Stochastic decomposition in discrete-time queues with generalized vacations and applications

For several specific queueing models with a vacation policy, the stationary system occupancy at the beginning of a rantdom slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. For models in continuous time with Poissonian arrivals, this result is well-known, and referred to as stochastic decomposition, with proof provided by Fuhrmann and Cooper. For models in discrete time, this result received less attention, with no proof available to date. In this paper, we first establish a proof of the decomposition result in discrete time. When compared to the proof in continuous time, conditions for the proof in discrete time are somewhat more general. Second, we explore four different examples: non-preemptive proirity systems, slot-bound priority systems, polling systems, and fiber delay line (FDL) buffer systems. The first two examples are known results from literature that are given here as an illustration. The third is a new example, and the last one (FDL buffer systems) shows new results. It is shown that in some cases the queueing analysis can be considerably simplified using this property

Using discrete event simulation to implement a conceptual model aiming at evaluating the performance of manufacturing lines

The assessment of an organisation's production systems is a crucial stage in the decision-making process for modifying or improving the existing systems. In this project a method of evaluation of the production lines was developed for a company in the educational toy manufacturing sector, being the focus of this project to determine the efficiency of these lines. For this purpose, it was used computer simulations as a tool to evaluate these systems, replicating the observed systems in a virtual environment through the determination and application of statistical distributions that allow mimicking the observed systems and their behaviour. Based on the models created, a set of indicators was analysed to determine which factors influenced the most the production capacity of the studied production lines. The analysis of the results revealed that the minimisation of throughput bottlenecks and their postponement downstream from the original site allows an increase in the productive capacity of the systems and consequently increase the efficiency of it. It was also observed that the use of the parameter efficiency of utilisation, provides powerful insights into the production systems by determining how the production lines are balanced.A avaliação dos sistemas de produção de uma organização é uma etapa crítica para a tomada de decisão no que diz respeito à alteração ou melhoria dos sistemas já existentes. Neste projeto foi desenvolvido um método de avaliação das linhas de produção para uma empresa do setor de produção de brinquedos educativos, sendo o foco deste projeto na determinação da eficiência das mesmas. Para tal recorreu-se ao uso de simulações, onde foi possível replicar os sistemas observados num ambiente virtual através da determinação de distribuições estatísticas que permitem mimetizar os sistemas observados e os seus comportamentos. A partir dos modelos criados um conjunto de indicadores foi analisado para determinar quais os fatores que influenciavam a capacidade produtiva das linhas de produção estudadas. Da análise dos resultados verificou-se que a minimização de estrangulamentos de produção e o seu adiamento para jusante do local original permite um aumento da capacidade produtiva dos sistemas. Verificou-se também que a utilização do parâmetro eficiência de utilização, fornece poderosas perspetivas acerca dos sistemas de produção, ao determinar de que forma as linhas de produção se encontram balanceadas

Matrix-structured manufacturing systems : Simulation performance analysis as a successor to dedicated production lines

