursions)– Elementary probability (convolution, etc.)

• Main results– Cycling in a round-robin manner across channels is close to being

optimal in most cases– Better performance is reasonably robust to errors in assumptions– Even when most of the above assumptions don’t hold, e.g.,

802.11, there are advantages to spreading transmissions across channels

49








50

Case Study 2• What is the cost of

going from this?• To that?

• And what’s the

best trade-off?

51

Why the Question?

• Mobile devices are increasingly powerful– They run pretty much the same range of applications as wired

devices– These applications exhibit a broad range of resources and

performance requirements

• Tight centralized control can optimize overall system performance, but may be a very poor match to individual user needs

• So it’s worth exploring the trade-off associated with giving user more independence in their transmission decisions and the impact this has on overall system throughput

52

System Overview

Internet

TelephoneNetwork

Base StationController

MobileSwitching

Center

InternetGateway

Base Station

53

Our Focus

54

Overview of CDMA Uplink

• CDMA uplink is interference limited– Each user has a spreading “orthogonal” code

• Allows simultaneous transmissions

• However, users interfere due to multi-path effects

• Users can select among multiple (discrete) transmission rates– Control loop based on pilot signal equalizes channel

among users

– Transmitted power is proportional to pilot strength AND selected rate

55

Uplink Operation

• Pilot Pi transmitted by device i=1,...,n+1– Pilot signals are power controlled by BS to all be received

with the same target SINR 1/Ф

• Giloss : Path loss; θPilot: Orthogonality factor; σ2 : Noise

• User i transmit power = Pi · TxT2P[R]

– R : Target data rate from discrete set – TxT2P[R] : Proportionality factor relative to Pilot

• User spends TxT2P[R] power tokens to transmit at rate R

1,,1,1 2

2

nin

PGPG

PG

Piloti

iloss

ijj

jlossPilot

iiloss

56

Sample TxT2P[R] Values

Target Data Rate TxT2P[R] dB

0 -∞

9.6 kbps 4.5

19.2 kbps 6.75

38.4 kbps 9.75

76.8 kbps 13.25

153.6 kbps 18.5

57

CDMA Uplink Interference Model

Pilotij

j

iiii

iiii

Di

i

ijj

jD

jloss

ii

Dilossi

ii

nRPTxT

RPTxTRGRSINR

RPTxTPRPR

WRG

RPG

RPGRGRSINR

2

2

2

,][2

][2)()(

][2)( andGain Processing :)(

factority orthogonal Data :,)(

)()()(

No Channel Effects(Perfect Power Control)

• Interferences from other users– The higher the rate a user chooses, the more

interference it creates!

58

Our Problem

1,,1,][2

][2)()(

2

niRPTxT

RPTxTRGRSINR

ijj

iiii

• Users make independent transmission and rate selection decisions– Greedy behavior by individual users can affect overall

performance

• What guidelines to mitigate negative impact of independent decisions

59

Related Works7. K. Kumaran, L. Qian, “Uplink Scheduling in CDMA Packet-Data

Systems.” Proc. INFOCOM 2003, San Francisco, CA, April 2003.8. R. Cruz, A. Santhanam, “Optimal Routing, Link Scheduling and Power

Control in Multi-Hop Wireless Networks.” Proc. INFOCOM 2003 , San Francisco, CA, April 2003.

9. P. Venkitasubramaniam, S. Adireddy, and L. Tong, “Opportunistic ALOHA and cross-layer design in sensor networks.” Proc. IEEE MILCOM, Boston, MA, October 2003.

10. P. Venkitasubramaniam, Q. Zhao, and L. Tong, “Sensor networks with multiple mobile access points.” Proc. 38th Annual Conference on Information Systems and Sciences, Princeton, NJ, March 2004.

11. X. Qin and R. A. Berry, “Distributed approaches for exploiting multiuser diversity in wireless networks.” Trans. Infor. Theory, vol. 52, no. 2, pp. 392-413, February 2006.

12. A. Sridharan, R. Subbaraman, and R. Guerin, “Distributed Uplink Scheduling in CDMA Networks.” Proc. Networking'2007, Atlanta, GA, May 2007. (Extended version – Sprint Research Report).

http://acsp.ece.cornell.edu/papers/VenkitasubramaniamAdireddyTong03MILCOM.pdf

http://acsp.ece.cornell.edu/papers/VenkZhaoTong04CISS.pdf

http://www.ece.northwestern.edu/~rberry/Aloha2.pdf




http://ipmon.sprint.com/publications/uploads/RR06-ATL080139.pdf

60

Our Initial Model• Homogenous, unconstrained users

– All users (n+1 users in a sector) employ the same policy– Users always have data and are able to transmit whenever the

policy schedules a transmission• Probabilistic On-Off transmission policy

– Transmit at rate R in a slot with probability p• Transmit power is therefore 0 with probability 1-p and

~TxT2P[R] with probability p• Simple but useful model

– Similar to Aloha– But with a contention model based on soft interferences (CDMA)

rather than “collisions”• Questions

– At what rate R should a user transmit?– How often (what p value) should a user transmit?

