[12] Nup 07 3

Protokolle der OSI-Schicht 2
Performance Modelling MAC
Kapitel 7.3

Netze und Protokolle
Dr.-Ing. Jan Steuer

Institut für Kommunikationstechnik
www.ikt.uni-hannover.de

Literatur:

[Sieg99] Gerd Siegmund,“Technik der Netze“, 4.Auflage, Hüthig Verlag, Heidelberg, 1999,
ISBN 3-7785-2637-5

[Spra91] J.D.Spragins,et.all, Telecommunications Protocols and Design,
Addison Wesley Publishing Company, 1991, ISBN 0-201-09290-5

[Hals96] F.Halshall, „Data Communications, Computer Networks and Open Systems“, 4th edition,
Edison-Wesley, 1996, ISBN 0-201-42293-X

[Stall90] William Stallings, Local and Metropolitan Area Networks, 1990; MacMillen Publishing
Company, ISBN 0-02-415465-2

[Pap65] Papoulis, “Probability, Random Variables and Stochastic Processes”, MacGraw Hill, 1965

[Klein75] Kleinrock, „Queueing Systems“, Adison and Wesley

© UNI Hannover, Institut für Allgemeine
Nachrichtentechnik

Goals

An engineer working in the field of protocol development needs
to know
General principles of transmission systems,
General principles of switching systems,
Characteristics of networking and
How to evaluate the performance of protocols (subject of this lecture)
Here I concentrate on the performance of the MAC layer (higher
layers will follow)
First I am going to develop general principles using a generic network for
purposes of comparison
Second I will evaluate the performance of MAC strategies given before,
which are:
TDMA (application in PDH- and SDH-multiplexing)
ALOHA, slotted ALOHA (application in GSM)
CSMA (application on LAN´s)

(2)

In chapter 6.1 we have investigated the principles of different MAC strategies for scheduled access (TDMA)
and random access (ALOHA, slotted ALOHA, CSMA). This chapter shall now form the basic knowledge on
how to evaluate the performance of the MAC strategies dealt with. We will use the delay time for the
packets delivered to the access network and the throughput of the network to judge the performance. Most
of the equations used will be developed throughout this excurse. Few equations are just used and the
reader is referred to the literature.
Some hints are given, why the bad performance of e.g. the ALOHA protocol is not hindering us to apply it to
very modern protocols as for instance the GSM protocol stack.

Nachrichtentechnik

Generic Multi-access Network
- Performance Investigation -

λ
λ
1
M
transmission rate R

2
M-1
λ λ
max propagation time τ
Questions:
Assumptions:
• how long is the time to transmit a packet
• average arrival rate λ (packets of information between two stations?
per second), Poisson distributed • and what is the transfer delay (no waiting
• average packet length X (bits queue)?
per second), similar for all packets • what is the throughput of the network?
• each station on schedule • what does stability mean in the context of
transmits all packets available MAC?
• distance of all stations similar • what is the offered traffic?

(3)

The purpose of the creation of this generic multi access network is to allow the comparison of different MAC
methods. The assumptions are not in all cases realistic, there are often special design issues to enhance
the behavior of the network. It is not the intention of this exercise to deal with special solutions. Instead the
scenario shall be a framework to compare the qualities of different MAC-schemes.
Quality of Poisson distribution (for details see [Pap65] ):
1. all events of the random process are independent of each other
2. the number of events of the random process is indefinite (for all practical purposes:
large)
3. the random process is discrete
The maximum propagation time is between the most distant stations
The distance between all stations is of the same length. This is not very realistic, but it allows to compare
the calculated results of the different MAC schemes

Nachrichtentechnik

Transmission Time as measure of performance
in the Generic Multi-access Network
λ transmission time of packet with length X:
λ
1
X
M
transmission rate R
tX = + td + t w , 6.3.1
R
2
λ td : delay on transmission link ( propagation)
M-1
λ tw : waiting time due to buffering or queueing

average transmission time of packet with length X :
X
tX = + t d + t w 6.3.2
Assumptions: R
effective transmission time of packet with length X
λ (packets per second),
• average arrival rate using the effective transmission rate R´:
Poisson distributed X
E= + t d + t w 6.3.3
R′
• average packet length (bits per packet),
X
similar for all packets remarks:
• E is a random variable, if X (the packet
• each station on schedule transmits all
length) is a random variable
packets available • often td can be neglected on access networks,
depending on the length of the access link
• distance of all stations similar
• The transmission time is in view of an undisturbed
individual station