ABSTRACT: Growing demand for product variations has led to mass personalized production in the manufacturing industry. Many manufacturers still use traditional product line configurations based on a dedicated manufacturing system (DMS). This system is not considered compatible with ongoing manufacturing trend. The challenge is finding a manufacturing system that would combine high productivity with the flexibility to produce multiple types of products. To this end, a matrix-structured manufacturing system (MMS) was developed. In addition, a reconfigurable manufacturing system (RMS) has been researched as a replacement for the DMS. The problem is that these two systems are not compared performance-wise. Moreover, it has not been investigated in which cases MMS or RMS would provide better compatibility to replace the product line. This Master’s thesis aims to answer how MMS and RMS perform compared to DMS regarding productivity and flexibility. Furthermore, it is evaluated in which manufacturing scenarios MMS provide better performance than RMS and DMS. Finally, thesis seeks to answer what are the benefits and disadvantages of MMS compared to RMS and DMS. To fill this research gap in knowledge, thesis presents a discrete-event simulation experiment. Thesis follows principles of experimental research with deductive approach and collects quantitative data from manufacturing simulation. Theoretical review is conducted focusing on characteristics and background of manufacturing systems. This information is utilized when designing and constructing simulation experiment. Simulation results are evaluated from the following performance perspectives: efficiency, effectiveness, delivery, and operational flexibility. These are based on com mon manufacturing competitive priorities. It was discovered that MMS provides highest workstation utilization and overall production effectiveness. RMS performed best in efficiency, delivery, and flexibility perspective. Flexibility was measured with production scenarios which involved simulated production disturbances and changes in number of products in system. It was found that production flow in MMS is declined significantly when number of products in system increases to high level. DMS resulted lowest in every scenario and performance view. The problem is the inflexibility to alternative production routes making it sensitive to production disruptions. Both MMS and RMS provided notably better productivity and flexibility performance than DMS. Based on the results, MMS is recommended for production scenarios where product variety extends over product family with importance in production customization and high station utilization. RMS is suitable for scenarios where delivery performance with flexibility is crucial.TIIVISTELMÄ: Kasvava määrä tuotevarianttien kysynnälle johtanut massapersonointiin massatuotannossa. Monet teollisuuden yritykset käyttävät yhä perinteisiä tuotelinjakonfiguraatioita, jotka kuuluvat kiinteisiin työasemiin perustuviin tuotantojärjestelmiin (DMS). Kuitenkaan näiden ei nähdä soveltuvan käynnissä olevaan tuotantotrendiin. Haasteena on löytää valmistusjärjestelmä, jossa korkea tuottavuus yhdistyisi joustavuuteen tuottaa monenlaisia tuotteita. Tätä varten kehitettiin matriisirakenteinen valmistusjärjestelmä (MMS). Lisäksi uudelleen konfiguroitavaa valmistusjärjestelmää (RMS) tutkitaan korvaajaksi perinteiselle tuotantolinjalle. Ongelmana on, että näitä kahta järjestelmää ei ole vertailtu suorituskyvyllisesti. Lisäksi ei ole tutkittu, missä tapauksissa MMS tai RMS olisi parempi vaihtoehto perinteisen tuotelinjan korvaajaksi. Tämän Pro gradu -tutkielman tavoitteena on vastata kysymykseen, miten MMS ja RMS suoriutuvat verrattuna perinteiseen tuotelinjaan tarkasteltaessa järjestelmän tuottavuutta ja joustavuutta. Lisäksi arvioidaan, missä valmistusskenaarioissa MMS tarjoaa parempaa suorituskykyä kuin RMS ja DMS. Viimeisenä tutkielmassa pyritään vastaamaan mitkä ovat MMS:n edut ja haitat verrattuna RMS:ään ja DMS:ään. Tutkimusaukon täyttämiseksi opinnäytetyö esittää diskreetti tapahtumapohjaisen simulaation. Tutkielma noudattaa kokeellisen tutkimuksen periaatteita deduktiivisella lähestymistavalla, jossa kerätään kvantitatiivista dataa tuotantosimulaatiosta. Teoreettinen katsaus keskittyy valmistusjärjestelmien ominaispiirteisiin sekä taustaan. Tätä tietoa hyödynnetään suunniteltaessa ja rakentaessa simulaatiokoetta. Simuloinnin tuloksia arvioidaan seuraavista suorituskyvyn näkökulmista: hyötysuhde, tehokkuus, toimituskyky ja järjestelmän joustavuus. Nämä perustuvat yleisiin tuotannon kilpailuprioriteetteihin. Tutkielmassa havaittiin, että MMS tarjoaa korkeimman työaseman käyttöasteen ja tuotantojärjestelmän tehokkuuden. RMS suoriutui parhaiten hyötysuhteen, toimituskyvyn ja joustavuuden näkökulmista. Joustavuutta mitattiin tuotantoskenaarioilla, joissa simuloitiin tuotantohäiriöitä ja muutoksia yhtäaikaisesti valmistettavien tuotteiden määrässä tuotannossa. Tutkielmassa todettiin, että MMS:n tuotantovirta hidastuu merkittävästi, kun valmistettavien tuotteiden määrä järjestelmässä kasvaa korkealle tasolle. DMS suoriutui huonoiten kaikissa skenaarioissa ja suorituskykynäkökulmista. Tämä johtuu joustamattomuudesta vaihtoehtoisille tuotereiteille tekien siitä herkän häiriöille. Molemmat sekä MMS että RMS tarjosivat huomattavasti paremman tuottavuus- ja joustavuuskyvyn kuin DMS. Tutkimuksen tuloksiin perustuen MMS:ää suositellaan tuotantoskenaarioihin, joissa tuotevalikoima ulottuu myös yli tuoteperheen, ja jossa tuotannon kustomointikyky ja korkea työasemien käyttöaste on tärkeää. RMS sopii skenaarioihin, joissa tuotannon toimituskyky ja joustavuus on ratkaisevan tärkeää

