GSPN models of random, cyclic, and optimal 1-limited multiserver multiqueue systems

Generalized stochastic Petri nets (GSPiVs) are used to study symmetric multiserver multiqueue systems in which the polling order is either cyclic, or random, or optimized, and the service discipline is 1-limited. Exact numerical results are obtained by means of GreatSPIV, the software tool for the analysis of GSPNS, and are presented as curves of the average customer waiting and sojourn times for Markovian systems comprising a number of finite-capacity waiting lines. The numerical results indicate that the random and optimal polling strategies provide upper and lower bounds of acceptable tightness on the performance of the cyclic polling case, while being substantially simpler to study and solve.

[1]  D. Bertsimas,et al.  Stochastic and dynamic vehicle routing with general demand and interarrival time distributions , 1993, Advances in Applied Probability.

[2]  Hanoch Levy,et al.  Efficient Visit Orders for Polling Systems , 1993, Perform. Evaluation.

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

[4]  Onno Boxma,et al.  A globally gated polling system with server interruptions, and applications to the repairman problem , 1992 .

[5]  Onno Boxma,et al.  An M/G/1 queue with customer collection , 1993 .

[6]  Onno Boxma,et al.  The correlated M/G/1 queue , 1993 .

[7]  J. George Shanthikumar,et al.  Design of manufacturing systems using queueing models , 1992, Queueing Syst. Theory Appl..

[8]  Lazaros F. Merakos,et al.  Output process from a continuous token ring local area network , 1992, IEEE Trans. Commun..

[9]  Yair Arian,et al.  Algorithms for generalized round robin routing , 1992, Oper. Res. Lett..

[10]  Gideon Weiss,et al.  Dynamic priority rules when polling with multiple parallel servers , 1992, Oper. Res. Lett..

[11]  Zhen Liu,et al.  Stability, monotonicity and invariant quantities in general polling systems , 1992, Queueing Syst. Theory Appl..

[12]  Eitan Altman,et al.  On Elevator polling with globally gated regime , 1992, Queueing Syst. Theory Appl..

[13]  Sem C. Borst,et al.  Collection of customers: a correlated M/G/1 queue , 1992, SIGMETRICS '92/PERFORMANCE '92.

[14]  Marco Ajmone Marsan,et al.  Cycles and waiting times in symmetric exhaustive and gated multiserver multiqueue systems , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[15]  Paul E. Wright,et al.  GATED, EXHAUSTIVE, PARALLEL SERVICE , 1992 .

[16]  Hanoch Levy,et al.  Cyclic reservation schemes for efficient operation of multiple-queue single-server systems , 1992, Ann. Oper. Res..

[17]  F. Neri,et al.  On the construction of abstract GSPNs: an exercise in modeling , 1991, Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91.

[18]  Marco Ajmone Marsan,et al.  Multiserver multiqueue systems with limited service and zero walk time , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.

[19]  Kow C. Chang,et al.  Mean waiting time approximations in cyclic-service systems with exhaustive limited service policy , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.

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

[21]  Yavuz A. Bozer,et al.  Tandem Configurations for Automated Guided Vehicle Systems and the Analysis of Single Vehicle Loops , 1991 .

[22]  Awi Federgruen,et al.  Structured Partitioning Problems , 1991, Oper. Res..

[23]  Richard R. Muntz,et al.  Optimal Routing for Closed Queueing Networks , 1990, Perform. Evaluation.

[24]  Onno Boxma.  Analysis and optimization of polling systems , 1991 .

[25]  Kishor S. Trivedi,et al.  Stochastic Petri Net Models of Polling Systems , 1990, IEEE J. Sel. Areas Commun..

[26]  Marco Ajmone Marsan,et al.  GSPN Models of Markovian Multiserver Multiqueue Systems , 1990, Perform. Evaluation.

[27]  Moshe Sidi,et al.  Polling systems: applications, modeling, and optimization , 1990, IEEE Trans. Commun..

[28]  Onno J. Boxma,et al.  A pseudoconservation law for service systems with a polling table , 1990, IEEE Trans. Commun..

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

[30]  Marco Ajmone Marsan,et al.  Analysis of symmetric nonexhaustive polling with multiple servers , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.

[31]  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.

[32]  J. P. C. Blanc.  A numerical approach to cyclic-service queueing models , 1990, Queueing Syst. Theory Appl..

[33]  J.P.C. Blanc.  The power-series algorithm applied to cyclic polling systems , 1990 .