(4)

Throughout the following slides the configuration of the access network , the assumptions and constraints
used are shown on the left side in order to understand the development of formulae's at the right side.
In view of the individual subscriber the time which is needed to transport one or the average packet from
source to destination is an important quality measure. The delay is formed by three components, the time to
serialize the packet( X/R= time to serialize the packets of length X with the speed R), the traveling
(propagation) time of each bit on the transmission media and the waiting time to get transferred from the
queue to the transmission media. Because the packets are not of constant length X we need to calculate
with the average packet length E[X]. (E[X] expected value from X)
All these times can be calculated with the nominal transmission speed R. But, because the nominal
transmission time is not in all cases to be achieved it is more sensible to calculate with the effective
transmission time R´. For example take the IEEE802.3 network with a nominal transmission rate of 10
Mbit/s, this network often only achieves the effective transmission rate of 5 Mbit/s, due to the collisions on
the network.

Nachrichtentechnik

Throughput as measure of performance in
the Generic Multi-access Network
λ
λ
1
normalized network throughput of the access network:
M
transmission rate R

M λ X X ∑ i =1 λi
M

S= =
2 6.3.4
λ M-1 R R
λ
effective throughput of the access network :
X ∑ i =1 λi
M
MλX
S′ = = 6.3.5
R′ R′
with the average effective transmission time (see 6.1.3)
Assumptions:

λ
• average arrival rate (packets per second), X
E=
R′
Poisson distributed
the effective throughput of the access network gets :
X
similar for all packets
S′ = M λE 6.3.6
packets available
remark:
• distance of all stations similar • the effective throughput is in view of the entire
access network, not of an individual station

(5)

The throughput can be a performance measure of the individual subscriber and/or the network. In the slide
the entire packet arrival rate of all the subscribers (note the factor M in front of Lambda!). Thus we have
given the throughput of the network. If we would like to guide the attention to the individual throughput, we
just would have to replace the M by 1.

Nachrichtentechnik

Concept of offered traffic and stability

λ
λ
1 Stability:
M
transmission rate R [bits/sec] The system is stable if all offered traffic can be
handled without growing the input queues at each
2 station to indefinite, which means the normalized
λ M-1 network throughput S is not exceeding the effective
λ normalized network throughput S´ :
S ≤ S′ < 1 6.3.7
MλX MλX
≤ <1 6.3.8
R′
Assumptions: R
λ(packets per second), shared
• average arrival rate
transmission
Poisson distributed 1
medium
X
MAC
Queue
packets available
1average
queue length
question: under which conditions is the queue length permanently growing?

(6)

Nachrichtentechnik

Concept of offered traffic

λ The offered traffic G is the ratio of the average
λ
1 number of attempted packet transmissions per second
M
transmission rate R [bits/sec]
to the average number of packet transmissions
per second possible. In case there is no delay due to
2 scheduling or queuing:
λ M-1
λ
∑ λi
M
Mλ MλX
G= = = = S 6.3.9
i =1
R R R
X X
With delay due to scheduling and/or queuing the
Assumptions:
throughput is converging against a maximum value
λ (packets per second), (for details see [Klein75]):
S
Poisson distributed
• average packet length (bits per packet), Smax
X
packets available
G

(7)

We came across the concept of the offered traffic first with loss systems. For those Erlang formulated, that
the traffic in general is the ratio of the sum of the busy periods of the traffic sources by the maximum busy
time possible. The maximum busy time possible is usually the main traffic hour (60 successive minutes
during the day, when the traffic is maximal). If we have 100 traffic sources and each of them is busy on
average for a period of 1,8 minutes, the total busy time is 100 times 1,8 minutes. Which equals to 180 min.
The traffic is now 180 min/ 60 min=3 Erl. In case of traffic sources generating the traffic, it is called offered
traffic. Another expression for the traffic could be the utilization of the ressources.
The measure taken here to derive the offered traffic is not the time of occupation of ressources, but the
number of packets transmitted per time unit by the ressources. Again the ratio of the actual packets per
time to the maximum packets per time is the utilization of the transmission system, thus the traffic.

