Jonsson 4.912

- Introduction
- Polling Models - An Overview
- Review of
*H=\lambda G*and PASTA

- The
*M/G/1*Queue- Classical Departure-Chain Analysis
- Decomposition of the Waiting Time
- Arrival-Epoch Decomposition
- Generalizations

- The
*M/G/1*Vacation Model and Decomposition- Departure-Epoch Decomposition
- Arrival-Epoch Decomposition
- Applications

- The Zero-Switchover-Times Model
- The Nonzero-Switchover-Times Model
- Relationship between the Zero- and Nonzero-Switchover-Times Models
- Transform Relations
- Pseudo-Conservation Laws

- Other Results

- Boxma, O. J. [1989]. "Workloads and Waiting Times in Single-Server Systems with Multiple Customer Classes."
*Queueing Systems*,**5**, pp. 185-214. - Boxma, O. J., and W. P. Groenendijk [1987]. "Pseudo-Conservation Laws in Cyclic-Service Systems."
*Journal of Applied Probability*,**24**, pp. 949-964. - Cooper, R. B. [1970]. "Queues Served in Cyclic Order: Waiting Times."
*The Bell System Technical Journal*},**49**, pp. 399-413. - Cooper, R. B., and G. Murray [1969]. "Queues Served in Cyclic Order."
*The Bell System Technical Journal*,**48**, pp. 675-689. - Cooper, R. B., S.-C. Niu, and M. M. Srinivasan [1992]. "A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive."
*Operations Research*, to appear. - Eisenberg, M. [1972]. "Queues with Periodic Service and Changeover Times."
*Operations Research*,**20**, pp. 440-451. - Ferguson, M. J., and Y. J. Aminetzah [1985]. "Exact Results for Nonsymmetric Token Ring Systems."
*IEEE Transactions on Communications*,**COM-33**, pp. 223-231. - Fuhrmann, S. W. [1992]. "A Decomposition Result for a Class of Polling Models."
*Queueing Systems*,**11**, pp. 109-120. - Fuhrmann, S. W., and R. B. Cooper [1985]. "Stochastic Decompositions in the
*M/G/1*Queue with Generalized Vacations."*Operations Research*,**33**, pp. 1117-1129. - Konheim, A. G., H. Levy, and M. M. Srinivasan [1993]. "Descendant Set: An Efficient Approach for the Analysis of Polling Systems."
*IEEE Transactions on Communications*,**42**, pp. 1245-1253. - Niu, S.-C. [1995]. "Arrival-Epoch Stochastic Decompositions in
*M/G/1*Queues with Generalized Vacations." Draft paper. - Niu, S.-C., and R. B. Cooper [1993]. "Transform-Free Analysis of
*M/G/1/K*and Related Queues."*Mathematics of Operations Research*,**18**, pp. 486-510. - Sarkar, D., and W. I. Zangwill [1989]. "Expected Waiting Time for Nonsymmetric Cyclic Queueing Systems - Exact Results and Applications."
*Management Science*,**35**, pp. 1463-1474. - Srinivasan, M. M., S.-C. Niu, and R. B. Cooper [1993]. "Relating Polling Models with Zero and Nonzero Switchover Times."
*Queueing Systems*, to appear. - Takagi, H. [1986].
*Analysis of Polling Systems*. The MIT Press, Cambridge, Massachusetts. - Takagi, H. [1990]. "Queueing Analysis of Polling Models: An Update." In
*Stochastic Analysis of Computer and Communication Systems*, H. Takagi (ed.). North-Holland, Amsterdam. - Takagi, H. [1994]. "Queueing Analysis of Polling Models: Progress in 1990-93." Institute of Socio-Economic Planning, University of Tsukuba, Japan, May 11, 1994.

- Altman, E., and U. Yechiali [1994]. "Polling in a Closed Network."
*Probability in the Engineering and Informational Sciences*,**8**, pp. 327-343. - Browne, S., and U. Yechiali [1989]. "Dynamic Priority Rules for Cyclic-Type Queues."
*Advances in Applied Probability*,**21**, pp. 432-450. - Levy, H., M. Sidi, and O. J. Boxma [1990]. "Dominance Relations in Polling Systems."
*Queueing Systems*,**6**, pp. 155-172. - Daganzo, C. F. [1990]. "Some Properties of Polling Systems."
*Queueing Systems*,**6**, pp. 137-154. - Eisenberg, M. [1994]. "The Polling System with a Stopping Server."
*Queueing Systems*,**18**, pp. 387-431. - Federgruen, A., and Z. Katalan. [1994]. "Approximating Queue Size and Waiting-Time Distributions in General Polling Systems."
*Queueing Systems*,**18**, pp. 353-386. - Fuhrmann, S. W., and Y. Wang [1988]. "Analysis of Cyclic Service Systems with Limited Service: Bounds and Approximations."
*Performance Evaluation*,**9**, pp. 35-54. - Hofri, M., and K. W. Ross [1987]. "On the Optimal Control of Two Queues with Server Setup Times and Its Analysis."
*SIAM Journal on Computing*,**16**, pp. 399-420. - Kleinrock, L., and H. Levy [1988]. "The Analysis of Random Polling Systems."
*Operations Research*,**36**, pp. 716-732. - Lee, D.-S., and B. Sengupta [1992]. "An Approximate Analysis of a Cyclic Server Queue with Limited Service and Reservations."
*Queueing Systems*,**11**, pp. 153-178. - Liu, Z., P. Nain, and D. Towsley [1992]. "On Optimal Polling Policies."
*Queueing Systems*,**11**, pp. 59-84. - Sarkar, D., and W. I. Zangwill [1991]. "Variance Effects in Cyclic Production Systems."
*Management Science*,**37**, pp. 443-453. - Sidi, M., H. Levy, and S. W. Fuhrmann [1992]. "A Queueing Network with a Single Cyclically Roving Server."
*Queueing Systems*,**11**, pp. 121-144. - Srinivasan, M. M. [1991]. "Nondeterministic Polling Systems."
*Management Science*,**37**, 667-681. - Takagi, H. [1991]. "Analysis of Finite-Capacity Polling Systems."
*Advances in Applied Probability*,**23**, pp. 373-387. - Takagi, H. [1992]. "Analysis of an
*M/G/1//N*Queue with Multiple Server Vacations, and Its Applications to a Polling Model."*Journal of the Operations Research Society of Japan*,**35**, pp. 300-315. - Takine, T., and T. Hasegawa [1992]. "A Cyclic-Service Finite Source Model with Round-Robin Scheduling."
*Queueing Systems*,**11**, pp. 91-108.