Seminarium i matematisk statistik
torsdagen den 23 januari 16.15 i MH:227

Pascal Frantz
Dept of Computer Science
Technical University of Munich

Titel:
Efficient Techniques for Simulating Telecommunications Systems

Abstract:
Today, users will expect and should require that the quality of the
service of telecommunication systems must be high. Hence service
providers must make sure that networks are adjusted to the changes in
the number of subscribers, in the offered services, and in the service
usage patterns.

Therefore it is very important to be able to analyse a network with
respect to performance measures, which are important inputs to obtain
optimal dimensions of telecommuniction networks. In practice, the
analysis and the planing of telecommunication systems is often done by
simulations.

During my work, simulations of queuing systems for estimating rare
events -- here especially cell losses -- were analysed. Therefore the
simulation speed-up technique \emph{Importance Sampling} has been
applied to M/M/1, M/Hyp-2/1 and simple ON/OFF systems (MMPP/M/1).

For the M/M/1 queuing system the behaviour of the estimated probability
of a cell loss $\hat{z}$ during a time period $T$ because of a buffer
overflow was analysed in detail.

Four algorithms were analysed to estimate the probability of a cell loss
$z$ (i.~e. the probability of reaching buffer level $x=B+1$ before time
$T$ whereby $B$ is the provided buffer size) by simulation when this
event is rare.

Two of them can used for estimating $z$ by simulation, whereby each
algorithm works better for a time condition. The first algorithm is
based on exponential change of measure, the second uses a filtered Monte
Carlo argument.

These algorithms work well for M/M/1 and are a very promising approach
to estimate buffer overflow probabilities for other queuing systems.