Queueing Theory

Course Syllabus

Click here to get a copy of the syllabus in postscript format.

Course Objective

This course provides a systematic study of queues. A significant emphasis is placed on the development of sample-path methods for the analysis of queueing models.

Office Hours

Mondays, 3:00pm--5:00pm
Jonsson 4.912


To be announced.

Text and References

Text: Stochastic Modeling and the Theory of Queues, by Ronald W. Wolff. Prentice-Hall, Englewood Cliffs, New Jersey, 1989.



OPRE 6330 and OPRE 6331; or consent of the instructor.

Grading Scheme

Final: 50% (take-home exam)
Presentation: 50%

Course Outline

Chapters 5, 8, 9, 11, 10, 6, 7, and references listed above. Topics include:
  1. Basic queueing laws - L=\lambda W and PASTA
  2. Markovian queues
  3. M/G/1 and GI/M/c queues
  4. Busy-period analysis
  5. GI/G/1 queues, random walk, and duality
  6. M/G/1/K finite-capacity queues and extensions
  7. Insensitive queueing models
  8. Bounds and approximations
  9. Comparison of queues
  10. Priority queues
  11. Networks of queues

Papers Suggested for Presentation

  1. Sarkar, D., and Zangwill, W. I. [1989]. "Expected Waiting Time for Nonsymmetric Cyclic Queueing Systems - Exact Results and Applications. Management Science, 35, pp. 1463-1474.
  2. Boxma, O. J., and Groenendijk, W. P. [1987]. "Pseudo-Conservation Laws in Cyclic-Service Systems." Journal of Applied Probability, 24, pp. 949-964.
  3. Tembe, S. V., and Wolff, R. W. [1974]. "The Optimal Order of Service in Tandem Queues." Operations Research, 24, pp. 824-832.
  4. Fuhrmann, S. W., and Cooper, R. B. [1985]. "Stochastic Decompositions in the M/G/1 Queue with Generalzed Vacations." Operations Research, 33, pp. 1117-1129.
  5. Courtois, P.-J., and Scheys, G. [1991]. "Minimization of the Total Loss Rate for Two Finite Queues in Series." IEEE Transactions on Communications, 39, pp. 1651-1661.
  6. Ott, T. J. [1984]. "The Sojourn Time in the M/G/1 Queue with Processor Sharing." Journal of Applied Probability, 21, pp. 360-378.
  7. Tak\'acs, L. [1969]. "On Erlang's Formula." Annals of Mathematical Statistics, 40, pp. 71-78.
  8. Lavenberg, S. S. [1975]. "The Steady-State Queueing Time Distribution for the M/G/1 Finite-Capacity Queue." Management Science, 21, pp. 501-506.
  9. Shanthikumar, J. G., and Sumita, U. [1987]. "Convex Ordering of Sojourn Times in Single-Server Queues: Extremal Properties of FIFO and LIFO Service Disciplines." Journal of Applied Probability, 24, pp. 734-748.
  10. Wolff, R. W. [1970]. "Time Sharing with Priorities." SIAM Journal of Applied Mathematics, 19, pp. 566-574.