Modeling and analysis to improve the quality of healthcare services

For many healthcare services or medical procedures, patients have extensive risk of complication or face death when treatment is delayed. When a queue is formed in such a situation, it is very important to assess the suffering and risk faced by patients in queue and plan sufficient medical capabilities in advance to address the concerns. As the diversity of care settings increases, congestion in facilities causes many patients to unnecessarily spend extra days in intensive care facilities. Performance evaluation of current healthcare service systems using queueing theory gains more and more importance because of patient flows and systems complexity. Queueing models have been used in handsome number of healthcare studies, but the incorporation of blocking is still limited. In this research work, we study an efficient two-stage multi-class queueing network system with blocking and phase-type service time distribution to analyze such congestion processes. We also consider parallel servers at each station and first-come-first-serve non-preemptive service discipline are used to improve the performance of healthcare service systems

Stability criteria for controlled queueing networks

We give criteria for the stability of a very general queueing model under different levels of control. A complete classification of stability (or positive recurrence), transience and null-recurrence is presented for the two queue model. The stability and instability results are extended for models with N > 3 queues. We look at a broad class of models which can have the following features: Customers arrive at one, several or all of the queues from the outside with exponential inter arrival times. We often have the case where a arrival stream can be routed so that under different routing schemes each queue can have external arrivals, i.e. we assume we have some control over the routing of the arrivals. We also consider models where the arrival streams are fixed. We view the service in a more abstract way, in that we allow a number к of different service configurations. Under every such service configuration service is provided to some or all of the queues, length of service time can change from one service configuration to another and we can change from one configuration to another according two some control policy. The service times are assumed to be exponentially distributed. The queueing models we consider are networks where, after completion at one queue, a customer might be fed back into another queue where it will be served another time often under with a different service time. These feedback probabilities change with the service configurations. Our interest is in different types of control policies which allow us to change the routing of arrivals and configurations of the service from time to time so that the controlled queue length process (which in most cases is Markov) is stable. The semi-martingale or Lyapunov function methods we use give necessary and sufficient conditions for the stability classification. We will look at some two queue models with different inter arrival and service times where the queueing process is still Markov

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Performance analysis of networks on chips

Modules on a chip (such as processors and memories) are traditionally connected through a single link, called a bus. As chips become more complex and the number of modules on a chip increases, this connection method becomes inefficient because the bus can only be used by one module at a time. Networks on chips are an emerging technology for the connection of on-chip modules. In networks on chips, switches are used to transmit data from one module to another, which entails that multiple links can be used simultaneously so that communication is more efficient. Switches consist of a number of input ports to which data arrives and output ports from which data leaves. If data at multiple input ports has to be transmitted to the same output port, only one input port may actually transmit its data, which may lead to congestion. Queueing theory deals with the analysis of congestion phenomena caused by competition for service facilities with scarce resources. Such phenomena occur, for example, in traffic intersections, manufacturing systems, and communication networks like networks on chips. These congestion phenomena are typically analysed using stochastic models, which capture the uncertain and unpredictable nature of processes leading to congestion (such as irregular car arrivals to a traffic intersection). Stochastic models are useful tools for the analysis of networks on chips as well, due to the complexity of data traffic on these networks. In this thesis, we therefore study queueing models aimed at networks on chips. The thesis is centred around two key models: A model of a switch in isolation, the so-called single-switch model, and a model of a network of switches where all traffic has the same destination, the so-called network of polling stations. For both models we are interested in the throughput (the amount of data transmitted per time unit) and the mean delay (the time it takes data to travel across the network). Single-switch models are often studied under the assumption that the number of ports tends to infinity and that traffic is uniform (i.e., on average equally many packets arrive to all buffers, and all possible destinations are equally likely). In networks on chips, however, the number of buffers is typically small. We introduce a new approximation specifically aimed at small switches with (memoryless) Bernoulli arrivals. We show that, for such switches, this approximation is more accurate than currently known approximations. As traffic in networks on chips is usually non-uniform, we also extend our approximation to non-uniform switches. The key difference between uniform and nonuniform switches is that in non-uniform switches, all queues have a different maximum throughput. We obtain a very accurate approximation of this throughput, which allows us to extend the mean delay approximation. The extended approximation is derived for Bernoulli arrivals and correlated arrival processes. Its accuracy is verified through a comparison with simulation results. The second key model is that of concentrating tree networks of polling stations (polling stations are essentially switches where all traffic has the same output port as destination). Single polling stations have been studied extensively in literature, but only few attempts have been made to analyse networks of polling stations. We establish a reduction theorem that states that networks of polling stations can be reduced to single polling stations while preserving some information on mean waiting times. This reduction theorem holds under the assumption that the last node of the network uses a so-called HoL-based service discipline, which means that the choice to transmit data from a certain buffer may only depend on which buffers are empty, but not on the amount of data in the buffers. The reduction theorem is a key tool for the analysis of networks of polling stations. In addition to this, mean waiting times in single polling stations have to be calculated, either exactly or approximately. To this end, known results can be used, but we also devise a new single-station approximation that can be used for a large subclass of HoL-based service disciplines. Finally, networks on chips typically implement flow control, which is a mechanism that limits the amount of data in the network from one source. We analyse the division of throughput over several sources in a network of polling stations with flow control. Our results indicate that the throughput in such a network is determined by an interaction between buffer sizes, flow control limits, and service disciplines. This interaction is studied in more detail by means of a numerical analysis