[12] Nup 07 3

© UNI Hannover, Institut für Allgemeine Nachrichtentechnik

Institut für Kommunikationstechnikwww.ikt.uni-hannover.de

Protokolle der OSI-Schicht 2Performance Modelling MAC

Kapitel 7.3

Netze und ProtokolleDr.-Ing. Jan Steuer

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


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Goals

An engineer working in the field of protocol development needsto know

General principles of transmission systems,General principles of switching systems,Characteristics of networking andHow to evaluate the performance of protocols (subject of this lecture)

Here I concentrate on the performance of the MAC layer (higherlayers will follow)

First I am going to develop general principles using a generic network forpurposes of comparisonSecond 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)

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.


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Generic Multi-access Network - Performance Investigation -

1

2 M-1

Mtransmission rate R

max propagation time τ

λ

λ λ

λ

Assumptions:• average arrival rate λ (packets

per second), Poisson distributed• average packet length (bits

per second), similar for all packets• each station on schedule

transmits all packets available• distance of all stations similar

X

Questions:• how long is the time to transmit a packet

of information between two stations? • and what is the transfer delay (no waiting queue)?• what is the throughput of the network?• what does stability mean in the context of MAC?• what is the offered traffic?

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 other2. 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 stationsThe 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


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Transmission Time as measure of performancein the Generic Multi-access Network

1

2M-1



λ

λ λ

λ

Assumptions:

• average arrival rate λ (packets per second),

Poisson distributed• average packet length (bits per packet),

similar for all packets• each station on schedule transmits all

packets available• distance of all stations similar

Xremarks: • E is a random variable, if X (the packet

length) is a random variable• often td can be neglected on access networks,

depending on the length of the access link• The transmission time is in view of an undisturbed

individual station

transmission time of packet with length X:

, 6.3.1

: ( ):

X d w

d

w

Xt t tR

t delay on transmission link propagationt waiting time due to buffering or queueing

= + +

effective transmission time of packet with length Xusing the effective transmission rate R´:

3.3.6wd ttRXE ++′

=

2.3.6wdX ttRXt ++=

average transmission time of packet with length :X

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.


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Throughput as measure of performance in the Generic Multi-access Network

1

2M-1



λ

λ λ

λ

Assumptions:





normalized network throughput of the access network:

with the average effective transmission time (see 6.1.3)

RXE′

=

remark: • the effective throughput is in view of the entire access network, not of an individual station

X

1 6.3.4M

iiXM XS

R Rλλ == = ∑

effective throughput of the access network :

1 6.3.5M

iiXM XS

R Rλλ =′ = =

′ ′∑

the effective throughput of the access network gets :

6.3.6S M Eλ′ =

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.


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Concept of offered traffic and stability

1

2M-1

Mtransmission rate R [bits/sec]


λ

λ λ

λ

Assumptions:

• average arrival rate λ(packets per second),




X

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 normalizednetwork throughput S is not exceeding the effectivenormalized network throughput S´ :

1average queue length

MAC

sharedtransmissionmedium

Queue

1

question: under which conditions is the queue length permanently growing?

8.3.61

7.3.61

<′

≤

<′≤

RXM

RXMSS

λλ


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Concept of offered traffic

1

2M-1

Mtransmission rate R [bits/sec]


λ

λ λ

λ

Assumptions:





The offered traffic G is the ratio of the average number of attempted packet transmissions per second to the average number of packet transmissionsper second possible. In case there is no delay due to scheduling or queuing:

X

With delay due to scheduling and/or queuing the throughput is converging against a maximum value (for details see [Klein75]):

SSmax

G

9.3.61 SR

XM

XRM

XRG

M

i i ==== ∑ = λλλ

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.


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Concept of transfer delay

1

2M-1



λ

λ λ

λ

Assumptions:





X

normalized average transfer delay:is the ratio of the average transfer delay and theaverage packet transmission time (from 6.3.2) :

ˆ 1

: 6.3.10

ˆ 1

d wX

w

dX

X t tt RTX X

R Rwith t neglected

X tt RTX X

R R

+ += = ≥

+= = ≥

Remarks:- The transfer delay is the transmission timewithout time for queuing or buffering

- Normalization is done to achieve a dimensionless value2.3.6wdX tt

RXt ++=


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Concept of waiting time

MAC


Queue

λμ

λ: arrival rate [packets/sec]μ: service rate or here

transmission rate of packetsfrom this queue on the sharedmedium [packets/sec]

S ′==μλρ

waiting time in the single queue [Klein75]:

12.3.621

::

,:var:

11.3.621

2

2

2

EE

SSW

thenEYandS

iftimeservicesquaremeanY

timeservicemeannormalizedYstationeachbyseenEtimeontransmissi

packeteffectiveheretimeserviceaverageYtimeservicedenotingiablerandomYwith

YYW

′−′

=

=′=

′

′−=

ρ

ρρ


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

Something is neglected here, what is it?

