© W. Henkel, 2003

12 Aloha-Protokoll

© W. Henkel, 2003

1970 pure Aloha proposed by Norman Abramson (published 1970 and 77)1972 slotted Aloha introduced by Roberts

We treat slotted Aloha first:

Assumptions:1.) Slotted System2.) Poisson Arrivals3.) Collision or Perfect Reception4.) 0,1,e Immediate Feedback5.) Retransmission of Collisions6.a) No Buffering

b) Infinite Set of Nodes ( )

Rate of successful transmission: S = G e-G

Pure and Slotted Aloha:description and throughput analysis

m→∞

© W. Henkel, 2003

Poisson-Prozess als Netzwerk-Zugriffs-Modell

nk p pk n l − −( )1

( )

Falls und 1:( 1) ( 1)

1 (1 )

k

p n k n k p np

k n kpn n n k n

p e p e e− − − − −

<< <<

− − + ≅

− ≅ − ≅ ≅

Falls ein Ereignis mit der Wahrscheinlichkeit p eintritt, so folgt die Wahrscheinlichkeit innerhalb von n Versuchen k Ereignisse zu erhalten zu

⇒ − ≅− −

nk

p p enpk

k n l npk

( )( )

!1

© W. Henkel, 2003

Poisson-Theorem

Falls, 0 , ,

dann gilt

(1 )!

kk n k G

n

n p np G

n Gp p ek k

− −

→∞

→∞ → →

−

→

S = G e-G

© W. Henkel, 2003

Slotted Aloha: description and throughput analysis

G e-G

G=1G=0

e-1

l

DepartureRate

Arrival RateEquilibrium

The maximum throughput of slotted Aloha is just

1/e = 0.368 at G=1.

G →

© W. Henkel, 2003

Endliche Anzahl von Stationen

A more detailed analysis under Assumption 6.a:

Let n be the number of baglogged nodestransmitting with probability qr . m-n other notbaglogged nodes are transmitting with theprobability qa . Let Qa(i,n) and Qr(i,n)be the probabilities for access trials of iunbacklogged and backlogged nodes, respectively,

© W. Henkel, 2003

Q i nm n

iq q

Q i nni

q q

a am n i

ai

r rn i

ri

( , ) ( ) (

( , ) ( ) (

=−

−

=

−

− −

−

1

1

not backlogged)

backlogged)

[ ][ ]P

Q i nQ n Q nQ n Q n Q n Q nQ n Q n

i m niii

n n i

a

a r

a r a r

a r

,

( , ) ,( , ) ( , ) ,( , ) ( , ) ( , ) ( , ) ,( , ) ( , ) ,

( )

+ =−

+ −

≤ ≤ −=== −

1 1 01 0 0 1 10 1

210

1

State transitions:

The number of backlogged nodes n specifies the state.

© W. Henkel, 2003

Stability Issues:

Let Dn be the Drift , i.e., the expected number of new arrivalsaccepted into the system ( (m-n)qa ) less the number of successfultransmissions Psucc.

Dn= (m-n)qa - Psucc

Psucc= Qa(1,n)Qr(0,n)+Qa(0,n)Qr(1,n)

The attempt rate is G(n)=(m-n)qa+nqrIf qa and qr are small(Further assumption qr >qa)

P n G n e G nsucc ( ) ( ) ( )≈ −

Departure RateG e-G

Arrival Rate(m-n)qa

G m n q nqa r= − +( )G m q a=G = 0

m q a

n = 0

G m q r=n m= G, n

© W. Henkel, 2003

Back to the infinite-node assumption 6.b: G(n)=l+nqr

Departure Rate G e-G

Arrival Rate l

G nqr= +λG = λ

n = 0G, n

Stabilizing the Aloha Protocol

Pseudo-Bayesian Algorithm (Rivest):Let all access trials (backlogged and new) have a transmit probability of qrand thus, all are considered to be backlogged.Attempt rate: G(n)=nqrProb. of succ. transm.: Psucc=nqr(1-qr)n-1

