Abstract: The advantages of packet-switching networking over circuit switching made the packet-switching technology very successful (e.g. Internet). However, the cost of packet switching is that in each network node, packets are queued, resulting in delay and packet losses during buffer overflow periods. The queues in network nodes used to be modeled by a classic FIFO queue with Poisson arrivals. Since the beginning of 90's we have known that traffic in packet-switching networks is strongly autocorrelated and therefore we have to use much more advanced models for it. Markovian models like MMPP, MAP and BMAP were adopted for this purpose with good results. On the other hand, when modeling a queue in a network node, it is important that the finite size of the buffer is assumed, as finite buffer is responsible for packet losses.
The subject of this lecture is the performance analysis of a finite-buffer queue fed by Markovian arrival process. The lecture is particularly focused on a relatively new method of analysis of such queues - so called "potential method". At first, the method uses the Laplace transform technique in order to reduce a large system of integral equations to a system of linear equations. Then, with the help of a recurrent sequence called "potential", the large system is solved and the results are obtained in an explicit form. The method has some important advantages. It enables finding almost all queueing characteristics of interest. It gives results in a closed, easy to use form and this is a unique property among methods of analysis of finite-buffer queues. Moreover, both steady-state and transient performance characteristics can be obtained by means of the method.

Brief Biography of the Speaker:
Andrzej Chydzinski received his MSc (in applied mathematics), PhD (in computer science) and Habilitation (in computer science) degrees from the Silesian University of Technology, Gliwice, Poland, in 1997, 2002 and 2008, respectively. He is currently an Assistant Professor in the Institute of Computer Sciences of this university. His academic and professional interests include modeling and simulation of computer networks, active queue management in Internet routers, queueing theory and discrete-event network simulators. Dr. Chydzinski authored and co-authored more than fifty journal and conference papers and two books. His work is well recognized - Thomson Scientific reports that his publications were cited about 100 times (excluding self-citations) in ISI indexed journals. He was also awarded for his work by a major Polish magazine and was given (with R. Winiarczyk) the best paper award in modeling and simulation during the IEEE Symposium on Computers and Communications in 2006. He has been involved in several scientific projects, in some of them as a project leader.