Introduction To Queueing Theory

About the Course : This course gives a detailed introduction into queueing theory along with the stochastic processes techniques useful for modelling queueing systems. A queue is a waiting line, and a queueing system is a system which provides service to some jobs (customers, clients) that arrive with time and wait to get served (Examples: - a telecommunication system that processes requests for communication; - a hospital facing randomly occurring demand for hospital beds; - central processing unit that handles arriving jobs). Queueing theory is a branch of applied probability theory dealing with abstract representation and analysis of such systems. Its study helps us to obtain useful and unobvious answers to certain questions concerning the performance of systems which in turn would help to design better systems. INTENDED AUDIENCE : Students at advanced undergraduate and postgraduate level in Mathematics, Statistics, Computer Science & Engg, Communications Engg., Industrial Engineering, Operations Research, Management Science and allied areas interested in this field. PREREQUISITES : Calculus-based Probability TheoryINDUSTRY SUPPORT : Software/Manufacturing/Scheduling companies that employ advanced tools in their design and analysis of systems and networks.

Week 1 : Introduction to queues, measures of system performance, characteristics of queueing systems, Little’s law and other general results; Transforms and generating functions Week 2 : Stochastic processes overview, discrete-time Markov chains, classification and long-term behaviourWeek 3 : Continuous-time Markov chain, birth-death processes, Poisson process and exponential distribution Week 4 : Birth-death queueing systems: Single-server queues, multiserver queues, finite-capacity queuesWeek 5 : Birth-death queueing systems: Loss systems, infinite-server queues, finite-source queues, state-dependent queues, queues with impatience, overview of transient analysis and busy period analysis Week 6 : Non-birth-death Markovian queueing systems: Bulk input queues, bulk service queues, Erlangian modelsWeek 7 : Priority queues, retrial queues, discrete-time queues Week 8 : Queueing networks: Series, open Jackson networksWeek 9 : Queueing networks: Closed Jackson networks, cyclic queues, extensions of Jackson networks Week 10 : Renewal and semi-Markov processes; Semi-Markovian queuesWeek 11 : Semi-Markovian queues: Single server and multiserver general service and general input models Week 12 : General queueing models, queues with vacations