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 λ i λ ∑ – eg λ = λ λ = i i N i – Infinite buffer – Maximum stable capacity F • Infinite populaGon model λ max – N=∞ – Buffer limited to 1 unit. – A Poisson generaGon of node with one packet – Maximum stable capacity I F λ ≤ λ max max

Why infinite populaGon model is interesGng I • When λ < λ max E ( W ) – Average delivery delay is finite < ∞ Independent of N I F E ( W ) / N • When λ ≤ λ < λ max max E ( W ) O ( N ) – We expect = F – may vary with input reparGGon λ max – StarvaGon effects I F λ λ λ – Problem when N increases max max • Eg N=10 6 or larger

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 P (slot is empty) = e − ρ P (slot is success) = ρ e − ρ P (slot is collision) = 1 − (1 + ρ ) e − ρ – Poisson process, cumulated rate ρ packet per slot

Aloha and infinite populaGon I 0 • Is unstable for all λ>0: λ max = – Take B large number of waiGng packets: P (slot is success) = (1 − p ) B λ e − λ + Bp (1 − p ) B − 1 e − λ < λ – System diverges: B(t) at Gme t E ( B ( t + 1) − B ( t ) | B ( t ) = B ) = λ − P (slot is success) I – for binary exponenGal backoff (Ethernet, 0 λ max = Wifi)

Aloha and finite populaGon • N nodes – In this case max{B(t)}=N – System is stable when B=N and N − 1 P ( slot is success ) Np ( 1 p ) = − > λ – When p = O ( 1 N ) P ( slot is success ) Np exp( Np ) ≈ − • And max throughput F 1 e 0 . 36787 � − λ = ≈ max

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 λ max ≈ 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 } λ max ≈ 0.401599 !

Upper bound on colision resoluGon algorithms stability p 0 = P (algo returns 0) p 1 = P (algo returns 1) p 1 p 0 λ e − λ + p 1 e − λ = λ p 0 + p 1 ≤ 1 p 0 I I I e : 0 . 56714 � − λ λ ≤ max λ ≤ max max largest known 0 . 487 �

Aloha under small load • Infinite populaGon with λ << e − 1 • Transmission and retransmission is a Poisson process – cumulated rate ρ packet per slot P (slot is empty) = e − ρ P (slot is success) = ρ e − ρ P (slot is collision) = 1 − (1 + ρ ) e − ρ – Equilibrium equaGon: λ = ρ e − ρ

Takes exponenGal Gme exp( O ( 1 p λ )) λ Stable unstable point point

ALOHA in finite populaGon • Maximum throughput F pN pNe − λ = max – All buffers full pN ρ = – Takes long to aVain except if big burst of traffic – If pN<1: starvaGon pN

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 ρ 1 ( e 1 ) L ρ + − 2 max 1 ≈ − L

L=100

L Max throughput

RTS-CTS RTS packet emitter CTS ack Vorbidden period Intended receiver

CSMA/CA performances • Net throughput with RTS-CTS L ρ C = max 1 L ( e ρ 1 ) R + ρ + − 1 ( R ) β C 1 = ≈ − max ( R ) L β 1 + L

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 Next packet Previous packet – Bursts used to resolve contenGons

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 k 1 A { 1 , 01 , 001 , … , 0 1 } − • Sequence of super-alphabet = k

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) k log 1 N • In fact opGmal packing with super-symbols ρ i = 1 ∑ with ρ i = 1 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 A k – Residual collision may exist • Rate can be made negligible • Add to radio loss rate.

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 . losers • The winners are those with the largest losers binary sequence – Average elecGon duraGon log k 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 10 5 10 4 10 3 10 2 10 1 10 0

Energy cost saving (green) leader elecGon algorithm • Algorithm performs elecGon for n≤N – Average duraGon minislot k log k log N ( k N ) – Average global energy cost in O • 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%

green leader elecGon algorithm Part & Try GLE n

Energy cost saving (green) leader elecGon algorithm • Contender access key computaGon – Access key is made of L N = log k log N + O (1) super-symbols L N = 3 • Say – Scalar p shared by all nodes • Say p = 0.02 – Every contender selects a random integer X • X is geometric with probability rate 1 − p P ( X ≥ m ) = (1 − p ) m – The access key is k-ary translaGon of max{ k L N − X − 1,0}

Green leader elecGon algorithm X = 372 = 999 − 627 access key : 0 6 10 2 10 7 1 = 000000100100000001

Parameters of the algorithm • Residual collision rate, N=1,000,000 L N = 3 L N = 2 L N = 5 L N = 4 p

Parameters of the algorithm • Energy cost per elecGon, N=1,000,000 L N = 3 L N = 4 L N = 5 L N = 2 p

Parameters of the algorithm • Energy cost per successful elecGon, N=1,000,000 L N = 5 L N = 2 L N = 4 L N = 3 p

Extensibility of the Algorithm Energy cost per successful elecGon for L N = 3, N = 10 6 , 10 12 , 10 18 N = 10 18 N = 10 6 N = 10 12

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 10 N • Energy per packet proporGonal to ( ) O