Nonlinear Dynamics in Queueing Theory: Determining the Size of Oscillations in Queues with Delay

DOI10.1137/18M1170637zbMath1417.34202OpenAlexW2911654577WikidataQ128491099 ScholiaQ128491099MaRDI QIDQ5382441

Elizabeth Wesson, Sophia Novitzky, Jamol Pender, Richard H. Rand

Publication date: 14 June 2019

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1170637

zbMATH Keywords

Hopf bifurcationdelay differential equationqueueing theoryoperations researchperturbations methodLindstedt's method

Mathematics Subject Classification ID

Queues and service in operations research (90B22) Periodic solutions to functional-differential equations (34K13) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Perturbations of functional-differential equations (34K27)

Related Items (13)

A STOCHASTIC ANALYSIS OF BIKE-SHARING SYSTEMS ⋮ Queues with Updating Information: Finding the Amplitude of Oscillations ⋮ Multidelay Differential Equations: A Taylor Expansion Approach ⋮ Queues with Delayed Information: A Dynamical Systems Perspective ⋮ Examining the dynamics of reactive capacity allocation through a chaos Lens ⋮ Applications of fluid models in service operations management ⋮ Open Problem—Load Balancing Using Delayed Information ⋮ Controlled queueing systems G/G/1 with time shift ⋮ Effect of two forms of feedback on the performance of the rate control protocol (RCP) ⋮ Limiting the oscillations in queues with delayed information through a novel type of delay announcement ⋮ Unnamed Item ⋮ Breaking the Symmetry in Queues with Delayed Information ⋮ The fluid limit of a random graph model for a shared ledger

Cites Work

• Unnamed Item
• Unnamed Item
• Uniqueness and stability of slowly oscillating periodic solutions of delay equations with unbounded nonlinearity
• An infinite-server queue influenced by a semi-Markovian environment
• Uniqueness and stability of slowly oscillating periodic solutions of delay equations with bounded nonlinearity
• The multiplier equation and its application to \(S\)-solutions of a differential delay equation
• Introduction to functional differential equations
• An analysis of queues with delayed information and time-varying arrival rates
• Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations
• Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues
• Minimizing multimodular functions and allocating capacity in bike-sharing systems
• On the floquet multipliers of periodic solutions to nonlinear functional differential equations
• The Impact of Delaying the Delay Announcements
• “We Will Be Right with You”: Managing Customer Expectations with Vague Promises and Cheap Talk
• Differential-Delay Equations
• Analysis and Comparison of Queues with Different Levels of Delay Information
• Improving Service by Informing Customers About Anticipated Delays
• THE IMPACTS OF CUSTOMERS’ DELAY-RISK SENSITIVITIES ON A QUEUE WITH BALKING
• Discrete Choice Methods with Simulation
• On Customer Contact Centers with a Call-Back Option: Customer Decisions, Routing Rules, and System Design
• Specification Tests for the Multinomial Logit Model
• Characteristic Multipliers and Stability of Symmetric Periodic Solutions of . x   (t) = g(x(t - 1))
• A STOCHASTIC ANALYSIS OF BIKE-SHARING SYSTEMS
• The Impact of Delay Announcements in Many-Server Queues with Abandonment
• Queues with Choice via Delay Differential Equations
• INFORMATION AND UNCERTAINTY IN A QUEUING SYSTEM
• Applied Delay Differential Equations
• Limiting diffusion approximations for the many server queue and the repairman problem
• An Introduction to Delay Differential Equations with Applications to the Life Sciences

This page was built for publication: Nonlinear Dynamics in Queueing Theory: Determining the Size of Oscillations in Queues with Delay