Dr. A.B.Piunovskiy
Dept. of Mathem. Sciences,
The University of Liverpool, Peach St.,
Liverpool L69 7ZL, UK
Phone: +44-151-7944737 Fax: +44-151-7944754
E-mail: piunov@liv.ac.uk
http://www.maths.liv.ac.uk/ piunov
Abstract. Such processes are widely used in Engineering Sciences, Biology, Insurance, Inventory Theory and so on. After describing mathematical models, we shall present a series of meaningful examples. One of the most powerful methods of obtaining an optimal control strategy is Dynamic Programming. Another modern method of attack is so called Convex Analytic Approach. In this lecture the both methods will be briefly discussed. The second half of the lecture will be devoted to more special models. First, we concentrate on the processes with local transitions, like birth-and-death processes. They are known to be successfully approximated by deterministic differential equations under so called ”fluid scaling”. New results on the accuracy of such approximation will be presented. Secondly, a new look at the well known ”C-mu-rule”
in the Queuing Theory will be discussed: we shall compare the stochastic and deterministic versions. Finally, we shall stop on applications of the theory to the optimal buffer sizing for Internet routers. The last several minutes will be devoted to more general models, open questions and new challendging real life problems.
Plenary Speaker’s Brief Biography. Dr. A.Piunovskiy was born in Moscow, Russia, in 1954. He graduated from the Moscow Institute of Electronic Technology (MIEM) with degrees in Electrical Engineering and Applied Mathematics, and supported the PhD thesis in 1981. Dr.A.Piunovskiy worked in MIEM and IFTP (Moscow State Inst. of Physics and Technology). In 1999 he received the Doctor of Science degree in Applied Mathematics. Since Feb. 2000, he is with Dept. of Mathem. Sciences, the University of Liverpool, currently holding the post of Reader. Research interests include Optimal control of dynamical systems, Controlled random processes; Constrained problems of optimal control; Approximations to controlled random processes and their accuracy; Computer simulation; Application to optimization problems in Operational Research, in Technical Systems, in Reliability Theory, Queuing Theory, Teletraffic, Finances, Economics, Ecology, and Epidemiology. Dr. A.Piunovskiy received multiple grants from the Russian Fund for Basic Research, London Mathematical Society, the Royal Society, EPSRC and so on. He published more than 80 works, including a textbook and a scientific monograph. Another monograph is in preparation.
