The M/G/1 processor-sharing model: Transient behavior

DOI10.1007/BF01158868zbMath0802.68011OpenAlexW2066265020MaRDI QIDQ1319842

M. Yu. Kitaev

Publication date: 18 December 1994

Published in: Queueing Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01158868

zbMATH Keywords

branching processmarked point processrandom measurerandom time changepredictable projectiontransient behaviortime-sharingprocessor-sharingM/G/1 modelvirtual sojourn time distribution

Mathematics Subject Classification ID

Performance evaluation, queueing, and scheduling in the context of computer systems (68M20)

Related Items (12)

On the distribution of the number of customers in the symmetric M/G/1 queue ⋮ Some Time-Dependent Properties of Symmetric M/G/1 Queues ⋮ Additive functionals with application to sojourn times in infinite-server and processor sharing systems ⋮ Time-dependent properties of symmetric queues ⋮ The \(M/G/1\) processor-sharing queue with disasters ⋮ Splitting Trees Stopped when the First Clock Rings and Vervaat's Transformation ⋮ A new look at transient versions of Little's law, and M/G/1 preemptive last-come-first-served queues ⋮ Insensitive bounds for the moments of the sojourn time distribution in the \(M/G/1\) processor-sharing queue ⋮ Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates ⋮ Transient analysis of a Markovian queue with deterministic rejection ⋮ A useful relationship between epidemiology and queueing theory: The distribution of the number of infectives at the moment of the first detection ⋮ Sojourn times in the \(M/ PH/1\) processor sharing queue

Cites Work

• Processor-sharing queues: Some progress in analysis
• Point processes and queues. Martingale dynamics
• The \(M/G/1\) queue with processor sharing and its relation to a feedback queue
• The Fourier-series method for inverting transforms of probability distributions
• A new approach to the M/G/1 processor-sharing queue
• The sojourn-time distribution in the M/G/1 queue by processor sharing
• The M/G/1 processor sharing queue as the almost sure limit of feedback queues
• The steady-state appearance of the M/G/1 queue under the discipline of shortest remaining processing time
• Processor-Shared Time-Sharing Models in Heavy Traffic
• Transient behavior of the M/M/1 queue via Laplace transforms
• The steady-state distribution of spent service times present in theM/G/1 foreground–background processor-sharing queue
• On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes
• Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales
• Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation
• Limit Theorems for Markov Renewal Processes
• Waiting Time Distributions for Processor-Sharing Systems
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