Account of disasters in analysis of queueing systems modeled by the quasi-birth-and-death-process

DOI10.1007/978-3-031-32990-6_8OpenAlexW4376485311MaRDI QIDQ6201637

Alexander N. Dudin

Publication date: 25 March 2024

Published in: Information Technologies and Mathematical Modelling. Queueing Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-32990-6_8

zbMATH Keywords

stationary distributiondisasterquasi-birth-and-death process

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Kronecker products and their applications
• Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory
• Semi-stationary clearing processes
• Wiener-Hopf analysis of an M/G/1 queue with negative customers and of a related class of random walks
• Analysis of multiserver queueing system with opportunistic occupation and reservation of servers
• \(M A P + M A P / M_2 / N / \infty\) queueing system with absolute priority and reservation of servers
• Steady state analysis of level dependent quasi-birth-and-death processes with catastrophes
• Stochastic clearing systems
• A catastrophic queueing model with delayed action
• A disaster queue with Markovian arrivals and impatient customers
• A Pollaczek–Khintchine formula for M/G/1 queues with disasters
• New results on the single server queue with a batch markovian arrival process
• Queues with negative arrivals
• Product-form queueing networks with negative and positive customers
• TheM/M/1 queue with mass exodus and mass arrivals when empty
• BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery
• The censored Markov chain and the best augmentation
• A stable algorithm for stationary distribution calculation for a BMAP/SM/1 queueing system with Markovian arrival input of disasters
• A BMAP/SM/1 queueing system with Markovian arrival input of disasters
• Introduction to Matrix‐Analytic Methods in Queues 1
• The Theory of Queuing Systems with Correlated Flows
• Markov Chains with Hybrid Repeating Rows - Upper-Hessenberg, Quasi-Toeplitz Structure of the Block Transition Probability Matrix
• Markov renewal theory