Аналіз та оптимізація систем з повторними викликами і чергою зі змінною інтенсивністю вхідного потоку

Abstract

The paper is focused on in-depth study of the promising area of the stochastic systems theory related with scrutiny of queuing systems with repeated calls. We research Markov`s models of retrial systems with queue and variable rate of input flow controlled by threshold strategy with no restriction on the capacity of the orbit. We defined stationary regime existence conditions and investigated probability characteristics of process for two-dimension Markov process with continuous time which we took as a main model of the specified system. In stationary regime for probability characteristics of the service process were found explicit formulas. Research methods which we used are based on the initial process approximation by the process with bounded state space. Results of the research allow us to evaluate convergence rates of stationary distribution of finite systems with repeated calls to stationary distribution of infinite systems. Method of probability flow equating is used for obtain explicit expressions for stationary system probabilities through the closed path which are defined in a special way. For threshold control strategies the optimization problem of the total income of the system was stated and solved.