Plenary Lecture

Evaluation of the Mean Cycle Time in Stochastic Discrete Event Dynamic Systems

Associate Professor Nikolai Krivulin
Faculty of Mathematics and Mechanics
St. Petersburg State University
RUSSIA
E-mail: nkk@math.spbu.ru

Abstract: Actual systems in engineering, manufacturing, management, and other areas is frequently modeled as stochastic discrete event dynamic systems with their dynamics described by recursive equations for a set of state variables representing the occurrence time of system events. For many systems, the state evolution can be written in vector form with a state transition matrix through a vector equation that is linear in the sense of an idempotent semiring. The problem of interest is to evaluate, under various assumptions on the matrix entries, the mean system operation cycle time defined as the mean growth rate of state vector in the system.
We start with motivating examples drawn from manufacturing and telecommunications. We give an overview of early results of calculating the mean cycle time for systems with second-order matrices where the entries have exponential, continuous uniform, Bernoulli, geometric, and discrete uniform distributions. Furthermore, recent results are outlined which provide solutions when the entries in the system matrix include both exponentially distributed random variables and nonnegative constants. Finally, we present new results for matrices that have one random entry whereas the other entries may be arbitrary constants. We show that a particular form of the matrices makes it possible to obtain solution in a general form that does not rely on exponential distribution assumptions. As examples, the mean cycle time is calculated in the case when the random entries have exponential and continuous uniform distributions..

Brief Biography of the Speaker:
Nikolai Krivulin received a university degree in applied mathematics and operations research in 1983 from St. Petersburg State University (SPbSU). He got his Ph.D. degree in 1990 and D.Sc. degree in 2010 both in applied mathematics from SPbSU. In 1983 he joined the Computer Center at SPbSU as a system software engineer, and in 1985 started his Ph.D. study. In 1987 he joined the Faculty of Mathematics and Mechanics at SPbSU as an Assistant Professor, and became an Associate Professor there in 1990. From 1999 to 2002 he was the head of the Department of Information Management at the Graduate School of Management of SPbSU.
Nikolai Krivulin is currently an Associate Professor of the Department of Statistical Modelling at St. Petersburg State University. His research interests include theory and applications of idempotent algebra, modelling and performance evaluation of queueing systems, methods of optimization, computational statistics and computer simulation. He is an author and coauthor of more than 70 publications including papers in reviewed journals and conference proceedings, books chapters, textbooks, and a monograph. He was a grantee of national and international foundations, including the Russian Foundation for Basic Research, the Russian Foundation for Humanities Research, the NATO Science Foundation, the USIA and Eurasia Foundation (USA), and the Royal Society (UK). He served as a member of program and organizing committees of international conferences on mathematics, computer sciences, and information technology. He is a member of the St. Petersburg Mathematical Society, AMS, and SIAM.