CRITIQUEUE · Critical queues and reflected stochastic processes

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 largebody 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 atthe affiliated institution EURANDOM.