[12] Nup 07 3

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[12] Nup 07 3

  1. 1. 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
  2. 2. 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. © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  3. 3. 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  4. 4. 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 max propagation time τ 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. © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  5. 5. 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 : max propagation time τ 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 : • average packet length (bits per packet), X similar for all packets S′ = M λE 6.3.6 • each station on schedule transmits all 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. © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  6. 6. 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´ : max propagation time τ 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 • average packet length (bits per packet), X MAC similar for all packets Queue • each station on schedule transmits all packets available 1average queue length • distance of all stations similar question: under which conditions is the queue length permanently growing? (6) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  7. 7. 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 max propagation time τ 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]): • average arrival rate S Poisson distributed • average packet length (bits per packet), Smax X similar for all packets • each station on schedule transmits all packets available • distance of all stations similar 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. © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  8. 8. 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 max propagation time τ X X R R Assumptions: with tw neglected : 6.3.10 λ (packets per second), • average arrival rate + td X t R T= X = ≥1 ˆ Poisson distributed X X • average packet length (bits per packet), X R R similar for all packets Remarks: • each station on schedule transmits all - The transfer delay is the transmission time packets available without time for queuing or buffering • distance of all stations similar - Normalization is done to achieve a X tX = + t d + t w 6.3.2 dimensionless value R (8) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  9. 9. 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  10. 10. 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  11. 11. average transfer delay of the TDMA system 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  12. 12. average transfer delay of the TDMA system with fixed assignment (3) average normalized transfer delay ^T M=100 100 M=10 10 M=2 1 Througput S (12) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  13. 13. 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  14. 14. 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  15. 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 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  16. 16. 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: © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  17. 17. 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  18. 18. 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  19. 19. 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  20. 20. 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  21. 21. 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  22. 22. Unterteiltes ALOHA ALOHA, stability (1) Reines ALOHA 0.4 0.35 0.3 slotted ALOHA, S = G e-G 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: # 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  23. 23. Unterteiltes ALOHA ALOHA, stability (2) Reines ALOHA 0.4 0.35 0.3 slotted ALOHA, S = G e-G 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) 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) #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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  24. 24. Unterteiltes ALOHA ALOHA, stability Reines ALOHA 0.4 stable instable 0.35 0.3 slotted ALOHA, S = G e-G 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: # 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  25. 25. 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  26. 26. ALOHA, Delay-Performance 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  27. 27. ALOHA, Delay-Performance 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  28. 28. ALOHA, Delay-Performance 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); © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  29. 29. 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 (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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  30. 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 Wiederholung Problem: zwei sendebereite Stationen belegen den freigewordenen Kanal gleichzeitig (30) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  31. 31. 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 (31) 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 nonpersistend CSMA: wiederholtes Überprüfen auf freien Kanal nicht ständig (nonpersistent), sondern nach einer zufälligen Zeitspanne © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  32. 32. 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  33. 33. 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 (33) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  34. 34. p-persistent CSMA wie 1-persistent CSMA, allerdings wird der freie Kanal nur mit der Wahrscheinlichkeit p belegt (34) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  35. 35. 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 (35) 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 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  36. 36. 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  37. 37. 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  38. 38. The end (38) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  39. 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 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  40. 40. 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  41. 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: 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) © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  42. 42. Unterteiltes ALOHA ALOHA, stability (1) Reines ALOHA 0.4 0.35 0.3 slotted ALOHA, S = G e-G 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) Let us assume: the offered average load G1 increases temporarily to the 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik
  43. 43. Unterteiltes ALOHA ALOHA, stability (2) Reines ALOHA 0.4 0.35 0.3 slotted ALOHA, S = G e-G 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) Let us assume: the offered average load G1 increases temporarily to the 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: # 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 © UNI Hannover, Institut für Allgemeine Nachrichtentechnik

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