Nachrichtentechnik

Concept of transfer delay

λ
λ
1 normalized average transfer delay:
M
transmission rate R is the ratio of the average transfer delay and the
average packet transmission time (from 6.3.2) :
2
λ M-1
λ X +t +t
t
T= X = R
d w
≥1
ˆ
X X
R R
Assumptions:
with tw neglected : 6.3.10
λ (packets per second),
+ td
X
t R
T= X = ≥1
ˆ
Poisson distributed
X X
X R R
Remarks:
- The transfer delay is the transmission time
packets available
without time for queuing or buffering
- Normalization is done to achieve a
X
tX = + t d + t w 6.3.2 dimensionless value
R

(8)

Nachrichtentechnik

Concept of waiting time

waiting time in the single queue [Klein75]:
shared
μ transmission
λ ρ Y2
medium W= 6.3.11
1 − ρ 2Y ′
MAC
Queue with Y : random var iable denoting service time
Y : average service time, here effective packet
transmission time E seen by each station
Y ′ : normalized mean service time
λ: arrival rate [packets/sec] Y 2 :mean square service time
μ: service rate or here if
transmission rate of packets ρ = S ′ and Y = E
from this queue on the shared
then
medium [packets/sec]
S′ E 2
W= 6.3.12
1 − S ′ 2E
λ
= S′
ρ=
μ
(9)

Nachrichtentechnik

average transfer delay of the TDMA system
with fixed assignment
Each station is allowed to use the channel 1/M of the available time, thus the
capacity,
available to each station is R´= R/M.

Something is neglected here, what is it?
Let us assume that we use a constant packet length, than the mean square of E is
E 2 = ( E ) 2 6.3.13
the square of the mean and get for the waiting time
S′ E 2 S ′ (E )2 S′ E
W= = = 6.3.14
1 − S ′ 2E 1 − S ′ 2E 1 − S ′ 2

Now we remember:
X X XM
E= = = 6.3.15
R′ R R
M
which modifies again the waiting time:
S′ E S ′ MX
W= = 6.3.16
1 − S ′ 2 (1 − S ′)2 R

(10)

Nachrichtentechnik

with fixed assignment (2)

In TDMA with fixed assignment the effective throughput is equal to the normalized
network throughput:

S´=S , thus
S MX
W= 6.3.17
(1 − S )2 R

additional average delay we get from the statistical arrival of the packets and the
need to wait for the assigned slot. It is assumed that the arrival time is uniformly
distributed, which means we have to wait on average half of the frame time before
we get served:
MX
Wslotwait = 6.3.18
2R

The average transfer delay is now the sum of the transmission time, the time to wait
for a slot and the queueing time:
M S
X MX S MX
6.3.19 and normalized: T = 1 + +
ˆ
T= + + M 6.3.20
2 (1 − S )2
R 2 R (1 − S )2 R

(11)

Nachrichtentechnik

with fixed assignment (3)
average normalized transfer delay ^T

M=100
100

M=10
10 M=2

1
Througput S

(12)

Nachrichtentechnik

Performance of Random Access Methods

competing Protocols
pure ALOHA
slotted ALOHA
1-persistent CSMA
nonpersistent CSMA
p-persistent CSMA
CSMA/CD

(13)

pure ALOHA: an der Universität von Hawaii entwickeltes Verfahren zur Kanalzuteilung (Abramson et all.,
1970)
Sender schickt sein Paket sofort bei Sendebereitschaft auf das Medium
Empfänger sendet eine Quittung
Sender hört den Kanal ab, ob das Paket gestört wurde
Wiederholte Sendung des Pakets nach zufälliger Zeitspanne

Nachrichtentechnik

ALOHA

• constant packet length P
• Collisions detection: sending packets and waiting for acknowledgement. In
case of missing acknowledgement: repetition until transmission is
successful.
• other packets than the blue cannot start within the dangerous time without
colliding with the blue packet
user

packet with collision

Packet

P P
to-P to to+P time
dangerous time
(14)

