Asymptotics for the sojourn time distribution in the queue defined by a general QBD process with a countable phase space

作者：Ozawa Toshihisa^*

来源：Queueing Systems, 2014, 76(1): 73-103.

DOI：10.1007/s11134-013-9359-5

• Quasi-birth-and-death process
• Queueing model
• Sojourn time distribution
• Asymptotic property

We consider a FIFO queue defined by a QBD process. When the number of phases of the QBD process is finite, it has been proved that the stationary distribution of sojourn times in that queue can be represented as a phase-type distribution. In this paper, we extend this result to the case where the number of phases of the QBD process is countably many and obtain several kinds of asymptotic formula for the steady-state tail probability of sojourn times in the queue when the tail probability decays in exact exponential form.

• 出版日期2014-1