Feedback fluid queues with multiple tresholds

Cataloged from PDF version of article.Unlike discrete or continuous time queuing systems fed with point processes, workload in fluid queues arrives at the system as a fluid flow rather than jobs or packets. The rate of the fluid flow is governed by a continuous time Markov chain in Markov fluid queues. In first order fluid queues, rates are deterministically determined by a background Markov chain whereas in second order fluid queues, a Brownian motion is additionally inserted to the queue content process. Each of those queues can either accommodate a single regime or multiple regimes (equivalently multiple thresholds) in which the rates and the infinitesimal generator might be different in different regimes but they should be fixed within a single regime. In this thesis, we first generalize the existing solution of first order feedback fluid queues with multiple thresholds for the steady state distribution function of queue occupancy by also allowing the existence of repulsive type boundaries and states with zero rates. Secondly, we complete the boundary conditions for not only the transient but also the steady state solution of second order feedback fluid queues with multiple thresholds. Finally, we apply the theory of feedback fluid queues with multiple thresholds as an effective approximation to the Markov modulated discrete time queueing model that arises in the performance evaluation of an adaptive MPEG video streaming system in UMTS environment. By doing so, we eliminate the state space explosion problem that arises in the original discrete model.Kankaya, Hüseyin EmreM.S

Resource Allocation and Pricing in Secondary Dynamic Spectrum Access Networks

The paradigm shift from static spectrum allocation to a dynamic one has opened many challenges that need to be addressed for the true vision of Dynamic Spectrum Access (DSA) to materialize. This dissertation proposes novel solutions that include: spectrum allocation, routing, and scheduling in DSA networks. First, we propose an auction-based spectrum allocation scheme in a multi-channel environment where secondary users (SUs) bid to buy channels from primary users (PUs) based on the signal to interference and noise ratio (SINR). The channels are allocated such that i) the SUs get their preferred channels, ii) channels are re-used, and iii) there is no interference. Then, we propose a double auction-based spectrum allocation technique by considering multiple bids from SUs and heterogeneity of channels. We use virtual grouping of conflict-free buyers to transform multi-unit bids to single-unit bids. For routing, we propose a market-based model where the PUs determine the optimal price based on the demand for bandwidth by the SUs. Routes are determined through a series of price evaluations between message senders and forwarders. Also, we consider auction-based routing for two cases where buyers can bid for only one channel or they could bid for a combination of non-substitutable channels. For a centralized DSA, we propose two scheduling algorithms-- the first one focuses on maximizing the throughput and the second one focuses on fairness. We extend the scheduling algorithms to multi-channel environment. Expected throughput for every channel is computed by modelling channel state transitions using a discrete-time Markov chain. The state transition probabilities are calculated which occur at the frame/slot boundaries. All proposed algorithms are validated using simulation experiments with different network settings and their performance are studied

Analysis of generic discrete-time buffer models with irregular packet arrival patterns

De kwaliteit van de multimediadiensten die worden aangeboden over de huidige breedband-communicatienetwerken, wordt in hoge mate bepaald door de performantie van de buffers die zich in de diverse netwerkele-menten (zoals schakelknooppunten, routers, modems, toegangsmultiplexers, netwerkinter- faces, ...) bevinden. In dit proefschrift bestuderen we de performantie van een dergelijke buffer met behulp van een geschikt stochastisch discrete-tijd wachtlijnmodel, waarbij we het geval van meerdere uitgangskanalen en (niet noodzakelijk identieke) pakketbronnen beschouwen, en de pakkettransmissietijden in eerste instantie één slot bedragen. De grillige, of gecorreleerde, aard van een pakketstroom die door een bron wordt gegenereerd, wordt gekarakteriseerd aan de hand van een algemeen D-BMAP (discrete-batch Markovian arrival process), wat een generiek kader creëert voor het beschrijven van een superpositie van dergelijke informatiestromen. In een later stadium breiden we onze studie uit tot het geval van transmissietijden met een algemene verdeling, waarbij we ons beperken tot een buffer met één enkel uitgangskanaal. De analyse van deze wachtlijnmodellen gebeurt hoofdzakelijk aan de hand van een particuliere wiskundig-analytische aanpak waarbij uitvoerig gebruik gemaakt wordt van probabiliteitsgenererende functies, die er toe leidt dat de diverse performantiematen (min of meer expliciet) kunnen worden uitgedrukt als functie van de systeemparameters. Dit resul-teert op zijn beurt in efficiënte en accurate berekeningsalgoritmen voor deze grootheden, die op relatief eenvoudige wijze geïmplementeerd kunnen worden

Modelling activities in a Critical Care Unit

The Critical Care Unit (CCU) is the sector of the hospital where, as the name suggests, critically ill patients receive treatment. The main aim of this research is to identify and apply suitable Operational Research techniques to model patient flow in the CCU at the University Hospital of Wales, Cardiff. The Operational Research techniques employed in this thesis include queueing theory and simulation. These methods have been utilised previously in the field of healthcare with much success. The thesis begins by considering two aspects of queueing theory, namely batch service queueing theory and batch arrival queueing theory. The latter of these is utilised to model patient flow within the CCU. Although queueing theory may be used as a good approximation to activities in the Unit, it does not incorporate all aspects of real-life. Thus discrete-event simulation is suggested as an alternative approach. Two types of statistical analysis, CART and Regression, are applied to both length of stay and mortality variables. The results from these statistical tests are compiled and investigated in more depth. Finally, a discrete event simulation model is built in Visual Basic for Applications, for Microsoft Excel. This simulation model incorporates many of the complexities of a CCU, such as patient priority and cancellation of scheduled patients if all beds on the Unit are occupied. The model is then used to test various "what-if type" scenarios, including the possibility of funding additional beds, the concept of ring-fencing of beds for different levels of care, and the likely effect of reducing the impact of bed-blocking