Die gefährliche Zeit ist gleich der doppelten Nachrichtenlänge:
gerade etwas weniger als eine Nachrichtenlänge vor der Übertragung darf nichts von einer
anderen Station gesendet werden, und natürlich nicht während der Paketübertragung selber,
damit keine Kollision auftritt
kein vorheriges Abhören des Kanals!
Laufzeit zum und Bearbeitungszeit im Empfänger werden vernachlässigt

Nachrichtentechnik

Effizienz ALOHA (1)

während der konstanten Rahmenzeit t werden von
unendlich vielen Teilnehmern genau S Pakete nach einer
Poissonverteilung erzeugt:
für S >1 ist kein geordneter Verkehr möglich
Bedingung ist deshalb: 0 < S ≤ 1
k poissonverteilte (Annahme!) Übertragungsversuche
(neue und wiederholte) führen zu einer mittleren
Rahmenzahl G während einer Rahmenlänge t
bei wenig neuen Paketen S ~ 0 G~S
Allgemein:
p0: Wahrscheinlichkeit, dass keine Kollision stattfindet

S = G ⋅ p0 6.3.22

(15)

Rahmenzeit: die Zeit, die benötigt wird, um einen Standardrahmen zu übertragen (Länge des
Rahmens/Bitrate)

S>1: es finden nur noch Kollisionen statt

Nachrichtentechnik

Effizienz ALOHA (2)

die Wahrscheinlichkeit, dass während eines Paketes k
Pakete produziert werden, ist poissonverteilt:

G 'k −G '
pk = ⋅e 6.3.24
k!
• daraus folgt mit G’=2G, da “gefährliche Zeit” = 2t
( 2G ) 0 − 2 G
p0 = ⋅e 6.3.25
0!
• und damit

p 0 = e −2 G 6.3.26

(16)

vgl. Verkehrstheorie :
Poissonverteilung:

Nachrichtentechnik

Effizienz ALOHA (3)

Wahrscheinlichkeit, dass keine andere Sendeanforderung
während unseres Datenpaketes vorliegt (keine Kollision),
p = e −2 G 6.3.25
ist
0

S = G ⋅ e −2G
damit folgt für S: 6.3.26

dS
=0 G= 0,5
mit dem Maximum:
dG S = 0,5e - 0,5*2 = 0,18

die beste Performance des ALOHA liegt also bei einer
Wahrscheinlichkeit für die Sendeanforderung von 0,18.

(17)

Nachrichtentechnik

Protokolle für die dynamische Kanalzuordnung
ohne Verständigungsmöglichkeit der Sender
Konkurrierende Protokolle
pure ALOHA
slotted ALOHA
1- persistent CSMA
nonpersistent CSMA
p-persistent CSMA
CSMA/CD

(18)

pure ALOHA: an der Universität von Hawaii entwickeltes Verfahren zur Kanalzuteilung (Abramson et all.,
1970)
Sender schickt sein Paket sofort bei Sendebereitschaft auf das Medium
Empfänger sendet eine Quittung
Sender hört den Kanal ab, ob das Paket gestört wurde
Wiederholte Sendung des Pakets nach zufälliger Zeitspanne

slotted ALOHA: Weiterentwicklung des pure ALOHA (Roberts, 1972)
Einteilung der Zeitachse in Intervalle (Slots), zu deren Anfang ein Sendevorgang beginnen darf

Nachrichtentechnik

slotted ALOHA

Die Datenpakete dürfen nicht zu beliebigen Zeiten
anfangen, sondern immer nur zum für alle Sender
gleichen Synchronisationszeitpunkt.
Folge: quot;gefährliche” Zeit schrumpft auf die Hälfte!
Benutzer

mögl. Kollision

Paket

Zeit
to to+t to+2t
gefährliche Zeit

(19)

Nachrichtentechnik

slotted ALOHA

Wahrscheinlichkeit, dass keine andere Sendeanforderung
während unseres Datenpaketes vorliegt (keine Kollision),
ist −G
p0 = e .
Damit wird die Zahl der während eines Rahmens vorliegenden
Sendeanforderungen: −G
S = G ⋅e 6.3.27
dS G=1
mit dem Maximum: =0
dG S = e - 1 = 0,37

