Mathematical methods to study the polling systems

DOI10.1134/S0005117906020019zbMath1126.60321MaRDI QIDQ2457500

Yanyan Li

Publication date: 23 October 2007

Published in: Automation and Remote Control (Search for Journal in Brave)

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items (58)

Polling: past, present, and perspective ⋮ A duplex cyclic polling system for mixed queues ⋮ ON A GENERIC CLASS OF LÉVY-DRIVEN VACATION MODELS ⋮ The shorter queue polling model ⋮ Optimal routeing in two-queue polling systems ⋮ On two-level state-dependent routing polling systems with mixed service ⋮ An algorithm for the computation of mean delay of traffic at pre-timed control signals ⋮ Controlled mobility in stochastic and dynamic wireless networks ⋮ A polling model with smart customers ⋮ On open problems in polling systems ⋮ A mathematical model of transmitting a non-ordinary flow with periodic reservations and block acknowledgements in a channel with correlated noise ⋮ A model of the polling system for studying the broadband wireless networks ⋮ Queueing systems with correlated arrival flows and their applications to modeling telecommunication networks ⋮ On competitive analysis for polling systems ⋮ Performance analysis of polling systems with retrials and glue periods ⋮ Queue lengths and workloads in polling systems ⋮ Polling Models with Unequal Service Rates under Limited Service Policies—Sharp Asymptotics ⋮ Branching-type polling systems with large setups ⋮ Analysis of queueing system with non-preemptive time limited service and impatient customers ⋮ Queueing for an infinite bus line and aging branching process ⋮ Polling systems with batch service ⋮ Method of Generating Functions for Performance Characteristic Analysis of the Polling Systems with Adaptive Polling and Gated Service ⋮ Analysis of tandem polling queues with finite buffers ⋮ Multitype branching processes with immigration in random environment, and polling systems ⋮ Processor sharing: a survey of the mathematical theory ⋮ POLLING SYSTEMS WITH TWO-PHASE GATED SERVICE ⋮ On ergodicity conditions in a polling model with Markov modulated input and state-dependent routing ⋮ On two-queue Markovian polling systems with exhaustive service ⋮ Computing the Moments of Polling Models with Batch Poisson Arrivals by Transform Inversion ⋮ On a 2-class polling model with reneging and \(k_i\)-limited service ⋮ Transient analysis for exponential time-limited polling models under the preemptive repeat random policy ⋮ Heavy traffic analysis of a polling model with retrials and glue periods ⋮ Towards a unifying theory on branching-type polling systems in heavy traffic ⋮ Reduction of a polling network to a single node ⋮ A New Method for Deriving Waiting-Time Approximations in Polling Systems with Renewal Arrivals ⋮ On global near optimality of special periodic protocols for fluid polling systems with setups ⋮ DELAYS AT SIGNALIZED INTERSECTIONS WITH EXHAUSTIVE TRAFFIC CONTROL ⋮ Performance evaluation of a single-stage two-product manufacturing system operating under pull-type control ⋮ A polling model with reneging at polling instants ⋮ Polling models with multi-phase gated service ⋮ Gated polling with stationary ergodic walking times, Markovian routing and random feedback ⋮ Two queues with random time-limited polling ⋮ The impact of scheduling policies on the waiting-time distributions in polling systems ⋮ Heavy-traffic limits for polling models with exhaustive service and non-FCFS service order policies ⋮ An Analysis of Asymmetrical Threshold Polling Systems ⋮ Analysis of the waiting time distribution for polling systems with retrials and glue periods ⋮ Stability of periodic polling system with BMAP arrivals ⋮ Delay analysis of a discrete-timeGI−GI− 1 queue with reservation-based priority scheduling ⋮ Analysis of polling models with a self-ruling server ⋮ Investigation of the stochastic polling system and its applications to broadband wireless networks ⋮ Ordinal optimization of \(G/G/1/K\) polling systems with \(k\)-limited service discipline ⋮ A 2-class maintenance model with dynamic server behavior ⋮ The unobserved waiting customer approximation ⋮ A polling model with an autonomous server ⋮ On analysis of periodic polling systems ⋮ L\'evy-driven polling systems and continuous-state branching processes ⋮ Comments on: ``Polling: past, present and perspective ⋮ Asymptotic optimality of the binomial-exhaustive policy for polling systems with large switchover times

