Perturbation theory for unbounded Markov reward processes with applications to queueing

Consider a perturbation in the one-step transition probabilities and rewards of a discrete-time Markov reward process with an unbounded one-step reward function. A perturbation estimate is derived for the finite horizon and average reward function. Results from [3] are hereby extended to the unbounded case. The analysis is illustrated for one- and two-dimensional queueing processes by an M/M/1-queue and an overflow queueing model with an error bound in the arrival rate.

Sensitivity analysis for Markov reward structures until entrance times

This work presents an estimate of the error on a cumulative reward function until the entrance time of a continuous-time Markov chain into a set, when the infinitesimal generator of this chain is perturbed. The derivation of an error bound constitutes the first part of the paper while the second part deals with an application where the time until saturation is considered for a circuit switched network which starts from an empty state and which is also subject to possible failures.

Sensitivity analysis for Markov reward structures until entrance times

This work presents an estimate of the error on a cumulative reward function until the entrance time of a continuous-time Markov chain into a set, when the infinitesimal generator of this chain is perturbed. The derivation of an error bound constitutes the first part of the paper while the second part deals with an application where the time until saturation is considered for a circuit switched network which starts from an empty state and which is also subject to possible failures.