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(The following description was used when this course was taught during the Spring 2006 Semester. There will likely be differences in the instructor, textbook, and/or outline the next time the course is taught.)
Instructor : Dr. N. Gautam,
Text: No required textbook. Use class notes and other reading materials provided in class.
Reference:
- Fundamentals of Queueing Theory by Gross and Harris
- Queueing Networks and Markov Chains by Bolch et al (Have requested to put both on reserve in Evans library).
Description: Develop tools and techniques for quantitatively evaluating the performance of queueing systems and networks. These tools will be used in optimal design and control of
stochastic systems modeled as network of queues.Prerequisites: ISEN 421, ELEN 646, or an equivalent course on probability and stochastic processes. Prerequisite topics include: random variables, distributions, expected value, variance, conditional probability, discrete time Markov chains, and continuous time Markov chains (or Markov processes). Comfortable with algebra, calculus and scientific programming.
STAT 610 is also recommended.Course Topics
- Preliminaries
(a) Queueing fundamentals and Kendall notations
(b) Generating functions and transforms
(c) Exponential distribution, Poisson process and Renewal process
(d) Markov chains (DTMC) and Markov processes (CTMC)
(e) Key results: Little’s law and other properties- Single-Station and Single-Class Queues
(a) Birth and death chains (M/M/s/K type queues, i.e. M/M/1, M/M/1/K, Finite popl., etc)
(b) M/G/1, G/M/1 and M/G/1 queues
(c) MVA and other approximations (for G/G/1, M/G/s and G/M/s queues)- Single-Station and Multi-Class Queues
(a) Scheduling policies (work-conserving policies, priority, polling, SPT, SRT, Cμ rule)
(b) M/G/1 queues with priorities (non-preemptive, pre-emptive resume and pre-emptive repeat)
(c) M/G/1 queues with polling (and server-vacations)
(d) Stochastic knapsack problem, reversibility- Multi-Station and Single-Class Queues
(a) Departure processes
(b) Open and closed queueing networks
(c) Jackson networks, Kelley networks and other product form networks
(d) Approximations: diffusion, Brownian, heavy traffic
(e) Networks with blocking- Multi-Station and Multi-Class Queues
(a) Tandem queues, feed-forward networks, work conserving scheduling
(b) Approximations and bounds for general networks
(c) Stability issues
