Decomposition results for stochastic storage processes and queues with alternating Lévy inputs

In this paper we generalize known workload decomposition results for Lévy queues with secondary jump inputs and queues with server vacations or service interruptions. Special cases are polling systems with either compound Poisson or more general Lévy inputs. Our main tools are new martingale results, which have been derived in a companion paper.

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

[2]  J. George Shanthikumar,et al.  On Stochastic Decomposition in M/G/1 Type Queues with Generalized Server Vacations , 1988, Oper. Res..

[3]  Offer Kella,et al.  Useful Martingales for Stochastic Storage Processes with Lévy-Type Input , 1992, Journal of Applied Probability.

[4]  Decomposition results-the true story , 2012 .

[5]  D. Applebaum Lévy Processes and Stochastic Calculus: Preface , 2009 .

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

[7]  O. Kella An exhaustive lévy storage process with intermittent output , 1998 .

[8]  Ward Whitt,et al.  Queues with Server Vacations and Levy Processes with Secondary Jump Input , 1991 .

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

[10]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

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

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

[13]  W. Whitt,et al.  Useful martingales for stochastic storage processes with Lévy input , 1992, Journal of Applied Probability.

[14]  Robert B. Cooper,et al.  Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations , 1985, Oper. Res..

[15]  Offer Kella,et al.  Superposition of renewal processes and an application to multi-server queues , 2006 .

[16]  K. M. Kosinski,et al.  Queue lengths and workloads in polling systems , 2011, Oper. Res. Lett..

[17]  David Applebaum,et al.  Lévy Processes and Stochastic Calculus by David Applebaum , 2009 .

[18]  Uri Yechiali,et al.  Fluid polling systems , 2009, Queueing Syst. Theory Appl..

[19]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[20]  Offer Kella,et al.  Another look into decomposition results , 2013, Queueing Syst. Theory Appl..