Cites Work

• A new approach to analysis of polling systems
• Two queues with alternating service and server breakdown
• Some properties of polling systems
• Dominance relations in polling systems
• Expected waiting times in polling systems under priority disciplines
• A numerical approach to cyclic-service queueing models
• Conditions of existence of steady-state modes in cyclic queueing systems
• Efficient visit frequencies for polling tables: Minimization of waiting cost
• On pseudo-conservation laws for the cyclic server system with compound Poisson arrivals
• Average waiting time of a symmetric polling system under Bernoulli scheduling
• Stability of token passing rings
• Stability, monotonicity and invariant quantities in general polling systems
• On optimal polling policies
• On Elevator polling with globally gated regime
• A cyclic-service finite source model with round-robin scheduling
• A decomposition result for a class of polling models
• A queueing network with a single cyclically roving server
• A note on the pseudo-conservation law for a multi-queue with local priority
• An approximate analysis of a cyclic server queue with limited service and reservations
• Performance evaluation of polling systems by means of the power-series algorithm
• Cyclic reservation schemes for efficient operation of multiple-queue single-server systems
• Polling systems with synchronization constraints
• Dynamic priority rules when polling with multiple parallel servers
• A continuous polling system with general service times
• Performance analysis and optimization of a cyclic-service tandem queueing system with multi-class customers
• Optimal robot scheduling for web search engines
• Some reflections on the renewal-theory paradox in queueing theory
• Dynamic server assignment in a two-queue model
• A two-queue model with Bernoulli service schedule and switching times
• Threshold start-up control policy for polling systems
• Beyond the \(c\mu\) rule: Dynamic scheduling of a two-class loss queue
• Polling systems in heavy traffic: Higher moments of the delay
• Decomposition results for general polling systems and their applications
• Pseudo-cyclic policies for multi-queue single server systems
• Stochastic bounds for a polling system
• Stability conditions for a pipeline polling scheme in satellite communications
• Stability and continuity of polling systems
• Ergodicity of a polling network
• Approximating queue size and waiting time distributions in general polling systems
• The polling system with a stopping server
• On polling systems with infinitely many stations
• Exact analysis of asymmetric random polling systems with single buffers and correlated input process
• Polling on a space with general arrival and service time distribution
• Analysis of an asymmetric polling system
• Exponents for the tails of distributions in some polling models
• Two parallel finite queues with simultaneous services and Markovian arrivals
• Assigning a single server to inhomogeneous queues with switching costs
• Polling systems in heavy traffic: Exhaustiveness of service policies
• Polling systems with breakdowns and repairs.
• Analysis of random polling system with an infinite number of coupled servers and correlated input process.
• On the value function of a priority queue with an application to a controlled polling model
• Closed polling models with failing nodes
• Gated polling models with customers in orbit.
• Large deviations rate function for polling systems
• Exact analysis of the state-dependent polling model
• Gated polling systems with Lévy inflow and inter-dependent switchover times: A dynamical-systems approach
• Finite buffer polling models with routing
• Discrete-time queueing systems and their application to analysis of optical-fiber communication networks
• Numerical study of the optimal control of a system with heterogeneous servers
• A stability criterion via fluid limits and its application to a polling system
• Ergodicity of a polling network with an infinite number of stations
• Analysis of infinite servers polling systems with correlated input process and state dependent vacations
• A production system with two job classes, changeover times and revisitation
• Production scheduling in a flexible manufacturing system under random demand
• Waiting-time distributions in polling systems with simultaneous batch arrivals
• A communication multiplexer problem: Two alternating queues with dependent randomly-timed gated regime
• Exact asymptotics for \(k_i\)-limited exponential polling models
• Two-queue polling models with a patient server
• Polling systems in the critical regime.
• Polling systems with periodic server routing in heavy traffic: renewal arrivals
• Relating polling models with zero and nonzero switchover times
• Stochastic scheduling of parallel queues with set-up costs
• Stability of non-Markovian polling systems
• Polling systems with zero switchover times: A heavy-traffic averaging principle
• Dynamic scheduling with convex delay costs: The generalized \(c\mu\) rule
• Polling systems with multiple coupled servers
• Stability of polling systems with exhaustive service policies and state-dependent routing
• Optimal control of polling models for transportation applications
• The archievable region method in the optimal control of queueing systems; formulations, bounds and policies
• Markovian polling systems with mixed service disciplines and retrial customers
• An interpolation approximation for expected wait in a time-limited polling system
• Polling systems and multitype branching processes
• Polling systems with state-dependent setup times
• LIMIT THEOREMS FOR POLLING MODELS WITH INCREASING SETUPS
• GEOMETRIC DECAY OF THE STEADY-STATE PROBABILITIES IN A QUASI-BIRTH-AND-DEATH PROCESS WITH A COUNTABLE NUMBER OF PHASES
• Polling Systems in Heavy Traffic: A Bessel Process Limit
