Guest lecture
Laitoksellamme vierailee 24.-28.8.Hän pitää meillä kaksi luentoa (salissa A414, Teollisuuskatu 23, Vallila) tiistaina 25.8 kello 14:15 - 15:30 ja keskiviikkona 26.8 kello 14:15 - 16:30. Lisäksi hän pitää kolmannen luennon Teknillisessä korkeakoulussa torstaina 27.8 kello 14:15 - 16:30 (salissa S2, Sähkö- ja tietoliikennetekniikan osasto, Otakaari 5A, Otaniemi). Prof. Dieter Baum
University of Trier, Germany
Luennot muodostavat miniluentosarjan yleisotsakkeella
jossa toinen ja kolmas luento riippuvat hieman ensimmäisen luennon antamasta johdannosta käytettyyn formalismiin. Some lectures on stochastic modelling of communication networks
Nämä luennot sopivat erityisesti hajautettujen järjestelmien suorituskykyanalyysistä samoinkuin stokastiikan ja jonoteorian sovelluksista kiinnostuneille.
Tervetuloa kuuntelemaan luentoja, joiden tiivistelmät on annettu alla.
Martti Tienari
Abstract I
COMMUNICATION NETWORK MODELLING WITH Batch Markovian arrival processes (BMAPs), as special Markov additive processes, have been introduced by Lucantoni et alii in 1989. They represent a powerful tool for the performance analysis of high speed integrated services networks - as well as similar systems with differing temporally correlated input streams. This first lecture shall provide an intro- duction, and shall sketch a unifying approach based on the convolution calculus for matrix sequences. The analysis of stochastic models with arrival or service processes of BMAP type requires the solution of non-linear matrix equations. We demonstrate here the possibility to compute the fundamental period matrix via semi-convolutions. Although resulting algorithms, in general, do not outperform known algorithms, they nevertheless allow the direct computation of step matrices (such as the "arrival matrices" and the component matrices ) and even turn out to be among the fastest in special - although very simple - cases with small matrix dimension and fast decay of norms.
BATCH MARKOVIAN ARRIVAL PROCESSES:
THE MATRIX CONVOLUTION CALCULUS
Abstract II
APPROXIMATE ANALYSIS OF We consider infinite capacity multi-queue systems with distinct batch Markovian arrival processes, which are characterized by the requirement, that only one job per arrival stream is admitted at a time into a central queue-server facility (those jobs which are not allowed into the central facility have to wait in stream-specific queues until the service of the respective predecessor of this stream has been completed). Service time is assumed to be stream-independent deterministic. Such models typically are non-cyclic in their dynamic behaviour, and are playing an important role in the performance analysis of distributed systems: The DQDB network, ISDN switches using ATM technology, etc. Recently, for the case of Poisson arrival streams, an approximate solution method for the DQDB analysis problem has been proposed, which was based on techniques originally developed for queueing networks with restricted capacity. In this lecture an improved version of that approach is presented, where non-Markovian arrival streams are taken into account.
NON-CYCLIC MULTI-QUEUE SYSTEMS FOR
DQDB AND/OR ATM SWITCH ANALYSIS
Abstract III
MARKOVIAN SPATIAL ARRIVAL PROCESSES Spatial point processes have been used increasingly over the last decade in different areas as, for instance, image processing and pattern recognition, statistical mechanics, and applied mathematics. Recently, the computer science branch of telecommunications has recognized their applicability and benefit for the performance modelling of cellular mobile communication systems. In this lecture we show the chronological evolution of (in case marked) spatial Poisson point distributions can be controlled by Markovian arrival processes, and how these constructs may be applied to determine the spread of active users over urban or rural areas in mobile communication systems. Introducing adequate service models, this leads to powerful analysis methods.
FOR THE PERFORMANCE ANALYSIS OF
COMMUNICATION NETWORKS