Performance Modelling and Optimisation of Multi-hop Networks

A major challenge in the design of large-scale networks is to predict and optimise the total time and energy consumption required to deliver a packet from a source node to a destination node. Examples of such complex networks include wireless ad hoc and sensor networks which need to deal with the effects of node mobility, routing inaccuracies, higher packet loss rates, limited or time-varying effective bandwidth, energy constraints, and the computational limitations of the nodes. They also include more reliable communication environments, such as wired networks, that are susceptible to random failures, security threats and malicious behaviours which compromise their quality of service (QoS) guarantees. In such networks, packets traverse a number of hops that cannot be determined in advance and encounter non-homogeneous network conditions that have been largely ignored in the literature. This thesis examines analytical properties of packet travel in large networks and investigates the implications of some packet coding techniques on both QoS and resource utilisation. Specifically, we use a mixed jump and diffusion model to represent packet traversal through large networks. The model accounts for network non-homogeneity regarding routing and the loss rate that a packet experiences as it passes successive segments of a source to destination route. A mixed analytical-numerical method is developed to compute the average packet travel time and the energy it consumes. The model is able to capture the effects of increased loss rate in areas remote from the source and destination, variable rate of advancement towards destination over the route, as well as of defending against malicious packets within a certain distance from the destination. We then consider sending multiple coded packets that follow independent paths to the destination node so as to mitigate the effects of losses and routing inaccuracies. We study a homogeneous medium and obtain the time-dependent properties of the packet’s travel process, allowing us to compare the merits and limitations of coding, both in terms of delivery times and energy efficiency. Finally, we propose models that can assist in the analysis and optimisation of the performance of inter-flow network coding (NC). We analyse two queueing models for a router that carries out NC, in addition to its standard packet routing function. The approach is extended to the study of multiple hops, which leads to an optimisation problem that characterises the optimal time that packets should be held back in a router, waiting for coding opportunities to arise, so that the total packet end-to-end delay is minimised

A survey of health care models that encompass multiple departments

In this survey we review quantitative health care models to illustrate the extent to which they encompass multiple hospital departments. The paper provides general overviews of the relationships that exists between major hospital departments and describes how these relationships are accounted for by researchers. We find the atomistic view of hospitals often taken by researchers is partially due to the ambiguity of patient care trajectories. To this end clinical pathways literature is reviewed to illustrate its potential for clarifying patient flows and for providing a holistic hospital perspective

A tool for model-checking Markov chains

Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker EÎMC2, where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of EÎMC2

