Illés Horváth

Extremal P 4 -stable graphs

Abstract We call a graph G k -stable (with respect to some graph H ) if, deleting any k edges of G , the remaining graph still contains H as a subgraph. For a fixed H , the minimum number of edges in a k -stable graph is denoted by S ( k ) . We prove general bounds on S ( k ) and compute the exact value of the function S ( k ) for H = P 4 . The main result can be applied to extremal k -edge-Hamiltonian hypergraphs.

Extremal P4-stable graphs

Abstract We call a graph G k -stable (with respect to some graph H ) if, deleting any k edges of G , the remaining graph still contains H as a subgraph. For a fixed H , the minimum number of edges in a k -stable graph is denoted by S ( k ) . We prove general bounds on S ( k ) and compute the exact value of the function S ( k ) for H = P 4 . The main result can be applied to extremal k -edge-Hamiltonian hypergraphs.

Mean field for performance models with generally distributed-timed transitions

In this paper we extend the mean-field limit of a class of stochastic models with exponential and deterministic delays to include exponential and generally-distributed delays. Our main focus is the rigorous proof of the mean-field limit.

Concentrated Matrix Exponential Distributions

We revisit earlier attempts for finding matrix exponential (ME) distributions of a given order with low coefficient of variation (\(\hbox {cv}\)). While there is a long standing conjecture that for the first non-trivial order, which is order 3, the \(\hbox {cv}\) cannot be less than 0.200902 but the proof of this conjecture is still missing.

A constructive proof of the phase-type characterization theorem

The paper presents a new proof of O’Cinneide’s characterization theorem.[7] It is much simpler than the original one and constructive in the sense that we not only show the existence of a phase type representation, but present a procedure which creates a phase-type representation. We prove that the procedure succeeds when the conditions of the characterization theorem hold.

On the Canonical Representation of Order 3 Discrete Phase Type Distributions

In spite of the fact that discrete phase type (DPH) distributions are used almost as often as continuous phase type (CPH) distributions canonical representation is not available for general (cyclic) order 3 DPH distributions yet.In this paper we investigate the canonical representation of DPH distributions of order 3. During the course of this investigation we find that the problem of canonical representation of order 3 DPH distributions is far more complex than the one of order 3 CPH distribution. As a result we needed to distinguish 8 different subclasses of order 3 DPH distributions, while it was enough to distinguish 3 subclasses of order 3 CPH distributions for their canonical representation. Additionally, we were not able to prove all subclasses of DPH distributions with the relatively simple methodology which was sufficient for the canonical representation of order 3 DPH distributions.

Extremal P4P4-stable graphs

Abstract We call a graph G k -stable (with respect to some graph H ) if, deleting any k edges of G , the remaining graph still contains H as a subgraph. For a fixed H , the minimum number of edges in a k -stable graph is denoted by S ( k ) . We prove general bounds on S ( k ) and compute the exact value of the function S ( k ) for H = P 4 . The main result can be applied to extremal k -edge-Hamiltonian hypergraphs.

Modelling Large Timescale and Small Timescale Service Variability

The performance of service units might depend on various randomly changing environmental effects. It is quite often the case that these effects varies on different time scales. In this paper we consider short and long scale service variability, where the short scale variability affects the instantaneous service speed of the service unit and the large scale effect is defined by a modulating background Markov chain. The main modelling challenge is that the considered short and long range variation results randomness along different axes, the short scale variability along the time axis and the long scale variability along the work axis. The work presents mostly simulation results; the mathematical setup for analytical results is provided, but the actual analysis is subject to future research.

Markovian Queue with Garbage Collection

Garbage collection is a fundamental component of memory management in several software frameworks. We present a general two-dimensional Markovian model of a queue with garbage collection where the input process is Markov-modulated and the memory consumption can be modeled with discretisation. We derive important performance measures (also including garbage collection-related measures like mean garbage collection cycle length). The model is validated via measurements from a real-life data processing pipeline.

Fingerprinting and Reconstruction of Functionals of Discrete Time Markov Chains

We explore various fingerprinting options for functionals of Markov chains with a low number of parameters describing both stationary behaviour and correlation over time. We also present reconstruction methods using lazy Markov chains for the various options. The proposed methods allow for efficient simulation of input data with statistical properties similar to actual real data to serve as realistic input of a data processing system. Possible applications include resource allocation in data processing systems. The methods are validated on data from real-life telecommunication systems.