Asymptotics for the stationary distribution in a discrete-time two-dimensional quasi-birth-and-death process

作者：Ozawa Toshihisa^*

来源：Queueing Systems, 2013, 74(2-3): 109-149.

DOI：10.1007/s11134-012-9323-9

• Quasi-birth-and-death process
• Stationary distribution
• Asymptotic property
• Decay rate
• Matrix analytic method
• Two-dimensional reflecting random walk
• Two-queue model
• k-Limited service

We consider a discrete-time two-dimensional process on with a background process {J (n) } on a finite set, where individual processes and are both skip free. We assume that the joint process is Markovian and that the transition probabilities of the two-dimensional process are modulated depending on the state of the background process {J (n) }. This modulation is space homogeneous, but the transition probabilities in the inside of and those around the boundary faces may be different. We call this process a discrete-time two-dimensional quasi-birth-and-death (2D-QBD) process, and obtain the decay rates of the stationary distribution in the coordinate directions. We also distinguish the case where the stationary distribution asymptotically decays in the exact geometric form, in the coordinate directions.

• 出版日期2013-6