Diffusion approximations for queues with server vacations

DOI10.2307/1427465zbMath0713.60101OpenAlexW2335474922MaRDI QIDQ3198669

Ward Whitt, Offer Kella

Publication date: 1990

Published in: Unnamed Author (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1427465

zbMATH Keywords

renewal processstochastic decompositiontraffic intensityreflected Brownian motionsingle-server queueing systemsHeavy-traffic diffusion approximations

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items (27)

Heavy-traffic limits for an infinite-server fork-join queueing system with dependent and disruptive services ⋮ Diffusion approximations for open queueing networks with service interruptions ⋮ Heavy-traffic limits for many-server queues with service interruptions ⋮ Further applications of a general rate conservation law ⋮ Another look into decomposition results ⋮ Customer-Server Population Dynamics in Heavy Traffic ⋮ A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation ⋮ Fluid approximation and its convergence rate for GI/G/1 queue with vacations ⋮ Boundary behavior and product-form stationary distributions of jump diffusions in the orthant with state-dependent reflections ⋮ Heavy traffic approximation for the stationary distribution of stochastic fluid networks ⋮ Many-server heavy-traffic limit for queues with time-varying parameters ⋮ On functional limit theorems for the cumulative times in alternating renewal processes ⋮ An interpolation approximation for expected wait in a time-limited polling system ⋮ Sub-exponential rate of convergence to equilibrium for processes on the half-line ⋮ Diffusion approximations for \(GI/M/s\) queues with service interruptions ⋮ Fluid approximation for generalized Jackson network with vacations ⋮ Existence and characterization of product-form invariant distributions for state-dependent stochastic networks in the heavy-traffic diffusion limit ⋮ Continuity of a queueing integral representation in the \(M_{1}\) topology ⋮ On product-form stationary distributions for reflected diffusions with jumps in the positive orthant ⋮ Optimal control of assignment of jobs to processors under heavy traffic ⋮ Brownian models of multiclass queueing networks: Current status and open problems ⋮ Asymptotic independence of regenerative processes with a special dependence structure ⋮ A radial basis function approach to compute the first-passage probability density function in two-dimensional jump-diffusion models for financial and other applications ⋮ Explicit Rates of Exponential Convergence for Reflected Jump-Diffusions on the Half-Line ⋮ On Singular Control Problems, the Time-Stretching Method, and the Weak-M1 Topology ⋮ Heavy-traffic asymptotics for networks of parallel queues with Markov-modulated service speeds ⋮ \(\mathrm{G}/\mathrm{GI}/N (+ \mathrm{GI})\) queues with service interruptions in the Halfin-Whitt regime

This page was built for publication: Diffusion approximations for queues with server vacations