Generalized Folding Algorithm for Transient Analysis of Finite QBD Processes and Its Queueing Applications

Li, San-Qi; Sheng, Hong-Dah

doi:10.1007/978-1-4615-2241-6_26

Cited by 21 publications

(5 citation statements)

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“…The steady-state analysis of the QBD processes is to obtain the solution vector from the linear equation where is the generator of the QBD process. The algorithm has been generalized to solve any set of linear equations of the type where is the boundary vector [17] and is any matrix having a block tridiagonal structure. Hence, in the GFA, the vector will also be permutated and reduced simultaneously with the permuation-reduction of the matrix in each reduction step.…”

Section: A the Generalized Folding Algorithmmentioning

confidence: 99%

“…Appendix B contains a brief description of the term "time scales." Refer to [17] and [18] for a detailed description of the GFA and its applications to the transient solutions of a QBD queueing system.…”

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confidence: 99%

“…The advantage of QBD modeling lies in the efficient solution technique for systems of linear equations of the type , for a matrix with a block tridiagonal structure. This solution technique is called the Generalized Folding Algorithm [17] which exploits the block tridiagonal structure of the matrix to solve for . A special case would be the solution of which is the steady-state solution of a QBD system with generator [16].…”

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confidence: 99%

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Performance analysis of a rate-based feedback control scheme

Kulkarni

1998

IEEE/ACM Trans. Networking

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In this paper, we present a numerical approach to the performance study of a delayed feedback system with one congested node and multiple connections. This approach consists of modeling the feedback system as a finite quasibirth-death process. Due to the peculiar block tridiagonal nature of its generator, efficient techniques exist for its steady-state and transient solutions. Using these techniques, we examine a simple parsimonious feedback system for issues such as throughput/loss performance, fairness, and stability. Our approach has the flexibility to study the effect of several additional factors such as asynchronous feedback, two-level control, and explicit rate notification in the presence of underlying high-priority traffic. This study brings to light the tradeoffs between system performance and the complexity of the feedback scheme. Our study shows that the time scales of correlation of the feedback system have a dominant effect on its performance. These time scales are associated with the feedback delay, the durations of active/idle periods of traffic sources, and the time scales of the underlying high-priority traffic. We also examine the effect of the time scales on the convergence time for the transient queueing system.

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Section: A the Generalized Folding Algorithmmentioning

confidence: 99%

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confidence: 99%

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Performance analysis of a rate-based feedback control scheme

Kulkarni

1998

IEEE/ACM Trans. Networking

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“…Finally, Section 8 concludes the transient study of the finite QBD-queueing system. The reader may refer to [18] for a detailed description of the Generalized Folding-algorithm and a comparison of its computational complexity with other existing methods for the solution of matrix equations.…”

Section: Introductionmentioning

confidence: 99%

“…A modified version of this algorithm (the Generalized Folding-algorithm) was used to solve xP = a for a boundary condition vector a ([MI). In [18], the algorithm was used to analyze the sojourn time behaviour on a subset of the stationary queueing process such as the time behaviour of the blocking period, busy period and the overload period.…”

Section: Introductionmentioning

confidence: 99%

Transient behaviour of queueing systems with correlated traffic

Kulkarni

1998

Communications in Statistics. Stochastic Models

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In this paper, we present the time-dependent solutions of various stochastic processes associated with a finite Quasi-Birth-Death queueing system. These include the transient queueing solutions, the transient departure and loss intensity processes and certain transient cumulative measures associated with the queueing system. The focus of our study is the effect of the arrival process correlation on the queueing system before it reaches steady-state. These time-dependent solutions require the computation of the exponential of the stochastic generator matrix G which may be of very large order. This precludes the use of known techniques to solve the matrix exponential such as the eigenvalue decomposition of G . We present a numerical technique based on the computation of the Laplace Transform of the matrix exponential which may then be numerically inverted to obtain the time-dependent solutions. We also propose new QoS metrics based on transient measures and efficient techniques for their computation.

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Transient distributions of level dependent quasi-birth-death processes with linear transition rates

Shin

2000

Korean J. Comput. & Appl. Math

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Generalized Folding Algorithm for Transient Analysis of Finite QBD Processes and Its Queueing Applications

Cited by 21 publications

References 3 publications

Performance analysis of a rate-based feedback control scheme

Performance analysis of a rate-based feedback control scheme

Transient behaviour of queueing systems with correlated traffic

Transient distributions of level dependent quasi-birth-death processes with linear transition rates

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