Queue lengths and workloads in polling systems

Abstract For a single-server multi-station polling system, we focus on the generating function and Laplace–Stieltjes transform of the time-stationary joint queue length and workload distributions, respectively, under no further assumptions on the service discipline. We express these quantities as expressions involving the generating functions of the joint queue length distribution at visit beginnings and visit completions at the various stations. The latter is known for a broad variety of cases. Finally, we identify a workload decomposition result.

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

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

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

[4]  V. M. Vishnevskii,et al.  Mathematical methods to study the polling systems , 2006 .

[5]  Jacques Resing,et al.  Polling systems and multitype branching processes , 1993, Queueing Syst. Theory Appl..

[6]  Hideaki Takagi,et al.  Queueing analysis of polling models: progress in 1990-1994 , 1998 .

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

[8]  J. Kingman.  THE SINGLE SERVER QUEUE , 1970 .

[9]  Sem C. Borst,et al.  Polling Models With and Without Switchover Times , 1997, Oper. Res..

[10]  Hideaki Takagi,et al.  Analysis and Application of Polling Models , 2000, Performance Evaluation.

[11]  Tetsuya Takine,et al.  Distribution of the workload in multiclass queueing systems with server vacations , 1992 .

[12]  Geert-Jan van Houtum,et al.  A STATE-DEPENDENT POLLING MODEL WITH k-LIMITED SERVICE , 2009, Probability in the Engineering and Informational Sciences.

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

[14]  Onno Boxma,et al.  Lévy-driven polling systems and continuous-state branching processes , 2009, 1006.0384.

[15]  Hideaki Takagi,et al.  Application of Polling Models to Computer Networks , 1991, Comput. Networks ISDN Syst..

[16]  Onno Boxma,et al.  Queueing theory and its applications : liber amicorum for J.W. Cohen , 1988 .