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An efficient computational method for solving nonlinear matrix equation and its application in queuing analysis

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Abstract

The matrix analytic analysis of queues with complex arrival, vacation and service characteristics requires the solution of nonlinear matrix equation. The complexity and large dimensionality of the model require an efficient and smart algorithm for the solution. In this paper, we propose an efficient Adaptive Newton-Kantorovich (ANK) method for speeding up the algorithm solving the nonlinear matrix equation which is an inevitable step in the analysis of the queue with embedded Markov chain such as BMAP/SMSP/1/∞ queue or its discrete version. BMAP/SMSP/1/∞ is a queuing model with a Semi Markov Service time Process (SMSP) and a Batch Markovian Arrival Process (BMAP). The numerical result is presented for the discrete case of N-MMBP/D/1 queue which arises in analyzing traffic aspect of computer communication network, where MMBP is Markov Modulated Bermoulli Process. The comparisons of Adaptive Newton-Kantorovich (ANK) with Modified Newton-Kantorovich (MNK) show that ANK saves 30% of CPU time when the number of userN is 50.

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Authors and Affiliations

  1. Department of Electrical & Computer Engineering, Concordia University, 1455 de Maisonneuve Blvd. W., H3G 1M8, Montreal, Quebec, Canada

    Huang Jun, Zhu Tao & Jeremiah F. Hayes

Authors
  1. Huang Jun
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  2. Zhu Tao
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  3. Jeremiah F. Hayes
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Corresponding author

Correspondence to Huang Jun.

Additional information

HUANG Jun obtained his Ph.D. degree in electrical engineering from Southeast University in 1992. He is currently a Research Associate in the Department of Electrical Engineering at Concordia University. His research interests are in the area of queuing theory and performance evaluation of telecommunication networks.

ZHU Tao received her Ph.D. degree in electrical engineering from Southeast University in 1993. She is now working for BNR/NT. Her research interests include performance analysis and simulation study with AI technique, traffic modelling and congestion control in BISDN.

J. F. HAYES is a tenure Professor of Department of Electrical Engineering at Concordia University in Montreal. He received his Ph.D. from Berkeley University. He is the senior editor of IEEE Journal of Selected Areas in Communication and the Fellow of IEEE. He published two books and a number of papers in digital and computer communications.

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Huang, J., Zhu, T. & Hayes, J.F. An efficient computational method for solving nonlinear matrix equation and its application in queuing analysis. J. of Comput. Sci. & Technol. 11, 272–285 (1996). https://doi.org/10.1007/BF02943134

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  • DOI: https://doi.org/10.1007/BF02943134

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