• Optimization of Multiclass Queueing Networks with Changeover Times Via the Achievable Region Approach: Part II, The Multi-Station Case
• Control of a Single-Server Tandem Queueing System with Setups
• Models for Design and Control of Single Server Polling Computer and Communication Systems
• Dynamic Scheduling of a Two-Class Queue with Setups
• Heavy Traffic Analysis of Polling Systems in Tandem
• Performance Bounds and Pathwise Stability for Generalized Vacation and Polling Systems
• When Does Forced Idle Time Improve Performance in Polling Models?
• Stability of Polling Networks with State-Dependent Server Routing
• DYNAMIC VISIT-ORDER RULES FOR BATCH-SERVICE POLLING
• Polling systems with station breakdowns
• Study of a class of partially ordered service strategies for a system of two discrete-time queues
• Optimization of polling systems with Bernoulli schedules
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cyclic Bernoulli polling
• A golden ratio control policy for a multiple-access channel
• Sojourn times in vacation and polling systems with Bernoulli feedback
• Analysis of polling systems with mixed service disciplines
• Heavy Traffic Analysis of Dynamic Cyclic Policies: A Unified Treatment of the Single Machine Scheduling Problem
• Pseudo-conservation laws in cyclic-service systems
• Queuing analysis of polling models
• Analysis of cyclic service systems with limited service: Bounds and approximations
• Nondeterministic Polling Systems
• ANALYSIS OF BATCH ARRIVAL CYCLIC SERVICE MULTIQUEUE SYSTEMS WITH LIMITED SERVICE DISCIPLINE
• Optimal scheduling of two competing queues with blocking
• The power-series algorithm applied to cyclic polling systems
• Polling systems with zero switch-over periods: a general method for analyzing the expected delay
• Discrete-time priority queues with two-state markov modulated arrivals
• Waiting Lines and Times in a System with Polling
• Dynamic server allocation to parallel queues with randomly varying connectivity
• A single server n-line queue in which a customer may receive special treatment
• Expected delay analysis of polling systems in heavy traffic
• General dynamic programming algorithms applied to polling systems
• Polling systems with periodic server routing in heavy traffic
• On the stability of polling models with multiple servers
• Polling systems with permanent and transient jobs
• Delay in polling systems with large switch-over times
• The Power-Series Algorithm for Polling Systems with Time Limits
• Efficient visit orders for polling systems
• Delay analysis of various service disciplines in symmetric token passing networks
• Performance analysis of Markovian polling systems with single buffers
• Gated–type polling systems with walking and switch-in times
• Queueing in space
• Computing distributions and moments in polling models by numerical transform inversion
• Analysis of a two-queue model with Bernoulli schedules
• Analysis of multiple-server polling systems by means of the power-series algorithm
• A Closed Form Solution for the Asymmetric Random Polling System with Correlated Levy Input Process
• Heuristic Scheduling of Parallel Heterogeneous Queues with Set-Ups
• Polling Models With and Without Switchover Times
• Heavy traffic analysis for continuous polling models
• An optimal service policy for buffer systems
• Analysis of a priority polling system with group services
• Polling under the randomly timed gated regime
• A POLLING MODEL WITH RETRIAL CUSTOMERS
• A Two‐Queue Polling Model with Regularly Varying Service and/or Switchover Times
• Polling systems with periodic server routeing in heavy traffic: distribution of the delay
• PERFORMANCE ANALYSIS OF A TWO-QUEUE MODEL WITH AN (M,N)-THRESHOLD SERVICE SCHEDULE
• MORE ON USING FORCED IDLE TIME TO IMPROVE PERFORMANCE IN POLLING MODELS
• Control of Polling in Presence of Vacations in Heavy Traffic with Applications to Satellite and Mobile Radio Systems
• MEAN WAITING TIMES OF THE ALTERNATING TRAFFIC WITH STARTING DELAYS
• SECOND MOMENTS OF THE WAITING TIME IN SYMMETRIC POLLING SYSTEMS
• A novel approach to queue stability analysis of polling models
• Distribution of the delay in polling systems in heavy traffic
• OPTIMAL CONTROL OF PARALLEL QUEUES WITH BATCH SERVICE
• Waiting times in a two-queue model with exhaustive and Bernoulli service
• Optimal Control of Arrivals to Token Ring Networks with Exhaustive Service Discipline
• Polling, Greedy and Horizon Servers on a Circle
• A State-Dependent Polling Model with Markovian Routing
• Parallel Service with Vacations
• A two-queue model with exhaustive and limited service disciplines
• Ergodicity, moment stability and central limit theorems of station times in polling systems
• PSEUDO-CONSERVATION LAW FOR DISCRETE-TIME MULTI-QUEUE SYSTEMS WITH PRIORITY DISCIPLINES
• Setups in polling models: does it make sense to set up if no work is waiting?
• On the Stability of Greedy Polling Systems with General Service Policies
• Dynamic scheduling in single-server multiclass service systems with unit buffers
• ANALYSIS OF AN M/G/1//N QUEUE WITH MULTIPLE SERVER VACATIONS, AND ITS APPLICATION TO A POLLING MODEL
• Monotonicity of Optimal Performance Measures for Polling Systems
• A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive
• Modeling And Analysis Of A Single-Buffer Polling System Interconnected With External Networks
• The snowblower problem
• Optimal open-loop control of vacations, polling and service assignment
• Polling systems with switch-over times under heavy load: Moments of the delay
• Queueing models with multiple waiting lines
• The relationship between preventive maintenance and manufacturing system performance
• Monotone control of queueing systems with heterogeneous servers
• Approximations for the waiting time distribution in polling models with and without state-dependent setups

This page was built for publication: Mathematical methods to study the polling systems