Alg. uses an estimate n of n and the transmit probability is set toqr(n) = min{1,1 / n}^ ^

^

© W. Henkel, 2003

Estimation of the backlog:

{ }max , ,( ) ,

nn

n ekk

k+ −=

+ −+ + −

1 1

12

λ λλ

for idle or successfor collision

Some reasoning:

For idle case or success:backlog + new - successful

For collision:Note: I/n ~ 1/e, S/n~1/e,

C/n~1-2/e=(e-2)/e

© W. Henkel, 2003

Stabilizing the Aloha (contd.)

Binary Exponential Backoff Algorithm:

After i collisions, a system waites for arandom number of slots between 0 and 2i-1.This means that low traffic leads to short delays,still being able to adapt to situations withmore traffic.

There may be some limit for the number of slots(e.g., 1023) and also some limit for the numberof collisions before giving up (e.g., 16).

© W. Henkel, 2003

T

t-T t t+T

1 12

23 3

Vulnerable Period

Pure Aloha: description and throughput analysis

P e eS n G n e

gT G

G nsucc = =

=

− −

−

2 2

2( ) ( ) ( )

0

0.1

0.2

0.3

0.4

0.001 0.01 0.1 1 10 100

1/(2e)

1/eSlotted Aloha

Pure Aloha

G n q r= +λ

G e G−

G e G− 2

© W. Henkel, 2003

Pure Aloha

2

2

erfolgreich

erfolgreich

/ ( )

( )

( ) ( ) ( )

g G

XG

vor nachG

S G P

P T X ge d e

P P T X P T X e

S Ge

τ τ∞

− −

−

−

=

≥ = =

= ≥ ⋅ ≥ =

⇒ =

∫

© W. Henkel, 2003

CSMA, Carrier Sense Multiple Access

Listen before talk !

Let t be the maximum delay of the transmissionmedium. Then a transmitted packet can only behit during this interval.

T tBusyperiodB

IdleperiodI

IdleperiodI

BusyperiodB

BusyperiodB

Different CSMA Schemes:Non-persistent 1-persistent (p-persistent)

Non-slotted

Slotted

© W. Henkel, 2003

Idle period:

no packet scheduled during x

Mean: I =

Useful time: Successful periodUnsuccessful period

Uno arrival in the period [t, t + ]] = e

U e

succ

succ

F x P I x P I xPe

/g

U=T

E U TPP P

T

I

gx

-g

-g

( ) ( ) ( )[ ]

,,{ }

[

= ≤ = − > == − =

= −

= =

=

=

−

1111

0

τ τ

τ

Busy time:

Let Y be a random variable such that t+Ydenotes the starting time of the last interferingpacket.

© W. Henkel, 2003

B T YF y P Y y

P y ef y e y g e

E Yeg

E T Y Teg

Sg T e

g T eG e

G a ea T

N o te

Yg y

Yg g y

g

g

g

g

a G

a G

a

= + += ≤ =

= − =

= +

= −−

= + + = + −−

=+

=+ +

=+ +

=

− −

− − −

−

−

−

−

−

−

→

τ

τ

δ

τ

τ τ

ττ

τ

τ τ

τ

τ

τ

τ

( ) [ ][ ]

( ) ( )

{ }

{ }

( ) ( )/

lim

( )

( )

n o p a c k e t a rr iv a l d u rin g

B

UB I

w ith

:

1

21

2 1 2

0S

GG

=+1 CSMA, a=0

00.10.20.30.40.50.60.70.80.9

1

0.01 0.1 1 10 100

Slotted Aloha

Pure Aloha

CSMA, a=0.01

CSMA, a=0.1

S

G

© W. Henkel, 2003

CSMA/CD, Carrier Sense Multiple Accesswith Collision Detection

Stop talking when someone interrupts you and try again later!

Distance

A

Bt1

t0

t0+t

t1+t

t0+t +tcd

t1+t +tcd

t0+t +tcd +tcr

t0+g

t1+g

t0+T

t0+T+t

Time

t1+t +tcd +tcr

Unsuccessful Transmission

Successful Transmission

g=2t+tcd+tcrSuccessful transmission period: T+tUnsuccessful transmission period: g+t

tcd: Time for Collision Detectiontcr: Time for Consensus Reenforcement Procedure

© W. Henkel, 2003

P ro b a b il i ty o f a s in g le a c c e s s f ro m a s e t o f t r a n s c e iv e r s :

w i l l b e m a x im iz e d fo r ( fo r

P ro b a b il i ty o f a w a i t in g t im e o f m in i s lo ts :

A v e ra g e w a it in g t im e in m in i s lo ts (p lu s th e a d d i t io n a l fo r s u c c e s s fu l t r a n s m is s io n s ) d u e to c o ll is io n s

T h e th ro u g h p u t fo l lo w s to b e

W ith a f r a m e le n g th , a d a ta r a te , , a c a b le le n g th , th e p ro p a g a t io n v e lo c i ty , a n d w e o b ta in

nA n p p

A p = /n A e n

jA A

jA A A

ST

T AF B T = F /B L

c A = /e

S

n

j

j

j

= −→ → ∞

−

− =

=+

=+

−

−

−

=

∞

∑

( )/ )

( )

( ) /

/

,

11 1

1

1 1

2

11

1 2

1

1

1

1

τ

τ

B L e c F/

0.10.20.30.40.50.60.70.80.9

Thro

ughp

ut

0

1

1 2 4 8 16 32 64 128 256Number of transceivers

Packet size

64 Byte128 Byte256 Byte512 Byte

1024 Byte

Simplified Throughput Computationwithout Consensus Reenforcement Procedure

© W. Henkel, 2003

ExamplesEthernet:• CSMA/CD• Slotted• 1-Persistent• Consensus Reenforcement• Truncated Packet Filtering• Packet Error Detection

Type Cable Max. segment length

Max. unit noper segment

10Base 5 Thickwire Coax 500 m 100 10Base2 Thinwire Coax 200 m 30 10Base-T Twisted Pair 100 m 1024 10Base-F Optical 2000 m 1024

Application Telnet, FTP, SMTP, DNS, etc.

Transport TCP, UDP

Network IP

Link LAN, e.g., Ethernet

TCP/IP reference model:

© W. Henkel, 2003

S-ALOHA

modem preamble

FH cont

rol

AC

K

Downlinkperiod

ABR/UBR VBR CBR

Dynamicallocation

Fixed & sharedallocation

Fixedallocatíon

48 Bytepayload

wireless header ATM header(compressed)

CRCpreamble

wireless header ATM header(compressed)

CRC

48 Bytepayload

Uplink period

Wireless ATM

© W. Henkel, 2003

BibliographyTanenbaum, Andrew S.: Computernetzwerke, Prentice Hall

Bertsekas, Dimitri; Gallager, Robert: Data Networks, Prentice Hall

Rom, Raphael; Side, Moshe: Multiple Access Protocols, Springer

Stephens, W. Richard: TCP/IP Issustrated, Volume 1, Addison-Wesley

Wilder, Floyd: A Guide to the TCP/IP Protocol Suite, Artech House

Abramson, Norman, Ed.: Multiple Access Communications, IEEE Press

Abramson, Norman: The Throughput of Packet BroadcastingChannels, IEEE Trans. Comm., Vol. Com-25, No. 1, pp. 117-128, Jan. 1977.

Metcalfe, Robert M.; Boggs, David R.: Ethernet: DistributedPacket Switching for Local Computer Networks,Communications of the ACM, Vol. 19, No. 7, July 1976.

Raychaudhuri, Dipankar: Wireless ATM Networks: Architecture, System Design, and Prototyping, IEEE Personal Communications, pp. 42-49, Aug. 1996.

© W. Henkel, 2003

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