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

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

[36]  Laxmi N. Bhuyan,et al.  Approximate Analysis of Single and Multiple Ring Networks , 1989, IEEE Trans. Computers.

[37]  V. C. Hamacher,et al.  Approximate Analysis of Non-Exhautive Multiserver Polling Systems with Applications to Local Area Networks , 1989, Comput. Networks.

[38]  U. Yechiali,et al.  Dynamic priority rules for cyclic-type queues , 1989, Advances in Applied Probability.

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

[40]  C. H. Chen,et al.  Design and analysis of multiple token ring networks , 1988, IEEE INFOCOM '88,Seventh Annual Joint Conference of the IEEE Computer and Communcations Societies. Networks: Evolution or Revolution?.

[41]  G. S. Lueker,et al.  Asymptotic Methods in the Probabilistic Analysis of Sequencing and Packing Heuristics , 1988 .

[42]  Onno J. Boxma,et al.  Waiting times in discrete-time cyclic-service systems , 1988, IEEE Trans. Commun..

[43]  Edward G. Coffman,et al.  Two Queues with Alternating Service Periods , 1987, Performance.

[44]  J. W. Cohen.  A Two-Queue Model with Semi-Exhaustive Alternating Service , 1987, Performance.

[45]  O. Boxma,et al.  Pseudo-conservation laws in cyclic-service systems , 1987, Journal of Applied Probability.

[46]  Marco Ajmone Marsan,et al.  Generalized Stochastic Petri Nets Revisitied: Random Switches and Priorities , 1987, PNPM.

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

[48]  Onno J. Boxma,et al.  Waiting-Time Approximations in Multi-Queue Systems with Cyclic Service , 1987, Perform. Evaluation.

[49]  Onno Boxma,et al.  Two queues with alternating service and switching times , 1987 .

[50]  Michael J. Ferguson.  Mean waiting time for a token ring with station dependent overheads , 1986 .

[51]  David Everitt.  Simple Approximations for Token Rings , 1986, IEEE Trans. Commun..

[52]  Edward G. Coffman,et al.  A continuous polling system with constant service times , 1986, IEEE Trans. Inf. Theory.

[53]  Onno J. Boxma,et al.  Waiting-time approximations for cyclic-service systems with switch-over times , 1986, SIGMETRICS '86/PERFORMANCE '86.

[54]  D. Everitt.  A conservation-type law for the token ring with limited service , 1986 .

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

[56]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[57]  Michael J. Ferguson,et al.  Exact Results for Nonsymmetric Token Ring Systems , 1985, IEEE Trans. Commun..

[58]  A. A. Fredericks,et al.  Approximate analysis of a generalized clocked schedule , 1985, AT&T Technical Journal.

[59]  B. T. Doshi,et al.  Analysis of clocked schedules — High-priority tasks , 1985, AT&T Technical Journal.

[60]  M. H. Ackroyd.  Numerical computation of delays in clocked schedules , 1985, AT&T Technical Journal.

[61]  Onno J. Boxma.  Two Symmmetric Queues with Alternating Service and Switching Times , 1984, Performance.

[62]  Mario Gerla,et al.  Load Balancing in Distributed Systems with Multiple Classes and Site Constraints , 1984, International Symposium on Computer Modeling, Measurement and Evaluation.

[63]  Marco Ajmone Marsan,et al.  A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems , 1984, TOCS.

[64]  Tom W. Berrie,et al.  Queues and Point Processes , 1983 .

[65]  Shaler Stidham,et al.  The Relation between Customer and Time Averages in Queues , 1980, Oper. Res..

[66]  M. Eisenberg.  Two Queues with Alternating Service , 1979 .

[67]  Jeffrey P. Buzen,et al.  Optimal Load Balancing in Memory Hierarchies , 1974, IFIP Congress.

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

[69]  Martin Eisenberg.  Two Queues with Changeover Times , 1971, Oper. Res..

[70]  Vincent Hodgson,et al.  The Single Server Queue. , 1972 .

[71]  Robert B. Cooper.  Queues served in cyclic order: Waiting times , 1970, Bell Syst. Tech. J..

[72]  Robert B. Cooper,et al.  Queues served in cyclic order , 1969 .

[73]  William L. Maxwell,et al.  Queuing with Alternating Priorities , 1965 .

[74]  L Fournier,et al.  EXPECTED WAITING TIMES IN CYCLIC SERVICE SYSTEMS UNDER PRIORITY , .