Queueing systems analysis and optimization: учебная программа учреждения высшего образования по учебной дисциплине для специальности: 7-06-0533-05 Applied Mathematics and Computer Science Profiling: Computer Data Analysis. № УД-1379/м.

Abstract

TEACHING MATERIAL CONTENTS Section 1. Methods to study classical queuing systems Topic 1.1. Mathematical methods to study classical queuing systems Introduction. Input flow, service time. Markov random processes. Probability generating function, Laplace and Laplace-Stieltjes transforms. Single-server Markovian queuing systems. Semi-Markovian queuing systems. Multi-server queues. Priority queues. Multiphase queues. Section 2. Methods to study queuing systems with correlated arrivals Topic 2.1. Methods to study queuing systems with correlated arrivals Batch Markovian arrival process (BMAP). Phase-type distribution. Multidimensional birth-and-death processes. 𝐺/𝑀/1-type Markov chains. 𝑀/𝐺/1-type Markov chains. 𝑀/𝐺/1-type Markov chains with finite state space. Asymptotically quasi-Toeplitz discrete-time Markov chains. Asymptotically quasi-Toeplitz continuous-time Markov chains. Section 3. Queuing systems with waiting space and correlated arrivals Topic 3.1. Queuing systems with waiting space and correlated arrivals 𝐵𝑀𝐴𝑃/𝐺/1 queue. 𝐵𝑀𝐴𝑃/𝑃𝐻/𝑁 queue. 𝐵𝑀𝐴𝑃/𝑃𝐻/𝑁/𝑁 queue. Section 4. Retrial queuing systems with correlated input flows Topic 4.1. Retrial queuing systems with correlated input flows 𝐵𝑀𝐴𝑃/𝑃𝐻/𝑁 retrial system. 𝐵𝑀𝐴𝑃/𝑃𝐻/𝑁 retrial system in the case of a phase distribution of service time and a large number of servers.