Random access and massive wireless networks Philippe Jacquet Nokia - - PowerPoint PPT Presentation

Random access and massive wireless networks

Philippe Jacquet Nokia Bell Labs

Terminal network interface model

Packets internally generated Network interface buffer Network interface Server (one packet max)

Traffic Poisson model

• Finite populaGon model

– Poisson model traffic per slot for node i – eg – Infinite buffer – Maximum stable capacity

• Infinite populaGon model

– N=∞ – Buffer limited to 1 unit. – A Poisson generaGon of node with one packet – Maximum stable capacity

λi

∑

=

i i

λ λ

N

i

λ λ =

F max

λ

F I max max

λ λ ≤

Why infinite populaGon model is interesGng

• When

– Average delivery delay is finite Independent of N

• When

– We expect – may vary with input reparGGon – StarvaGon effects – Problem when N increases

• Eg N=106 or larger

I max

λ λ < ∞ < ) (W E

F I max max

λ λ λ < ≤

) ( ) ( N O W E =

N W E / ) (

I max

λ

F max

λ

λ

F max

λ

ALOHA Performance

• Packet generaGon over all nodes

– Poisson process, cumulated rate λ packet per slot

• ALOHA Packet transmission aVempt process: Two

model cases:

– infinite populaGon: nodes transmit only one packet and die; – Finite populaGon nodes are permanent and manage a queue of packets – Poisson process, cumulated rate ρ packet per slot

P(slot is empty) = e−ρ P(slot is success) = ρe−ρ P(slot is collision) =1− (1+ ρ)e−ρ

Aloha and infinite populaGon

• Is unstable for all λ>0:

– Take B large number of waiGng packets: – System diverges: B(t) at Gme t – for binary exponenGal backoff (Ethernet, Wifi) P(slot is success) = (1− p)B λe−λ + Bp(1− p)B−1e−λ < λ E(B(t +1) − B(t) | B(t) = B) = λ − P(slot is success)

max = I

λ

max = I

λ

Aloha and finite populaGon

• N nodes

– In this case max{B(t)}=N – System is stable when B=N and – When

• And max throughput

λ > − =

−1

) 1 ( ) success is slot (

N

p Np P

p = O( 1 N )

) exp( ) success is slot ( Np Np P − ≈

• 36787

.

1 max

≈ =

−

e

F

λ

Stack collision resoluGon in infinite populaGon

• Stack algorithm

local procedure C←0;

While packet to transmit{ if (C=0) then { transmit; if collision then C←rand(0,1)} else { if listen=collision then C←C+1; else C←C-1 }

Stack algorithm stability condiGon

ABC AB

• AB

A B C C AB C B C C C

λmax ≈ 0.360177!

Ternary Stack collision resoluGon

• Ternary Stack algorithm

local procedure C←0;

While packet to transmit{ if (C=0) then { transmit; if collision then C←rand(0,1,2)} else { if listen=collision then C←C+1; else C←C-1 }

λmax ≈ 0.401599!

Upper bound on colision resoluGon algorithms stability p0 = P(algo returns 0) p1 = P(algo returns 1) p0λe−λ + p1e−λ = λ p0 + p1 ≤1 p0 p1

• 56714

. :

max max

max

≤ ≤

− I I

I

e λ λ

λ

• 487

. known largest

Aloha under small load

• Infinite populaGon with
• Transmission and retransmission is a Poisson

process

– cumulated rate ρ packet per slot – Equilibrium equaGon:

P(slot is empty) = e−ρ P(slot is success) = ρe−ρ P(slot is collision) =1− (1+ ρ)e−ρ λ << e−1 λ = ρe−ρ

λ

Stable point unstable point Takes exponenGal Gme exp(O( 1

pλ))

ALOHA in finite populaGon

• Maximum

throughput

– All buffers full – Takes long to aVain except if big burst of traffic – If pN<1: starvaGon

pN

pN F

pNe− =

max

λ

pN = ρ

Protocol CSMA (Wifi)

• Mini-slots

Performances of staGonary CSMA

• Poisson model:

– ρ: per mini-slot load – L: packet length (in mini-slots)

• Net throughput

L e L ) 1 ( 1 − +

ρ

ρ

L 2 1 max − ≈

L=100

L Max throughput

RTS-CTS

emitter Intended receiver packet ack Vorbidden period RTS CTS

CSMA/CA performances

• Net throughput with

RTS-CTS

R e L L C ) 1 ( 1

max

− + + =

ρ

ρ ρ

L R L R C ) ( 1 ) ( 1 1

max

β β − ≈ + =

Green contenGon

• Hypothesis: we know an upper bound of the

populaGon.

