On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

DOI10.1239/jap/1110381381zbMath1077.60070OpenAlexW2020928982MaRDI QIDQ5312851

Yutaka Sakuma, Masakiyo Miyazawa

Publication date: 25 August 2005

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/jap/1110381381

zbMATH Keywords

decay ratesstationary distributionfinite truncation

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Large deviations (60F10) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items (10)

Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes ⋮ Performance analysis of service systems with priority upgrades ⋮ Rare event asymptotics for a random walk in the quarter plane ⋮ Light tail asymptotics in multidimensional reflecting processes for queueing networks ⋮ Solving Quadratic Matrix Equations Arising in Random Walks in the Quarter Plane ⋮ On the exponential of semi-infinite quasi-Toeplitz matrices ⋮ Queues with boundary assistance: The effects of truncation ⋮ Pure threshold strategies for a two-node tandem network under partial information ⋮ Decay rates for quasi-birth-and-death processes with countably many phases and tridiagonal block generators ⋮ Comments on: Light tail asymptotics in multidimensional reflecting processes for queueing networks

Cites Work

• Unnamed Item
• A Markov renewal approach to \(M/G/1\) type queues with countably many background states
• Non-negative matrices and Markov chains. 2nd ed
• The ruin problem for finite Markov chains
• Asymptotics of first passage times for random walk in an orthant
• On the Markov renewal theorem
• Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process
• GEOMETRIC DECAY OF THE STEADY-STATE PROBABILITIES IN A QUASI-BIRTH-AND-DEATH PROCESS WITH A COUNTABLE NUMBER OF PHASES
• On the Theory of Markov Renewal
• A CONVEXITY PROPERTY OF POSITIVE MATRICES
• CONJECTURES ON DECAY RATES OF TAIL PROBABILITIES IN GENERALIZED JACKSON AND BATCH MOVEMENT NETWORKS
• ASYMPTOTIC PROPERTIES OF STATIONARY DISTRIBUTIONS IN TWO-STAGE TANDEM QUEUEING SYSTEMS
• The stationary tail asymptotics in the GI/G/1-type queue with countably many background states

This page was built for publication: On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network