Thesis (MSc)--University of Stellenbosch, 2005. / ENGLISH ABSTRACT: The majority of tra c on the Internet uses the Transmission Control Protocol (TCP) as a
transport layer protocol for the end-to-end control of information transfer. Measurement,
simulation and analytical models are the techniques and tools that can be used to understand
and investigate the Internet and its performance. Measurements can only be used to explore
existing network scenario or otherwise become costly and in
exible with the growth and
complexity of the Internet. Simulation models do not scale with the growth of network
capacities and the number of users. Computationally e cient analytical models are therefore
important tools for investigating, designing, dimensioning and planning IP (Internet Protocol)
networks.
Existing analytical models of TCP performance are either too simple to capture the internal
dynamics of TCP or are too complex to be used to analyze realistic network topologies with
several bottleneck links. The literature shows that the xed point algorithm (FPA) is a very
useful way of solving analytical models of Internet performance. This thesis presents fast and
accurate analytical models of TCP performance with the FPA used to solve them.
Apart from what is observed in experimental literature, no comprehensive proof of the convergence
and uniqueness of the FPA is given. In this thesis we show how the FPA of analytical
models of reliable Internet protocols such as TCP converges to a unique xed point. The
thesis speci es the conditions necessary in order to use the FPA for solving analytical models
of reliable Internet protocols. We also develop a general implementation algorithm of the
FPA of analytical models of TCP performance for realistic and arbitrary network topologies
involving heterogenous TCP connections crossing many bottleneck links.
The models presented in this thesis give Internet performance metrics, assuming that only
basic network parameters such as the network topology, the number of TCP connections, link
capacity, distance between network nodes and router bu er sizes are known. To obtain the
performance metrics, TCP and network sub{models are used. A closed network of :=G=1
queues is used to develop each TCP sub-model where each queue represents a state of a TCP
connection. An M=M=1=K queue is used for each network sub{model which represents the
output interface of an IP router with a bu er capacity of K ��������1 packets. The two sub-models
are iteratively solved. We also give closed form expressions for important TCP performance values and distributions.
We show how the geometric, bounded geometric and truncated geometric distributions can
be used to model reliable protocols such as TCP. We give models of the congestion window
cwnd size distribution by conditioning on the slow start threshold ssthresh distribution and
vice-versa. We also present models of the probabilities of TCP timeout and triple duplicate
ACK receptions.
Numerical results based on comparisons against ns2 simulations show that our models are
more accurate, simpler and computationally more e cient than another well known TCP
model. Our models can therefore be used to rapidly analyze network topologies with several
bottlenecks and obtain detailed performance metrics. / AFRIKAANSE OPSOMMING: Die meerderheid van die verkeer op die Internet gebruik die Transmission Control Protocol
(TCP) as `n vervoer laag protokol vir die einde-tot-einde kontrole van inligting oordrag.
Meting, simulasie en analitiese modelle is die tegnieke en gereedskap wat gebruik kan word om
die Internet te ondersoek en verstaan. Meting kan slegs gebruik word om bestaande netwerke
scenarios te verken. Meting is duur en onbuigsaam met die groei en samegesteldheid van
die Internet. Simulasie modelle skaal nie met die groei van netwerk kapasiteit en gebruikers
nie. Analitiese modelle wat berekening e ektief is is dus nodige gereedskap vir die ondersoek,
ontwerp, afmeting en beplanning van IP (Internet Protocol) netwerke.
Bestaande analitiese TCP modelle is of te eenvoudig om die interne dinamiek van die TCP
saam te vat of hulle is te ingewikkeld om realistiese netwerk topologie met heelwat bottelnek
skakels te analiseer. Literatuur toon dat die xed point algorithm (FPA) baie handig is vir die
oplos van analitiese modelle van Internet verrigting. In hierdie tesis word vinnige en akkurate
analitiese modelle van TCP verrigting opgelos deur FPA weergegee.
Buiten wat deur eksperimentele literatuur aangedui word is daar geen omvattende bewyse
van die konvergensie en uniekheid van die FPA nie. In hierdie tesis word aangedui hoe die
FPA van analitiese modelle van betroubare Internet protokolle soos die TCP konvergeer na
`n unieke vaste punt. Hierdie tesis spesi seer die voorwaardes benodig om die FPA te gebruik
vir die oplos van analitiese modelle van realistiese Internet protokolle. `n Algemene uitvoer
algoritme van die FPA van analitiese modelle van TCP vir realistiese en arbitr^ere netwerk
topogra e insluitende heterogene TCP konneksies oor baie bottelnek skakels is ontwikkel.
Die model in hierdie tesis gee Internet verrigting metodes met die aanname dat slegs basiese
netwerk parameters soos netwerk topologie, die aantal TCP konneksies, die konneksie kapasiteit,
afstand tussen netwerk nodusse en die roete bu er grotes bekend is. Om die verrigting
metodes te verkry, word TCP en netwerk sub-modelle gebruik. `n Geslote netwerk van :=G=1
rye is gebruik om elke TCP sub-model, waar elke ry 'n toestand van `n TCP konneksie voorstel,
te ontwikkel. `n M=M=1=K ry is gebruik vir elke netwerk sub-model wat die uitset
koppelvlak van `n IP roetemaker met `n bu er kapasiteit van K ������� 1 pakkies voorstel. Die
twee submodelle word iteratief opgelos.
Geslote vorm uitdrukkings vir belangrike TCP verrigting waardes en verspreidings word gegee.
Daar word getoon hoe geometriese, begrensde geometriese en geknotte geometriese verspreidings
gebruik kan word om betroubare protokolle soos die TCP te modelleer. Modelle van
die kongestie venster cwnd grootte verspreiding word gegee deur die kondisionering van die stadige aanvang drempel ssthresh verspreiding en andersom. Modelle van die voorspelling van
TCP tyduit en trippel duplikaat ACK resepsie word weergegee.
Numeriese resultate gebaseer op vergelykings met ns2 simulasies wys dat ons modelle meer
akkuraat, eenvoudiger en berekeningsgewys meer e ektief is as ander wel bekende TCP modelle.
Ons modelle kan dus gebruik word vir vinnig analise van netwerk topologie met verskeie
bottelnekke en om gedetailleerde verrigting metodes te bekom.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/16608 |
| Date | 10 1900 |
| Creators | Kassa, Debassey Fesehaye |
| Contributors | Krzesinski, A.E., University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Institute for Applied Computer Science. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | xx, 179 leaves : ill. |
| Rights | University of Stellenbosch |
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