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What are the mathematical models used to analyze controllable arrival rates in a queue system?

Layered queueing network

Network congestion

Event (particle physics)

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Mathematical models such as finite capacity, finite source, Markovian queueing models with despondent arrivals , fluid-flow models for queuing networks , Gt/GI/st+GI time-varying fluid models integrated with nonlinear integer programming , single-server retrial queues with event-dependent arrival rates , and single-server exponential queuing systems with arrival and service rates dependent on a Markov chain are utilized to analyze controllable arrival rates in queue systems. These models consider factors like system characteristics, occupancy regulation, inter-arrival time adjustments, event-dependent arrival rates, and state-dependent arrival and service rates to study the impact of controlled arrival rates on queue behavior, delays, and system performance. Each model offers unique insights into managing and optimizing arrival processes within queueing systems for improved efficiency and reduced congestion.

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Book Chapter•DOI Queuing Systems Having Phase-Dependent Arrival and Service Rates John N. Daigle, David M. Lucantoni - Show less +1 more 30 Jun 2021 2 Citations	The paper utilizes a single-server exponential queuing system with phase-dependent arrival and service rates modeled by a Markov chain, employing Neuts's matrix geometric approach for analysis.
Open access•Journal Article•DOI A single server retrial queue with event-dependent arrival rates Ioannis Dimitriou 21 Mar 2023-Annals of Operations Research 1 Citations	Mathematical models in the paper analyze a single-server retrial queue with event-dependent arrival rates, focusing on stability conditions, stationary distribution, and performance measures under high retrial rates.
Open access•Journal Article•DOI Controlling Aircraft Inter-Arrival Time to Reduce Arrival Traffic Delay via a Queue-Based Integer Programming Approach Koki Higasa, Eri Itoh - Show less +1 more 28 Oct 2022-Aerospace 5 Citations	The paper utilizes the Gt/GI/st+GI time-varying fluid model and nonlinear integer programming to analyze and control aircraft inter-arrival times in a queue system.
Open access•Journal Article•DOI Robust Control of Arrivals Into a Queuing Network 01 May 2022-IEEE Transactions on Intelligent Transportation Systems 2 Citations	The paper utilizes a fluid-flow model and sliding mode control approach with predictor-based feedback to regulate arrivals in queuing networks, ensuring desired queue lengths are maintained.
Open access•Journal Article•DOI Investigation of n-policy markovian queueing system with despondent arrivals, retainment of reneged customers and controllable arrival rates Antline Nisha B, Saradha M, Varalakshmi M - Show less +2 more 12 Oct 2022-Journal of Pharmaceutical Negative Results	The mathematical model used is a finite capacity, finite source, Markovian queueing system with despondent arrivals, retainment of reneged customers, and controllable arrival rates.

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