Die beste Performance des slotted ALOHA liegt also bei einer
Wahrscheinlichkeit für die Sendeanforderung von 0,37.
Gegenüber dem reinen ALOHA ist eine Verbesserung von 0,18
nach 0,37 zu verzeichnen
(20)

Nachrichtentechnik

ALOHA, Throughput-Performance

Unterteiltes ALOHA
0,368 0,184
Reines ALOHA

0.4
0.35
0.3 slotted ALOHA, S = G e-G
0.25
0.2
S (Throughput)

0.15
0.1
0.05
pure ALOHA, S = G e-2G
0
0.5
0.01 0.1 1 10
G (offered load)

(21)

#Bildgroesse:
# post landscape: 10inch*7inch=25.4cm*17.78cm
# eps: Alles halb so gross
# Breite 12.7cm, Hoehe mitskaliert:
set autoscale xy
# Anzahl der Markierungen auf den Achsen (mit Beschriftung) festlegen
set ytics 0,0.05,0.4

# Abtastwertanzahl
set sample 50
# Positionierung der Legende
set key 9,2.5

# Logarithmische Skalierung
set logscale x

# Achsenbeschriftung

set xlabel 'G (Versuche pro Paket)'
set ylabel 'S (Durchsatz pro Rahmen)' 0
set grid
set term windows color quot;Arialquot; 16
# hier bitte die zuplotenden Funktionen angeben
# mit Titel und Beschriftung der Achsen
# und Liniensytle
plot [0.01:10] [0:0.4] x*exp(-x) title 'Unterteiltes ALOHA' with lines,
x*exp(-2*x) title 'Reines ALOHA' with lines

Nachrichtentechnik

Unterteiltes ALOHA
ALOHA, stability (1)
Reines ALOHA
0.4
0.35
0.25S2
0.2
S (Throughput)

S1
0.15
0.1
0.05
0
G1 G20.5
0.01 0.1 1 10
G (offered load)
Let us assume: the offered average load G1 increases temporarily to the
average value G2
What happens
- with regard to the throughput
- with regard to the collisions
- and in case of G2 lowers down to G1 again?

(22)

#Bildgroesse:
set autoscale xy

# Abtastwertanzahl
set sample 50
set key 9,2.5

set logscale x


set grid
# und Liniensytle

Nachrichtentechnik

Unterteiltes ALOHA
Reines ALOHA
0.4
0.35
0.25S1
0.2
S (Throughput)

S
0.15 2
0.1
0.05
0
G1 G2
0.5
0.01 0.1 1 10
G (offered load)
average value G2
What happens
- with regard to the throughput
- with regard to the collisions
- and in case of G2 lowers down to G1 again?

(23)

#Bildgroesse:
set autoscale xy

# Abtastwertanzahl
set sample 50
set key 9,2.5

set logscale x


set grid
# und Liniensytle

Nachrichtentechnik

Unterteiltes ALOHA
ALOHA, stability
Reines ALOHA

0.4
stable instable
0.35
0.25
0.2
S (Throughput)

0.15
0.1
0.05
0
0.5
0.01 0.1 1 10
G (offered load)

(24)

#Bildgroesse:
set autoscale xy

# Abtastwertanzahl
set sample 50
set key 9,2.5

set logscale x


set grid
# und Liniensytle

Nachrichtentechnik

ALOHA, Delay-Performance

1retransmission will be repeated until
the packet is successfully acknowledged,

station learns missing packet
number of repetitions is H

(no acknoledgement)
user

first first
transmission retransmission1

Paket
Paket Backoff time B

to-P to to+P to+P +2τ to+P +2τ+B to+2P +2τ+B
Zeit
vulnerable period

T = P + 2τ + H ( B + P + 2τ ), with B = E ( B )
the total transfer delay is:

(25)

T: Total transfer delay
P: packet length in time
τ: propagation time on transmission media
H: number of transmission retries
B: Backoff time
Bquer: average Backoff time

