Critical queues and reflected stochastic processes

Recognition: ERCStartingScientific

Description

Our primary motivation stems from queueing theory, the branch of applied probability that deals with congestion phenomena. Congestion levels are typically nonnegative, which is why reflected stochastic processes arise naturally in queueing theory. Other applications of reflected stochastic processes are in the fields of branching processes and random graphs. We are particularly interested in critically-loaded queueing systems (close to 100% utilization), also referred to as queues in heavy traffic. Heavy-traffic analysis typically reduces complicated queueing processes to much simpler (reflected) limit processes or scaling limits. This makes the analysis of complex systems tractable, and from a mathematical point of view, these results are appealing since they can be made rigorous. Within the large body of literature on heavy-traffic theory and critical stochastic processes, we launch two new research lines: (i) Time-dependent analysis through scaling limits. (ii) Dimensioning stochastic systems via refined scaling limits and optimization. Both research lines involve mathematical techniques that combine stochastic theory with asymptotic theory, complex analysis, functional analysis, and modern probabilistic methods. It will provide a platform enabling collaborations between researchers in pure and applied probability and researchers in performance analysis of queueing systems. This will particularly be the case at TU/e, the host institution, and at the affiliated institution EURANDOM.
Degree of recognitionInternational
OrganisationsEuropean Research Council

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Heavy Traffic
Scaling Limit
Applied Probability
Queue
Stochastic Processes
Queueing Theory
Queueing System
Congestion
Queueing Process
Traffic Analysis
Dimensioning
Line
Complex Analysis
Probabilistic Methods
Branching process
Functional Analysis
Asymptotic Theory
Random Graphs
Stochastic Systems
Performance Analysis