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This course provides a systematic study of queues. A significant emphasis is
placed on the development of sample-path methods for the analysis of
To be announced.
Text and References
Stochastic Modeling and the Theory of Queues, by Ronald
W. Wolff. Prentice-Hall, Englewood Cliffs, New Jersey, 1989.
- Heyman, D. P., and Stidham, S., Jr. . "The Relation Between Customer and Time Averages in Queues." Operations Research, 28, pp. 983-994.
- Niu, S.-C. . "Inequalities Between Arrival Averages and Time Averages in Stochastic Processes Arising from Queueing Theory." Operations Research, 32, pp. 785-795.
- Niu, S.-C. . "Representing Workloads in GI/G/1 Queues through the Preemptive-Resume LIFO Queue Discipline." Queueing Systems, 3, pp. 157-178.
- Niu, S.-C., and Cooper, R. B. . "Duality and Other Results for M/G/1 and GI/M/1 Queues, via a New Ballot Theorem." Mathematics of Operations Research, 14, pp. 281-293.
- Niu, S.-C., and Cooper, R. B. . "Transform-Free Analysis of M/G/1/K and Related Queues." Mathematics of Operations Research, 18, pp. 486-510.
- Wolff, R. W. . "Poisson Arrivals See Time Averages." Operations Research, 30, pp. 223-231.
OPRE 6330 and OPRE 6331; or consent of the instructor.
Final: 50% (take-home exam)
Chapters 5, 8, 9, 11, 10, 6, 7, and references listed above. Topics include:
- Basic queueing laws - L=\lambda W and PASTA
- Markovian queues
- M/G/1 and GI/M/c queues
- Busy-period analysis
- GI/G/1 queues, random walk, and duality
- M/G/1/K finite-capacity queues and extensions
- Insensitive queueing models
- Bounds and approximations
- Comparison of queues
- Priority queues
- Networks of queues
Papers Suggested for Presentation
- Sarkar, D., and Zangwill, W. I. . "Expected Waiting Time for Nonsymmetric Cyclic Queueing Systems - Exact Results and Applications. Management Science, 35, pp. 1463-1474.
- Boxma, O. J., and Groenendijk, W. P. . "Pseudo-Conservation Laws in Cyclic-Service Systems." Journal of Applied Probability, 24, pp. 949-964.
- Tembe, S. V., and Wolff, R. W. . "The Optimal Order of Service in Tandem Queues." Operations Research, 24, pp. 824-832.
- Fuhrmann, S. W., and Cooper, R. B. . "Stochastic Decompositions in the M/G/1 Queue with Generalzed Vacations." Operations Research, 33, pp. 1117-1129.
- Courtois, P.-J., and Scheys, G. . "Minimization of the Total Loss Rate for Two Finite Queues in Series." IEEE Transactions on Communications, 39, pp. 1651-1661.
- Ott, T. J. . "The Sojourn Time in the M/G/1 Queue with Processor Sharing." Journal of Applied Probability, 21, pp. 360-378.
- Tak\'acs, L. . "On Erlang's Formula." Annals of Mathematical Statistics, 40, pp. 71-78.
- Lavenberg, S. S. . "The Steady-State Queueing Time Distribution for the M/G/1 Finite-Capacity Queue." Management Science, 21, pp. 501-506.
- Shanthikumar, J. G., and Sumita, U. . "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.
- Wolff, R. W. . "Time Sharing with Priorities." SIAM Journal of Applied Mathematics, 19, pp. 566-574.
- Assignment #1
- Assignment #2