By deriving a new set of tight perturbation bounds, it is shown that all stationary probabilities of a finite irreducible Markov chain react essentially in the same way to perturbations in the transition probabilities. In particular, if at least one stationary probability is insensitive in a relative sense, then all stationary probabilities must be insensitive in an absolute sense. New measures...

Commonsense sometimes predicts events to be likely or unlikely rather than merely possible. We extend methods of qualitative reasoning to predict the relative likelihoods of possible qualitative behaviors by viewing the dynamics of a system as a Markov chain over its transition graph. This involves adding qualitative or quantitative estimates of transition probabilities to each of the transitio...

Objective: In this study we consider a two-state retrial queueing system with feedback having two identical parallel servers. Transient state probabilities for exact number of arrivals and departures from the will be obtained when both, one or none servers is busy. Numerical graphical solutions also obtained. Methods: The difference-differential equations governing are solved recursively, Lapla...

This study aims to determine the transient behavior of blended queue. Priority customers arrive over time and benefit from a threshold reservation policy, while non-priority ones can be contacted at any time. We show how compute Laplace transforms probabilities. Using uniformization technique, we prove some monotonicty properties expected number in queue, explaining why optimal should lower tha...

This paper analyzes large deviation probabilities related to the number of customers in a Markov modulated infinite-server queue, with state-dependent arrival and service rates. Two specific scalings are studied: in the first, just the arrival rates are linearly scaled by N (for large N ), whereas in the second in addition the Markovian background process is sped up by a factor N , for some > 0...

Time dependent system size probabilities of a birth and death process related to the Rogers-Ramanujan continued fraction are obtained. The range for the parameter in this continued fraction is obtained to ensure the positivity of the recursively defined birth and death rates. The general behavior of the birth and death rates is described and the asymptotic behavior of the transition probabiliti...