Çok eşikli geribeslemeli akışkan kuyruk sistemleri

Unlike discrete or continuous time queuing systems fed with point processes, workload influid queues arrives at the system as a fluid flow rather than jobs or packets. The rate of thefluid flow is governed by a continuous time Markov chain in Markov fluid queues. In firstorder fluid queues, rates are deterministically determined by a background Markov chainwhereas in second order fluid queues, a Brownian motion is additionally inserted to the queuecontent process. Each of those queues can either accommodate a single regime or multipleregimes (equivalently multiple thresholds) in which the rates and the infinitesimal generatormight be different in different regimes but they should be fixed within a single regime. In thisthesis, we first generalize the existing solution of first order feedback fluid queues withmultiple thresholds for the steady state distribution function of queue occupancy by alsoallowing the existence of repulsive type boundaries and states with zero rates. Secondly, wecomplete the boundary conditions for not only the transient but also the steady state solutionof second order feedback fluid queues with multiple thresholds. Finally, we apply the theoryof feedback fluid queues with multiple thresholds as an effective approximation to theMarkov modulated discrete time queueing model that arises in the performance evaluation ofan adaptive MPEG video streaming system in UMTS environment. By doing so, we eliminatethe state space explosion problem that arises in the original discrete model.Keywords: Markov fluid queues, fluid queues with multiple thresholds, second order fluidqueues, Brownian motion.