arXiv subjects

Werner Scheinhardt

Publications and source records attributed to Werner Scheinhardt.

3 recordsLinked to original sources

arXiv2026

Exact analysis of transient behavior of finite-capacity MAP-driven queues

This paper studies the workload distribution of a finite-capacity queue driven by a spectrally one-sided Markov additive process (MAP). Our main result provides the Laplace-Stieltjes transform of the workload at an exponentially distributed time, thereby uniquely characterizing its transient distribution. The proposed approach combines several decompositions with established fluctuation-theoretic results for spectrally one-sided L\'evy processes. For the special case of Markov-modulated compound Poisson input, we additionally derive results for the idle time and the cumulative amount of lost work. We conclude this paper with a series of numerical experiments.

math.PR↗

arXiv2021

Diffusion Parameters of Flows in Stable Multi-class Queueing Networks

We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes the system stable. We study the variability of flows within the network. Computable expressions for quantifying flow variability have previously been discussed in the literature. However, in this paper, we shed more light on such analysis to justify the use of these expressions in the asymptotic analysis of network flows. Towards that end, we find a simple diffusion limit for the inter-class flows and establish the relation to asymptotic (co-)variance rates.

math.PR↗

arXiv2018

Path-ZVA: general, efficient and automated importance sampling for highly reliable Markovian systems

We introduce Path-ZVA: an efficient simulation technique for estimating the probability of reaching a rare goal state before a regeneration state in a (discrete-time) Markov chain. Standard Monte Carlo simulation techniques do not work well for rare events, so we use importance sampling; i.e., we change the probability measure governing the Markov chain such that transitions `towards' the goal state become more likely. To do this we need an idea of distance to the goal state, so some level of knowledge of the Markov chain is required. In this paper, we use graph analysis to obtain this knowledge. In particular, we focus on knowledge of the shortest paths (in terms of `rare' transitions) to the goal state. We show that only a subset of the (possibly huge) state space needs to be considered. This is effective when the high dependability of the system is primarily due to high component reliability, but less so when it is due to high redundancies. For several models we compare our results to well-known importance sampling methods from the literature and demonstrate the large potential gains of our method.

math.PR↗