average transfer delay of the TDMA system with fixed assignment

Let us assume that we use a constant packet length, than the mean square of E is

the square of the mean and get for the waiting time

Now we remember:

which modifies again the waiting time:

13.3.6)( 22 EE =

15.3.6RMX

MRX

RXE ==′

=

14.3.6212

)(121

22 ES

SE

ES

SE

ES

SW′−

′=

′−′

=′−

′=

16.3.62)1(21 R

XMS

SES

SW′−′

=′−

′=


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average transfer delay of the TDMA system with fixed assignment (2)

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

S´=S , thus

additional average delay we get from the statistical arrival of the packets and theneed to wait for the assigned slot. It is assumed that the arrival time is uniformlydistributed, which means we have to wait on average half of the frame time beforewe get served:

The average transfer delay is now the sum of the transmission time, the time to waitfor a slot and the queueing time:

and normalized:

17.3.62)1( R

XMS

SW−

=

18.3.62R

XMWslotwait =

19.3.62)1(2 R

XMS

SRXM

RXT

−++= 20.3.6

2)1(21ˆ M

SSMT−

++=


(12)

average transfer delay of the TDMA system with fixed assignment (3)

Througput S

aver

age

norm

aliz

edtr

ansf

erde

lay

^T

M=2M=10

M=100

10

100

1


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Performance of Random Access Methods

competing Protocolspure ALOHA slotted ALOHA1-persistent CSMAnonpersistent CSMAp-persistent CSMACSMA/CD

pure ALOHA: an der Universität von Hawaii entwickeltes Verfahren zur Kanalzuteilung (Abramson et all., 1970)

Sender schickt sein Paket sofort bei Sendebereitschaft auf das MediumEmpfänger sendet eine QuittungSender hört den Kanal ab, ob das Paket gestört wurdeWiederholte Sendung des Pakets nach zufälliger Zeitspanne


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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

packet with collision

Packet

time

user

to-P to to+Pdangerous time

PP

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 auftrittkein vorheriges Abhören des Kanals!Laufzeit zum und Bearbeitungszeit im Empfänger werden vernachlässigt


(15)

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 möglichBedingung 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 ~ SAllgemein: p0: Wahrscheinlichkeit, dass keine Kollision stattfindet

22.3.60pGS ⋅=

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

S>1: es finden nur noch Kollisionen statt


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• daraus folgt mit G’=2G, da “gefährliche Zeit” = 2t

• und damit

Effizienz ALOHA (2)

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

24.3.6!' 'Gk

k ek

Gp −⋅=

25.3.6!0)2( 2

0

0GeGp −⋅=

26.3.620

Gep −=

vgl. Verkehrstheorie :Poissonverteilung:


(17)

Wahrscheinlichkeit, dass keine andere Sendeanforderung während unseres Datenpaketes vorliegt (keine Kollision),ist

damit folgt für S:

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

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

dSdG

= 0

Effizienz ALOHA (3)

25.3.620

Gep −=

26.3.62GeGS −⋅=


(18)

Protokolle für die dynamische Kanalzuordnungohne Verständigungsmöglichkeit der Sender

Konkurrierende Protokollepure ALOHA slotted ALOHA1- persistent CSMAnonpersistent CSMAp-persistent CSMACSMA/CD

pure ALOHA: an der Universität von Hawaii entwickeltes Verfahren zur Kanalzuteilung (Abramson et all., 1970)

Sender schickt sein Paket sofort bei Sendebereitschaft auf das MediumEmpfänger sendet eine QuittungSender hört den Kanal ab, ob das Paket gestört wurdeWiederholte 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


(19)

Paket

Zeit

Ben

utze

r

to to+t to+2tgefährliche Zeit

mögl. Kollision

slotted ALOHA

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


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Wahrscheinlichkeit, dass keine andere Sendeanforderung während unseres Datenpaketes vorliegt (keine Kollision),ist

Damit wird die Zahl der während eines Rahmens vorliegenden Sendeanforderungen:

mit dem Maximum: G=1S = 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

p e G0 =

− .

dSdG

= 0

slotted ALOHA

27.3.6GeGS −⋅=


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0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.01 0.1 1 10

S (T

hrou

ghpu

t)

G (offered load)

ALOHA, Throughput-Performance

slotted ALOHA, S = G e-G

pure ALOHA, S = G e-2G

0.5

0,368 0,184Unterteiltes ALOHA

Reines ALOHA

#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) festlegenset ytics 0,0.05,0.4

# Abtastwertanzahlset sample 50# Positionierung der Legendeset key 9,2.5

# Logarithmische Skalierungset logscale x

# Achsenbeschriftung

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


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Unterteiltes ALOHAReines ALOHA ALOHA, stability (1)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.01 0.1 1 10

S (T

hrou

ghpu

t)

G (offered load)


0.5G1

S1

G2

S2

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?







(23)

ALOHA, stability (2)


What happens- with regard to the throughput- with regard to the collisions- and in case of G2 lowers down to G1 again?

