Analysis of a queuing system with correlated arrival flows and variable priorities

Приоритетные системы массового обслуживания могут использоваться для решения задач проектирования и оптимизации различных реальных систем, в частности телекоммуникационных систем, систем оказания скорой медицинской помощи. Различные схемы предоставления приоритетов в последние годы дополнились динамическими приоритетами. Такие схемы предполагают изменение приоритетов запросов во время ожидания начала обслуживания. В данной работе рассматривается приоритетная система массового обслуживания, на вход которой поступает марковский входной поток разнотипных запросов. Приоритеты запросов изменяются динамически. Предусмотрена зависимость поведения запросов, находящихся в буфере, а также интенсивности обслуживания от типа запроса

Self-Service System with Rating Dependent Arrivals

A multi-server infinite buffer queueing system with additional servers (assistants) providing help to the main servers when they encounter problems is considered as the model of real-world systems with customers’ self-service. Such systems are widely used in many areas of human activity. An arrival flow is assumed to be the novel essential generalization of the known Markov Arrival Process (MAP) to the case of the dynamic dependence of the parameters of the MAP on the rating of the system. The rating is the process defined at any moment by the quality of service of previously arrived customers. The possibilities of a customers immediate departure from the system at the entrance to the system and the buffer due to impatience are taken into account. The system is analyzed via the use of the results for multi-dimensional Markov chains with level-dependent behavior. The transparent stability condition is derived, as well as the expressions for the key performance indicators of the system in terms of the stationary probabilities of the Markov chain. Numerical results are provided

Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia