Asymptotic behaviors of the loss probability for a finite buffer queue with QBD structure

作者：Miyazawa Masakiyo^*; Sakuma Yutaka; Yamaguchi Shuhlei

来源：Stochastic Models, 2007, 23(1): 79-95.

DOI：10.1080/15326340601141919

• asympotic behaviour
• finite buffer queue
• finite level QBD
• loss probability
• many server loss system
• Markovian arrival process

We are concerned with a finite buffer queue with arrival and service process that are generated by a continuous time Markov chain with a finitely many states. this model includes a many-service queue, and is described by a truncated QBD, where QBD stands for a quasi-birth-and-death process. It is shown that the loss probability of this queue geometrically decays with a constant prefactor as the buffer size goes to infinity if the corresponding queue with an unlimited buffer is stable. For this, we first consider asymtotic behaviours of the truncated QBD. We then specialize this result for a many- server queue with a finite buffer and Markovian arrival and service process of Neuts. Using the asymptotic results, we also numerically consider an approximation of the loss probability.

• 出版日期2007