Quasi-stationary distributions of single-server phase-type queues
Mathematics of Operations Research
Queueing analysis of polling models: progress in 1990-1994
Frontiers in queueing
PMCCN '97 Proceedings of the IFIP TC6 / WG6.3 & WG7.3 International Conference on the Performance and Management of Complex Communication Networks
Analysis and Application of Polling Models
Performance Evaluation: Origins and Directions
Queueing Systems: Theory and Applications
A state-dependent polling model with k-limited service
Probability in the Engineering and Informational Sciences
Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks
Mathematics of Operations Research
Exact tail asymptotics in a priority queue--characterizations of the non-preemptive model
Queueing Systems: Theory and Applications
Geometric tail of queue length of low-priority customers in a nonpreemptive priority MAP/PH/1 queue
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Hi-index | 0.00 |
We consider a discrete-time two-dimensional process $\{(L_{n}^{(1)},L_{n}^{(2)})\}$ on $\mathbb{Z}_{+}^{2}$ with a background process {J n } on a finite set, where individual processes $\{L_{n}^{(1)}\}$ and $\{L_{n}^{(2)}\}$ are both skip free. We assume that the joint process $\{Y_{n}\}=\{(L_{n}^{(1)},L_{n}^{(2)},J_{n})\}$ is Markovian and that the transition probabilities of the two-dimensional process $\{(L_{n}^{(1)},L_{n}^{(2)})\}$ 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 $\mathbb{Z}_{+}^{2}$ 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.