Jonsson 4.912

**References:**

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*GI/G/1*Queues through the Preemptive-Resume LIFO Queue Discipline."*Queueing Systems*,**3**, pp. 157-178. - Niu, S.-C., and Cooper, R. B. [1989]. "Duality and Other Results for
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*Operations Research*,**30**, pp. 223-231.

Presentation: 50%

- 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

- Sarkar, D., and Zangwill, W. I. [1989]. "Expected Waiting Time for Nonsymmetric Cyclic Queueing Systems - Exact Results and Applications.
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*M/G/1*Queue with Generalzed Vacations."*Operations Research*,**33**, pp. 1117-1129. - 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. - Ott, T. J. [1984]. "The Sojourn Time in the
*M/G/1*Queue with Processor Sharing."*Journal of Applied Probability*,**21**, pp. 360-378. - Tak\'acs, L. [1969]. "On Erlang's Formula."
*Annals of Mathematical Statistics*,**40**, pp. 71-78. - Lavenberg, S. S. [1975]. "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. [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. - Wolff, R. W. [1970]. "Time Sharing with Priorities."
*SIAM Journal of Applied Mathematics*,**19**, pp. 566-574.

- Assignment #1
- Assignment #2