On markov structures of queueing models

Our main aim is to optimize the design of a Markov Queueing Model^[1] with exponential distribution. Ziya and Takage studied optimization problem for Queueing models with probability distribution. The main thrust is on deriving the characteristic properties of classification problem of discrete type and continuous type Queueing system and its fuzzy extension. The Perron-Frobenius eigenvalue of a nonnegative matrix provides information for a complete classification of the Markov process in developing a computational method to determine recurrent Markov process of matrix M/G/1 type with a tree structure. The conditions for identification of the positive recurrence and transience of the Markov processes of M/G/1 type has been derived by iterative method.