Extremes of Markov-additive processes with one-sided jumps, with queueing applications

DOI10.1007/s11009-009-9140-8zbMath1218.60077OpenAlexW2149004651MaRDI QIDQ539512

A. B. Dieker, M. R. H. Mandjes

Publication date: 30 May 2011

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-009-9140-8

zbMATH Keywords

queueing networksfluctuation theoryMarkov-additive processes

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Inventory, storage, reservoirs (90B05) Markov renewal processes, semi-Markov processes (60K15)

Related Items (13)

Splitting and time reversal for Markov additive processes ⋮ Extreme Value Analysis for a Markov Additive Process Driven by a Nonirreducible Background Chain ⋮ A ruin model with a resampled environment ⋮ Occupation densities in solving exit problems for Markov additive processes and their reflections ⋮ A note on Wiener-Hopf factorization for Markov additive processes ⋮ A factorization of a Lévy process over a phase-type horizon ⋮ First passage of time-reversible spectrally negative Markov additive processes ⋮ Singularities of the matrix exponent of a Markov additive process with one-sided jumps ⋮ First Passage of a Markov Additive Process and Generalized Jordan Chains ⋮ On a generic class of two-node queueing systems ⋮ The correlation function of a queue with Lévy and Markov additive input ⋮ Potential measures of one-sided Markov additive processes with reflecting and terminating barriers ⋮ Fluctuation identities for Omega-killed spectrally negative Markov additive processes and dividend problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Markov additive processes. I: Eigenvalue properties and limit theorems
• Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains
• Busy period analysis, rare events and transient behavior in fluid flow models
• Censoring, factorizations, and spectral analysis for transition matrices with block-repeating entries
• Simple approximations of ruin probabilities
• Superimposed renewal processes and storage with gradual input
• Hitting probabilities in a Markov additive process with linear movements and upward jumps: applications to risk and queueing processes.
• Hitting probabilities and hitting times for stochastic fluid flows
• Russian and American put options under exponential phase-type Lévy models.
• AN INTERMITTENT FLUID SYSTEM WITH EXPONENTIAL ON-TIMES AND SEMI-MARKOV INPUT RATES
• A TANDEM FLUID QUEUE WITH GRADUAL INPUT
• New results on the single server queue with a batch markovian arrival process
• A TANDEM QUEUE WITH LÉVY INPUT: A NEW REPRESENTATION OF THE DOWNSTREAM QUEUE LENGTH
• A Storage Model with a Two-State Random Environment
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• Understanding the Wiener–Hopf factorization for the simple random walk
• Stationary distributions for fluid flow models with or without brownian noise
• M/M/∞ transience revisited
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• MARKOV MODULATED FLUID QUEUES WITH BATCH FLUID ARRIVALS
• A multi-dimensional martingale for Markov additive processes and its applications
• FLUID MODELS WITH JUMPS
• ALGORITHMS FOR RETURN PROBABILITIES FOR STOCHASTIC FLUID FLOWS
• Applied Probability and Queues
• A MARKOV MODULATED FLUID QUEUE WITH BATCH ARRIVALS AND PREEMPTIONS
• A matrix exponential form for hitting probabilities and its application to a Markov-modulated fluid queue with downward jumps
• Spectral analysis of M/G/1 and G/M/1 type Markov chains
• Quasi-Product Forms for Lévy-Driven Fluid Networks
• Applications of factorization embeddings for Lévy processes
• On Maxima and Ladder Processes for a Dense Class of Lévy Process
• Markov additive processes. I
• Efficient algorithms for transient analysis of stochastic fluid flow models
• Joint distributions for interacting fluid queues
• Markov-modulated feedforward fluid networks

This page was built for publication: Extremes of Markov-additive processes with one-sided jumps, with queueing applications