Nachrichtentechnik

The total transfer delay (see last slide):
T = P + 2τ + H ( B + P + 2τ ), with B = E ( B ) 6.3.28
The average number of retransmissions is the ratio of offered load G1 and the throughput S
reduced by one for the first transmission:
G
H= − 1 6.3.29
S
Using equation 6.3.26:
G
S = G ⋅ e −2 G
H= − 1 = e 2G − 1 6.3.30 6 . 3 . 26
S
Substitution of 6.3.30 in 6.3.28:
T = P + 2τ + (e 2G − 1)( B + P + 2τ ), 6.3.31
Normalizing:
τ τ
B
T = 1+ 2 + (e 2 G − 1)( + 1 + 2 ),
P P P
τ
with α =
The offered load G includes
1
P
the attempts to repeat
B
T = 1 + 2α + (e 2 G − 1)( + 1 + 2α ) 6.3.32
P (26)

Nachrichtentechnik


The average backoff delay still needs to be solved. The backoff time is determined with
a random integer figure k, which can take the value between 0 and K-1. The value of K
determines the amount of collisions. A bigger K produces less collisions.

The average backoff time:
K −1

∑k K −1
B= P=
k =0
P 6.3.33
K 2
Together with 6.3.32:

k − 1 2G
T = (1 + 2α )e 2G + ( ) (e − 1)
ˆ 6.3.34
2

(27)

Nachrichtentechnik


K=10
maximal
throughput
K=1

(28)

Maple Skript:
with(plots):
> setoptions(title=` normalized average delay of the ALOHA MAC over offered traffic `, style=line,
axes=BOXED);
> alpha:=0;
>
> K:=1;
delay1:=plot((1+2*alpha)*exp(2*G)+((K-1)/2)*(exp(2*G)-1),G=0..2,T=0..100,colour=red);

> K:=10;

delay2:=plot((1+2*alpha)*exp(2*G)+((K-1)/2)*(exp(2*G)-1),G=0..2,T=0..100,colour=blue);
display(delay1,delay2);

Nachrichtentechnik

pure ALOHA
slotted ALOHA
1-persistent CSMA
nonpersistent CSMA
p-persistent CSMA
CSMA/CD

(29)

Trägererkennungsprotokolle:
persistent CSMA: (carrier sense, multiple access) (Kleinrock, Tabagi, 1975)
Sendebereite Stationen hören das Medium ständig (persistent) ab, ob bereits jemand Daten
überträgt (Trägererkennung) und warten ggf. bis der Kanal “frei” ist
(1-persistent CSMA, Sendevorgang beginnt mit der Wahrscheinlichkeit 1 bei freiem Kanal)
falls dann eine Kollision stattfindet, wartet die Station eine zufällige Zeit

Nachrichtentechnik

1-persistent CSMA (carrier sense,
multiple access) (Kleinrock, Tabagi, 1975)
Sendebereite Stationen hören das Medium ständig
(persistent) ab, ob bereits jemand Daten überträgt
(Trägererkennung) und warten ggf. bis der Kanal “frei” ist
(1-persistent CSMA, Sendevorgang beginnt mit der
Wahrscheinlichkeit 1 bei freiem Kanal)
wenn eine Kollision stattfindet, wartet die Station eine
zufällige Zeit bis zur Wiederholung
Problem: zwei sendebereite Stationen belegen den
freigewordenen Kanal gleichzeitig

(30)

Nachrichtentechnik

pure ALOHA
slotted ALOHA
1-persistent CSMA
nonpersistent CSMA
p-persistent CSMA
CSMA/CD

(31)

nonpersistend CSMA:
wiederholtes Überprüfen auf freien Kanal nicht ständig (nonpersistent), sondern nach einer
zufälligen Zeitspanne

Nachrichtentechnik

nonpersistent CSMA

wie persistent CSMA. Allerdings
• wiederholtes Überprüfen auf freien Kanal
nicht ständig (nonpersistent),
sondern nach einer zufälligen Zeitspanne
Folge
• bessere Kanalauslastung α =0
Ge −αG
• längere Wartezeit S=
(1 − 2α )G + e −αG α = 0,01

zur Durchsatzberechnung
• Durchsatz sinkt mit
steigender Propagation α = 0,1

(ungenutzte Zeiten nehmen zu)
α =1

(32)

Nachrichtentechnik

pure ALOHA
slotted ALOHA
1-persistent CSMA
nonpersistent CSMA
p-persistent CSMA
CSMA/CD

(33)