61

Revisiting our CDMA Uplink Model

• We have

• Achieved rate

• On-Off policy with parameters R and p

where for simplicity we have assumed SINRi(R)S0

(more on this later)

][2,)(

)(2 ii

iji

iiii RPTxTK

K

KRGRSINR

K

npp

j

n

jS

WppC Pilotinj

n

j

,)1(

1)(ˆ

00

][)(ˆ,)(

,min0

iiii

ii CEpCRS

RSINRRC

62

Rate-SINR Model

0S

iR

SINR

Ach

ieve

d R

ate Linear Model

Bounded Model

No matter how good the channel, you cannot get more bits out than you put in…

63

Main Results

• There exists an optimal p* (maximizes )– If 1 then p*=1– If < 1 then p* < 1– In both cases p* satisfies the following equality

– With few (many) users, and/or low (high) target rate R, users should transmit (in)frequently

• Higher target rates always achieve higher throughput, i.e.,– In the absence of other constraints

)(ˆ pC

1*)1(

1*)1(*

1

0 pnpp

j

n

jjnj

n

j

212*21

*1 ),,(ˆ),(ˆ RRRpCRpC if

K

n Pilot

64

Impact of

65

Hybrid Slotted/CDMA

66

Distributed Control

• Token bucket mechanism available in EV-DO Rev. A and HSUPA to “control” device transmissions– Token bucket depth and token fill rate are

controlled by Base Station– A device needs TxT2P[R] tokens to transmit at rate R– Aimed at limiting peak and average power to satisfy

fairness and QoS constraints• Question: How does the presence of a token

bucket affect the choice of “good” transmission decisions by devices?

67

Accounting for Token Buckets

• Given a token bucket configuration (,)– What are the optimal p* and K values?

• Two-step formulation1. Account for impact of token bucket on transmission

decisions• Transmissions conditioned on having at least K tokens

2. Explore possible combinations of p and K values– Note that optimality of higher rates need not hold any more

because of token constraints (token efficiency)

68

Token Efficiency

• With 24 users transmission at 153.6kbps yields a higher throughput but a lower token efficiency than transmission at 76.8kbps

69

Impact of Token Bucket

Conditional Transmission Probability

Token Bucket parameters:

σ = 21.5dB; = 7dB

More frequent transmissions at 76.8kbps yield a better throughput because of higher token efficiency

70

Token Bucket Formulation

• Let p and ptok denote conditional and unconditional transmission probabilities– Token bucket evolution governed by simple Markov chain

– So that

• Optimal (K,p*) value satisfies non-linear program N1

0 K+1K1 σ-K σ 1-p

1-p1-p1-p1-p

p p p

11

10,11

1

tok

K

iitok ppp

jntok

jtok

N

jtok

Kppp

j

n

jp

S

WKpCKpC

)1(1

),(ˆ where),,(ˆmax10

,

71

Solving Program N1

• Step 1: For each value of K, solve the unconstrained problem, i.e., look for actual transmission probability pu*(K) that maximizes throughput– Solved based on value of δ and fact that

• Step 2: For each value of K compute p*(K) that satisfies

• Step 3: Choose the pair (K,p*(K)) that yields the largest throughput

1*)1(

1*)1(*

1

0 pnpp

j

n

jjnj

n

j

1

1

* 1)()(minarg)(*K

iiu

pKpKpKp

72

Analysis vs. Reality

Token Bucket: σ = 21.5dB; = 7dB

Rate

(kbps)

Analysis Simulations

(bounded rate model)

p*A C*

A p*sim C*sim Csim(p*

A)

76.8 1.0 26.4 0.35 17.84 16.56

153.6 0.21 42.9 0.25 10.63 10.59

• Expected inaccuracies because of bounded rate

– But actual impact on throughput is small

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Related Results and Extensions

• Recent results– Similar results also hold for the bounded rate model– Characterized optimum centralized schedule

• A benchmark against to compare distributed policies• A combinatorial problem because of discrete rate values

• Extensions– Investigating the impact/use of token bucket for its

“original” purpose, namely, service differentiation• Rate vs. delay performance targets

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Summarizing Case Study 2

• What is the impact on the throughput of CDMA uplinks of uncoordinated user transmissions?– Used simple probabilistic policies to probe the effect of distributed

transmission decision– Extended the investigation to account for the effect for token

constraints imposed by the base station to “control” device transmissions

• Analytical tools– Algebraic manipulations and basic real analysis– Optimization techniques and Markov chains

• Main results– Identified optimal transmission strategy function of system load– Results also hold in more realistic setting of bounded rate model

investigating wireless systems two case studies

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