An Efficient Computational Method for Solving Nonlinear Matrix Equstion and Its Applicatio

An Efficient Computational Method for Solving Nonlinear Matrix Equstion and Its Application in

Queuing Analysis

HUANGJun;朱涛;等

【期刊名称】《计算机科学技术学报：英文版》 【年(卷),期】1996(011)003

【摘要】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 effcient and smart algorithm for the solution.In this paper,we propose and 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 Arfival 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 tim when the number of user N is 50.