Nachrichtentechnik

p-persistent CSMA

wie 1-persistent CSMA,
allerdings wird der freie Kanal nur mit der
Wahrscheinlichkeit p belegt

(34)

Nachrichtentechnik

pure ALOHA
slotted ALOHA
1-persistent CSMA
nonpersistent CSMA
p-persistent CSMA
CSMA/CD

(35)

nonpersistend CSMA:
wiederholtes Überprüfen auf freien Kanal nicht ständig (nonpersistent), sondern nach einer
zufälligen Zeitspanne
CSMA/CD: (collision detection)
sofortiges Beenden des Sendevorgangs bei erkannter Kollision (spart Zeit)

Nachrichtentechnik

CSMA/CD
(collision detection)
wie CSMA, allerdings
mit sofortigem Abbruch des Sendevorgangs bei erkannter
Kollision
spart Zeit und Bandbreite
Nach der erkannten Kollision wartet die Station eine
zufällige Zeit

(36)

Nachrichtentechnik

Comparison: ALOHA, CSMA
0.01 persistent CSMA
1.0

0.9

nonpersistent CSMA
0.8

0.7

0.6
0.1 persistent CSMA
S (Throughput)

0.5

0.4

0.3
slotted 0.5 persistent CSMA
ALOHA
0.2 1 persistent CSMA

pure
0.1
ALOHA

0 1 2 3 4 5 6 7 8 9 10
G (offered traffic)

(37)

Nachrichtentechnik

The end

(38)

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Concept of offered traffic and stability

Stability:
The system is stable if all offered traffic can be
handled without growing the input queues at each
station to indefinite, which means the normalized
network throughput S is not exceeding the effective
normalized network throughput S´ :

S ≤ S′ < 1
MλX MλX
≤ <1
question:
R′
R
under which conditions is the queue
length permanently growing? shared
transmission
1
medium
The average incoming traffic is more
MAC
than the average outgoing traffic, so
Queue
more and more packets need to be
queued
1average queue length

(39)

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TDMA (Time Division Multiple Access)

View on a shared media:

frame i frame i+1 frame i+2
time 1
guard time

station 1 station 2 station m-2 station m-1 station m
control data data data data data
time 2
View on a single terminal:

no packet
ready?
yes
wait for
assigned slot

transmit
packet

(40)

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with fixed assignment

Each station is allowed to use the channel 1/M of the available time, thus the capacity,
available to each station is R/M.

Something is neglected here, what is it?

hint:
frame i frame i+1 frame i+2
time 1
guard time

station 1 station 2 station m-2 station m-1 station m
control data data data data data
time 2

answer:

the control info is neglected!

(41)

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Unterteiltes ALOHA
Reines ALOHA
0.4
0.35

S
0.25
2
0.2
S (Throughput)

S1
0.15
0.1
0.05
0
G1 G2 0.5
0.01 0.1 1 10
G (offered load)
average value G2
What happens
- with regard to the throughput: increases to S2 but less then G1)
- with regard to the collisions: increases as well, reason for 1)
- and in case of G2 lowers down to G1 again? S2 lowers to S1 stable

(42)

Attention: the horizontal axis is divided log and the vertical linear
When G increases from G1 to G2, the Throughput S increases also from S1 to S2. But the difference in S is
smaller than in G. This is a result of the also growing number of collisions which increase the offered load in
addition.
When G decreases again, S will follow with a slight delay due to the necessary repetitions which have to be
done to compensate for the collisions. The system will come back to first state, the system is stable!

Don´t forget: G and S are average values

Nachrichtentechnik

Unterteiltes ALOHA
Reines ALOHA
0.4
0.35
0.25S1
0.2
S (Throughput)

S
0.15 2
0.1
0.05
0
G1 G2
0.5
0.01 0.1 1 10
G (offered load)
average value G2
What happens
- with regard to the throughput: the throughput decreases
- with regard to the collisions: the collisions will prevent a stable G2
- and in case of G2 lowers down to G1 again? Nothing!! Because G2 is instable

(43)

#Bildgroesse:
set autoscale xy

# Abtastwertanzahl
set sample 50
set key 9,2.5

set logscale x


set grid
# und Liniensytle

Nachrichtentechnik

[12] Nup 07 3

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[12] Nup 07 3