Classification of Markov Processes of Matrix M/G/1 type with a Tree Structure and its Applications to the MMAP[K]/G[K]/1 Queue
نویسنده
چکیده
The purpose of this paper is to study the classification problem of discrete time and continuous time Markov processes of matrix M/G/1 type with a tree structure. We begin this paper by developing a computational method to find whether a Markov process of matrix M/G/1 type with a tree structure is positive recurrent, null recurrent, or transient. The method is then used to study the impact of the last-come-first-served general preemptive resume (LCFS-GPR) service discipline on the stability of the MAP/PH/1 queue. The later portion of the paper identifies some sufficient conditions for positive recurrence and transience of Markov processes of matrix M/G/1 type with a tree structure. The results are used to show that the discrete time or continuous time MMAP[K]/G[K]/1 queue or the continuous time MMAP[K]/PH[K]/S queue with a work conserving service discipline is stable if and only if its traffic intensity is less than one, unstable if its traffic intensity is larger than one.
منابع مشابه
Classification of Markov Processes of Matrix M/G/1 type with a Tree Structure and its Applications to the MMAP[K]/G[K]/1 Queues
This paper studies the classification problem of discrete time and continuous time Markov processes of matrix M/G/1 type with a tree structure. It is shown that the Perron-Frobenius eigenvalue of a nonnegative matrix provides information for a complete classification of the Markov process of interest. A computational method is developed to find whether a Markov process of matrix M/G/1 type with...
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