Two-phase queuing system with a threshold strategy of retrial calls

A two-phase queuing system (QS) has been considered; its first phase is represented by a single-linear system with retrial calls, and the second phase is represented by a multilinear (multiple) unbuffered QS. Queries arrive to the system in the group Markov flow. The system has two operational modes that differ by the strategy of the retrial attempts. Depending on the number of retrial calls, either a decentralized or centralized strategy of retrials is used. A stationary distribution of the system’s state probabilities at the embedded epochs and arbitrary time moments has been found, and formulae for the main characteristics of the system’s productivity have been obtained. Numerical examples are presented.

[1]  Armin Heindl.  Decomposition of general tandem queueing networks with MMPP input , 2001, Perform. Evaluation.

[2]  Antonio Gómez-Corral,et al.  A matrix-geometric approximation for tandem queues with blocking and repeated attempts , 2002, Oper. Res. Lett..

[3]  Adhir K Basu,et al.  Introduction to Stochastic Process , 2002 .

[4]  Alexander N. Dudin,et al.  Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory , 2006, Queueing Syst. Theory Appl..

[5]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[6]  Paola Inverardi,et al.  A review on queueing network models with finite capacity queues for software architectures performance prediction , 2003, Perform. Evaluation.

[7]  David M. Lucantoni,et al.  New results for the single server queue with a batch Markovian arrival process , 1991 .

[8]  Alexander N. Dudin,et al.  Software Sirius++ for Performance Evaluation of Modern Communication Networks , 2002, ESM.

[9]  Christos Langaris,et al.  TWO QUEUES IN TANDEM WITH RETRIAL CUSTOMERS , 2001 .

[10]  Antonio Gómez-Corral,et al.  A bibliographical guide to the analysis of retrial queues through matrix analytic techniques , 2006, Ann. Oper. Res..

[11]  Huei-Wen Ferng,et al.  Path-wise performance in a tree-type network: Per-stream loss probability, delay, and delay variance analyses , 2007, Perform. Evaluation.

[12]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .