Descendant set: an efficient approach for the analysis of polling systems

Polling systems have been used to model a large variety of applications and much research has been devoted to the derivation of efficient algorithms for computing the delay measures in these systems. Recent research efforts in this area, which have focused on the optimization of these systems, have raised the need for very efficient such algorithms. This work develops the descendant set approach as a general efficient algorithm for deriving all moments of customer delay (in particular, mean delay) in these systems. The method is applied to a very large variety of model variations, including: 1) The exhaustive and gated service policies, 2) Fractional service policies, 3) The cyclic visit order, 4) Arbitrary periodic visit orders (polling tables), and 5) Customer routing. For most of these variations the method significantly outperforms the algorithms commonly used today. >

[1]  Leonard Kleinrock,et al.  The Analysis of Random Polling Systems , 1988, Oper. Res..

[2]  Hanoch Levy,et al.  Efficient visit frequencies for polling tables: minimization of waiting cost , 1991, Queueing Syst. Theory Appl..

[3]  Leslie D. Servi.  Average Delay Approximation of M/G/1 Cyclic Service Queues with Bernoulli Schedules , 1986, IEEE J. Sel. Areas Commun..

[4]  Kin K. Leung,et al.  A single-server queue with vacations and gated time-limited service , 1990, IEEE Trans. Commun..

[5]  Onno J. Boxma,et al.  Workloads and waiting times in single-server systems with multiple customer classes , 1989, Queueing Syst. Theory Appl..

[6]  Hanoch Levy.  Binomial-gated service: a method for effective operation and optimization of polling systems , 1991, IEEE Trans. Commun..

[7]  Mandyam M. Srinivasan,et al.  Nondeterministic polling systems , 1991 .

[8]  Hideaki Takagi,et al.  Analysis of polling systems , 1986 .

[9]  D. Sarkar,et al.  Expected waiting time for nonsymmetric cyclic queueing systems—exact results and applications , 1989 .

[10]  Gagan L. Choudhury.  Polling with a general service order table: gated service , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.

[11]  S. W. Fuhrmann.  Technical Note - A Note on the M/G/1 Queue with Server Vacations , 1984, Oper. Res..

[12]  Hanoch Levy.  Delay Computation and Dynamic Behavior of Non-Symmetric Polling Systems , 1989, Perform. Evaluation.

[13]  Onno J. Boxma,et al.  Waiting Times in Polling Systems with Markovian Server Routing , 1989, MMB.

[14]  Onno Boxma,et al.  Pseudo-conservation laws in cyclic-service systems , 1986 .

[15]  Moshe Sidi,et al.  A queueing network with a single cyclically roving server , 1992, Queueing Syst. Theory Appl..

[16]  Edward G. Coffman,et al.  Continuous Polling on Graphs , 1993 .

[17]  H. Levy,et al.  Polling systems with simultaneous arrivals , 1991, IEEE Trans. Commun..

[18]  Izhak Rubin,et al.  Polling with a General-Service Order Table , 1987, IEEE Trans. Commun..

[19]  Michael J. Ferguson.  Computation of the Variance of the Waiting Time for Token Rings , 1986, IEEE J. Sel. Areas Commun..

[20]  G. Boyd Swartz.  Polling in a Loop System , 1980, JACM.

[21]  Theodore E. Tedijanto,et al.  Exact Results for the Cyclic-Service Queue with a Bernoulli Schedule , 1990, Perform. Evaluation.

[22]  Martin Eisenberg,et al.  Queues with Periodic Service and Changeover Time , 1972, Oper. Res..

[23]  Richard O. LaMaire.  An M/G/1 Vacation Model of an FDDI Station , 1991, IEEE J. Sel. Areas Commun..

[24]  Hanoch Levy,et al.  Optimization of Polling Systems , 1990, International Symposium on Computer Modeling, Measurement and Evaluation.

[25]  Kin K. Leung.  Waiting time distributions for token-passing systems with limited-one service via discrete Fourier transforms , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.