Spring 2020 - MATH 895 G100

Reading (4)

Class Number: 3752

Delivery Method: In Person

Overview

  • Course Times + Location:

    Location: TBA

Description

COURSE DETAILS:

Goals/Objective: Students will gain an understanding of queueing theory, and more broadly of theory and applications of stochastic modelling. The course will focus primarily on Markovian queue models. Embedded Markov chain techniques for non Markovian models and heavy traffic approximations will be studied with a view to applying our much richer mathematical understanding of Markovian models to applied models, which are often non-Markovian. The course will end by exploring recent advances in accumulating priority queues, which have become important in healthcare applications.

Outline:
1. Stochastic Processes
• Markov chains
• continuous time Markov chains
• birth-and-death processes
• Poisson processes
• renewal processes
• regenerative processes

2. General Concepts in Queueing Systems
• queueing processes
• steady-state behaviour (stochastic equilibrium)
• Little’s formula
• characteristics of Poisson arrival processes

3. Birth-and-Death Queueing Systems: Exponential Models
• single server exponential queue (M/M/1 queues)
• queues with bounded waiting space (M/M/1/K queues)
• exponential queue with an infinite number of servers (M/M/∞ queues)
• Erlang loss model (M/M/c/c queues)
• models with finite input source
• multichannel queues

4. Non-Birth-and-Death Queueing Systems
• bulk queueing models
• queueing models with batch service

5. Queue Networks
• networks of Markovian queues
• Jackson networks

6. Non-Markovian Queueing Systems
• embedded Markov chain technique
• Pollaczek-Khinchin formula for the M/G/1 queue
• G/M/1 queues
• generalization of the Pollaczek-Khinchin formula for G/G/1 queues

7. Heavy Traffic Approximations
• Kingman’s approximation for G/G/1 queues
• heavy traffic approximation for G/M/c queues

8. Discrete Event Simulation of Queueing Systems
• event-based simulation
• application to queueing systems

9. Accumulating Priority Queues
• waiting time for the two-class accumulating priority queue (APQ)
• waiting time for the multi-class APQ
• simulation approaches

The group will meet twice weekly for 2-hour sessions. 

Grading

  • Presentation of reading material in class (organization, understanding, and clarity) 30%
  • Biweekly homework assignments (correctness and exposition) 30%
  • Final course project (20% for written report and 20% for 20-minute presentation) 40%

NOTES:

Enrollment through permission of instructor only; use Add/Drop form. Contact mathgsec@sfu.ca.

REQUIREMENTS:

Prerequisites: Math 348 or an equivalent course on probability models or stochastic processes. Students should
discuss whether they have the background for the course with the instructor.

Materials

MATERIALS + SUPPLIES:

Text: Medhi, J. Stochastic Models in Queueing Theory, 2nd edition, Academic Press (2003).

Additional Reading:

Gross, D., Shortle, J. F., Thompson, J. M., Harris, C. M., Fundamentals of Queueing Theory, 4th edition,
Wiley (2008).

Ross, S. M., Simulation, 5th edition, Academic Press (2013).

Stanford, D. A., Taylor, P., Ziedins, I., Waiting time distributions in the accumulating priority queue,
Queueing Systems, 77, 297-330 (2014).

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

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