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.01 0.1 1 10

S (T

hrou

ghpu

t)

G (offered load)


0.5 G1

S2

G2

S1

Unterteiltes ALOHAReines ALOHA







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0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.01 0.1 1 10

S (T

hrou

ghpu

t)

G (offered load)

ALOHA, stability


0.5

instablestable








(25)

ALOHA, Delay-Performance

Paket

Zeit

user

to-P to to+P to+P +2τ to+P +2τ+B to+2P +2τ+B

vulnerable period

stat

ion

lear

nsm

issi

ngpa

cket

(n

o ac

knol

edge

men

t)

PaketBackoff time B

firsttransmission

firstretransmission1

1retransmission will be repeated untilthe packet is successfully acknowledged,number of repetitions is H

the total transfer delay is: )(),2(2 BEBwithPBHPT =++++= ττ

T: Total transfer delayP: packet length in timeτ: propagation time on transmission mediaH: number of transmission retriesB: Backoff timeBquer: average Backoff time


(26)


28.3.6)(),2(2 BEBwithPBHPT =++++= ττThe total transfer delay (see last slide):

The average number of retransmissions is the ratio of offered load G1 and the throughput S reduced by one for the first transmission:

29.3.61−=SGH

Using equation 6.3.26:

30.3.611 2 −=−= GeSGH

Substitution of 6.3.30 in 6.3.28:31.3.6),2)(1(2 2 ττ ++−++= PBePT G

32.3.6)21)(1(21

),21)(1(21

2

2

αα

τα

ττ

++−++=

=

++−++=

PBeT

Pwith

PPBe

PT

G

G

1 The offered load G includesthe attempts to repeat

26.3.62 GeGS −⋅=

Normalizing:


(27)


The average backoff delay still needs to be solved. The backoff time is determined witha 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:

33.3.62

1

1

0 PKPK

kB

K

k −==

∑−

=

34.3.6)1()2

1()21(ˆ 22 −−

++= GG ekeT α

Together with 6.3.32:


(28)


K=10

K=1maximal

throughput

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);


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Protokolle für die dynamische Kanalzuordnung ohne Verständigungsmöglichkeit der Sender

Konkurrierende Protokollepure ALOHA slotted ALOHA1-persistent CSMAnonpersistent CSMAp-persistent CSMACSMA/CD

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


(30)

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 WiederholungProblem: zwei sendebereite Stationen belegen den freigewordenen Kanal gleichzeitig


(31)





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


(32)

nonpersistent CSMA

wie persistent CSMA. Allerdings• wiederholtes Überprüfen auf freien Kanal

nicht ständig (nonpersistent), sondern nach einer zufälligen Zeitspanne

Folge• bessere Kanalauslastung• längere Wartezeit

zur Durchsatzberechnung• Durchsatz sinkt mit

steigender Propagation(ungenutzte Zeiten nehmen zu)

G

G

eGGeS α

α

α −

−

+−=

)21(

0=α

01,0=α

1,0=α

1=α


(33)




(34)

p-persistent CSMA

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


(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)


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CSMA/CD(collision detection)

wie CSMA, allerdingsmit sofortigem Abbruch des Sendevorgangs bei erkannter Kollision

spart Zeit und BandbreiteNach der erkannten Kollision wartet die Station eine zufällige Zeit


(37)

Comparison: ALOHA, CSMA

0 2 6 1084G (offered traffic)

0.1

0.2

0.3

0.4

S (T

hrou

ghpu

t)

0.5

0.6

0.7

0.8

0.9

1.0

3 7 951

0.01 persistent CSMA

0.1 persistent CSMA

0.5 persistent CSMA1 persistent CSMA

slottedALOHA

pureALOHA

nonpersistent CSMA


(38)

The end


(39)

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 normalizednetwork throughput S is not exceeding the effectivenormalized network throughput S´ :

1

1

<′

≤

<′≤

RXM

RXMSS

λλ

MAC


Queue

1average queue length

1

question: under which conditions is the queue length permanently growing?

The average incoming traffic is more than the average outgoing traffic, so more and more packets need to be queued


(40)

TDMA (Time Division Multiple Access)

packetready?

wait forassigned slot

transmitpacket

no

yes

time 1

frame i frame i+1 frame i+2

time 2control data datadatadata data

station 1 station 2 station m-2 station m-1 station m

guard time

View on a shared media:

View on a single terminal:


(41)

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/M.

Something is neglected here, what is it?

hint:

time 1

frame i frame i+1 frame i+2

time 2control data datadatadata data

station 1 station 2 station m-2 station m-1 station m

guard time

answer:

the control info is neglected!


(42)

Unterteiltes ALOHAReines ALOHA ALOHA, stability (1)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.01 0.1 1 10

S (T

hrou

ghpu

t)

G (offered load)


0.5G1

S1

G2

S2


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

Attention: the horizontal axis is divided log and the vertical linearWhen 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


(43)

ALOHA, stability (2)


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

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.01 0.1 1 10

S (T

hrou

ghpu

t)

G (offered load)


0.5 G1

S2

G2

S1







Technology

[12] Nup 07 3