We are interested to problems related to the conception of architectures (in general terms). It is required to dimension some system components. In addition to qualitative aspects, quantitative analysis is compulsory. Queueing theory is often the most appropriate tool to this study. More recently, fluid models, meaning models including variables with a continuous state
space, have allowed to alleviate the analysis of some problems connected to high speed
networks (by considering the bursts scale instead of the packets scale).
My past work
We have modeled and analyzed a fluid queue driven by a Markov chain, trouvant de nombreuses application en technologie ATM ou Internet.
We have also worked on threshold queues with hysteresis.
These queues are often known to use the "optimal" policy, in relation with a cost function
to be specified according to the problem. These queues are promising, as thresholds smooth
the queue behaviour and hysteresis prevents from oscillations around thresholds .
Many applications exist in productics; a more recnt is the
soft-handover" of wireless networks.
We have analytically studied this kind of queue, in the markovian case,
when the number of used servers depends on the number of customers in the queue.
We have also modeled these queues by means of stochastic Petri nets and we have
shown that their analyse is then very simple, in the mono-class
as well as in the multi-class case. The markovian, non-Markovian and fluid case
have been studied.
Research in progress or for the future
Extension of previous work on threshold queues to a network.
B. Sericola and B. Tuffin, A Fluid Queue Driven by a Markovian Queue. Queuing Systems: Theory and Applications, Vol.31, pages 253-264, 1999.
B. Tuffin and L.M. Le Ny. Modeling and analysis of threshold
queues with hysteresis using stochastic Petri nets: the monoclass case.
In Proceedings of Petri Nets and Performance Models, PNPM'01,
pages 175-184, IEEE CS Press, Aachen, Germany, 2001.
L.M. Le Ny and B. Tuffin. A simple analysis of heterogeneous multi-server
threshold queues with hysteresis. In Proceedings of the Applied Telecommunication Symposium, San
Diego, USA, April 2002.
L.M. Le Ny and B. Tuffin. Modeling and analysis of multi-class
threshold-based queues with hysteresis using Stochastic Petri
Nets. In Proceedings the International Conference on Applications and
Theory of Petri Nets. Lecture Notes in Computer Science, Springer
H. Takagi. Queueing Analysis. A Foundation of Performance Evaluation.
(3 volumes). North Holland. 1993.
K. S. Trivedi. Probability and Statistics with Reliability, Queuing,
and Computer Science Applications . Englewood Cliffs,
Prentice-Hall, Inc., 1982.
G. Bolch and S. Greiner and H. de Meer and K. Trivedi. Queueing networks and Markov chains: modelling and performance evaluation
with computer science applications John Wiley & Sons Inc., 1998.