Preemption rates for a parallel link loss network
Performance Evaluation
On deriving and incorporating multihop path duration estimates in VANET protocols
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Compositional abstraction of PEPA models for transient analysis
EPEW'10 Proceedings of the 7th European performance engineering conference on Computer performance engineering
On the convergence rate of quasi lumpable markov chains
EPEW'06 Proceedings of the Third European conference on Formal Methods and Stochastic Models for Performance Evaluation
An embedded Markov chain approach to stock rationing
Operations Research Letters
Compositional approximate markov chain aggregation for PEPA models
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Compositional approximate markov chain aggregation for PEPA models
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
| Hi-index | 0.00 |
In this paper, it is shown that nearly completely decomposable (NCD) Markov chains are quasi-lumpable. The state space partition is the natural one, and the technique may be used to compute lower and upper bounds on the stationary probability of each NCD block. In doing so, a lower-bounding nonnegative coupling matrix is employed. The nature of the stationary probability bounds is closely related to the structure of this lower-bounding matrix. Irreducible lower-bounding matrices give tighter bounds compared with bounds obtained using reducible lower-bounding matrices. It is also noticed that the quasi-lumped chain of an NCD Markov chain is an ill-conditioned matrix and the bounds obtained generally will not be tight. However, under some circumstances, it is possible to compute the stationary probabilities of some NCD blocks exactly.