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

In: Computations with Markov Chains

Author

Listed:
  • San-qi Li

    (University of Texas at Austin, Department of Electrical and Computer Engineering)

  • Hong-Dah Sheng

    (University of Texas at Austin, Department of Electrical and Computer Engineering)

Abstract

In this paper we propose and implement a generalized Folding-algorithm for the transient analysis of finite QBD processes. It is a numerical method for the direct computation of xP= a where P is the QBD generator matrix in block tri-diagonal form. Define the QBD state space in two dimensions with N phases and K levels, so that $$P \in {{R}^{{NK \times NK}}}andx,a \in {{R}^{{J \times NK}}},\forall J$$ . The time complexity of the algorithm for solving x P = a is the greater of O(N 3 log2 K) and O(N 2 KJ). The algorithm is found to be highly stable with superior error performance. In numerical studies we analyze the transient performance of MMPP/M/1 queueing system with finite buffer capacity. The MMPP arrival process is constructed to reflect the diversity of the second-order input statistics. We examine the effect of the second-order input statistics on transient queueing performance.

Suggested Citation

  • San-qi Li & Hong-Dah Sheng, 1995. "Generalized Folding Algorithm for Transient Analysis of Finite QBD Processes and Its Queueing Applications," Springer Books, in: William J. Stewart (ed.), Computations with Markov Chains, chapter 26, pages 463-481, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-2241-6_26
    DOI: 10.1007/978-1-4615-2241-6_26
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