• Quasi channel transparency

– Delay are sublinear funcGon of N.

Improvement to CSMA: Bursty Preamble transmission

• Each primary transmits sequence of burst

before packet transmission

– Bursts used to resolve contenGons

Previous packet Next packet

Access keys

• Divide preamble in mini-slots

– Binary access paVern of a primary contender

• « 1 »: contender transmits a burst
• « 0 »: contender listens the slot

– Let integer k be the raGo frame/mini-slot (eg k=10)

• Access keys are constrained (0,k-1) sequences
• Run of zeros should not exceeds k-1

– to avoid desynchronisaGon

• Sequence of super-alphabet

} 1 , , 001 , 01 , 1 {

1 −

=

k k

A …

ContenGon resoluGon (leader elecGon)

• Contenders set their access keys before slot 1
• On i-th slot

– surviving contenders with a « 1 » as i-th bit

• Transmit a burst

– Surviving contenders with a « 0 » as i-th bit

• Listen to the slot
• If burst detected, the contender aborts contenGon

– Defer for the next elecGon.

ContenGon resoluGon (leader elecGon)

Access keys management

• DeterminisGc:

– The access keys are derived from node ID and are unique (over N nodes)

• In fact opGmal packing with super-symbols
• P. Jacquet, P. Mu ̈hlethaler, ”CogniGve networks: anew access scheme which

introduces a Darwinian approach” Wireless Days, 2012

Fairness obtained by round robin-like protocol.

• ProbabilisGc:

– The access keys can be probabilisGc – Eg super-symbols are drawn uniformly on – Residual collision may exist

• Rate can be made negligible
• Add to radio loss rate.

with ρi =1

i=1 k

∑

log 1

ρ

N

Ak

Part and try algorithm

• Case k=2 is the part and try algorithm

– BS Tsybakov, VA Mikhailov ”Random mulGple packet access: part-and-try algorithm” Problemy Peredachi Informatsii, 1980.

• The winners are those with the largest

binary sequence

– Average elecGon duraGon

losers losers

logk n

Energy cost issue

• Take the first burst.

– In average n/2 transmit & collide – If n is of order the million (urban area)

• The flash of the first burst can

create of 100 km interference radius

• Further bursts

– n/4, n/8, etc. – Average global energy cost per elecGon is n

Energy cost

• A global energy cost of one million bursts per

packet transmission is unacceptable

– Would run-down baVeries in seconds

105 104 103 102 101 100

Energy cost saving (green) leader elecGon algorithm

• Algorithm performs elecGon for n≤N

– Average duraGon minislot – Average global energy cost in

• N is a maximum network size.

– Residual collision rate bounded

• Can be made arbitrary small

– Example with k=10, N=1,000,000

• DuraGon 30 minislots
• Energy cost 5.5
• Collision rate less than 1%

klogk logN

( )

k N

O

green leader elecGon algorithm

GLE Part & Try n

Energy cost saving (green) leader elecGon algorithm

• Contender access key computaGon

– Access key is made of super-symbols

• Say

– Scalar p shared by all nodes

• Say

– Every contender selects a random integer X

• X is geometric with probability rate

– The access key is k-ary translaGon of

LN = logk logN + O(1) LN = 3 p = 0.02 1− p

P(X ≥ m) = (1− p)m max{k LN − X −1,0}

Green leader elecGon algorithm

X = 372 = 999 − 627

access key : 061021071= 000000100100000001

Parameters of the algorithm

• Residual collision rate, N=1,000,000

LN = 5 LN = 4 LN = 3 LN = 2 p

Parameters of the algorithm

• Energy cost per elecGon, N=1,000,000

LN = 5 LN = 4 LN = 3 LN = 2 p

Parameters of the algorithm

• Energy cost per successful elecGon,

N=1,000,000 LN = 5

LN = 4 LN = 3 LN = 2 p

Extensibility of the Algorithm

Energy cost per successful elecGon for LN = 3, N =106, 1012, 1018

N =106 N =1012 N =1018

Conclusion

• Random access

– Infinite populaGon model

• channel transparency

– Finite populaGon model

– Packet Delay proporGonal to N – Queues form on node, – unfairness and starvaGon may occur.

• Green collision resoluGon and leader elecGon

– Need a known upper bound N of populaGon size – Intermediate with channel transparency

• Packet Delay proporGonal to loglog N
• Energy per packet proporGonal to (

)

10 N

O