Queueing System Analysis A case study

Mestrado de dupla diplomação com a UTFPR - Universidade Tecnológica Federal do ParanáThe application of simulation tools in the construction of models that represent areal system is increasingly important in the analysis and optimization of production and management processes. This study aims to analyze and optimize a queuing system in a Health Care Unit in the district of Bragança, Portugal. In particular, the check-in process of patients/ customers in the health care unit is analyzed to carry out complementary diagnostic tests, treatments and external consultations in different medical specialities. The health care unit is faced with longer check-in waiting times than desired, so it is intended with this work to find solutions to increase the efficiency of the system. Thus, quantitative models for the management of queues will be approached and studied to indicate the expected performance of the system without having to quantify the waiting cost. Given the complexity of the system, the simulation technique will be used to develop different types of mathematical and logical models that reproduce the behaviour of the system under study. The system was modelled using the Simio R software, which is a tool for modelling discrete events by simulation, based on intelligent objects. A validation model was used to simulate the real system as a parameter for comparing the results obtained from the analysis of 4 alternative scenarios that present solutions for optimizing the queues. The results presented in this study can be used as a decision method and implemented following the reality of the Health Care Unit.A aplicação de ferramentas de simulação na construção de modelos que representem um sistema real tem se mostrado cada vez mais importante na análise e otimização de processos produtivos e administrativos. Esse estudo tem como objetivo a análise e otimização de um sistema de filas de espera numa unidade de saúde do distrito de Bragança, Portugal. Em particular, é analisado o processo de check-in dos pacientes/utentes na unidade de saúde para a realização de exames complementares de diagnóstico, tratamentos e consultas externas nas diferentes especialidades médicas. A unidade de saúde depara-se com tempos de espera de check-in superiores ao desejado, pelo que se pretende com este trabalho encontrar soluções que permitam aumentar a eficiência do sistema. Assim, serão abordados e estudados modelos quantitativos para a gestão de filas de espera com o propósito de indicar o desempenho esperado do sistema sem que seja necessário quantificar o custo de espera. Dada a complexidade do sistema, será usada a técnica de simulação para o desenvolvimento de diferentes tipos de modelos matemáticos e lógicos que reproduzam o comportamento do sistema em estudo. O sistema foi modelado utilizando o software Simio R , que é uma ferramenta de modelagem de eventos discretos por simulação, baseada em objetos inteligentes. Para simular o sistema real foi construído um modelo de validação utilizado como parâmetro de comparação dos resultados obtidos a partir da análise de 4 cenários alternativos que apresentam soluções para otimização das filas de espera. Os resultados apresentados nesse estudo podem ser utilizados como método de decisão e implementados em acordo com a realidade da unidade de saúde

Logistics performances of health care system using queue analysis

As there is a very high demand for health service that exceeds the available capacity, the public healthcare centers are overwhelmed with the long queues or they are delivering the service with relatively very low consultation time. In the existing conditions, patients go as early as they can to the healthcare facilities, waiting in queue, even before the opening and had to wait long time for examination, consultation and diagnosis. However, due to high number of patients at the outpatient departments relative to the number of physicians, it results in an increased workload on the physicians and it shortens the patient consultation time, which has an impact on the patients’ health. The main objective of this research was to study the logistic performances of the healthcare system using queuing analysis. This research used three key performance indicators namely, patient queue length, patient waiting time and consultation time length. The performance evaluation was conducted based on data from patients who visited 69 clinical, surgical and diagnosis departments at the outpatient clinics of the hospital. Queue analysis was performed to determine the operational characteristics using a queue scenario with Poisson arrival, exponential service, infinite population, First Comes First Served (FCFS) discipline and multiple server arrangement. The study showed that the patients’ arrival rate highly exceeded the service rate, in each respective clinical department. The outpatient clinics at the SPHMMC achieved an average total waiting time of 92 minutes to get consultation and nearly 70% of the patients waited for more than 95 minutes. The consultation time was as low as 5.71 minute at the Medical clinic and 6.16 minute at the Ophthalmology clinic and around 60% of the patients saw the doctor for a time less than 10 minutes. Therefore, this research recommends addressing the gaps in human resources and logistical supplies, to implement and enforce a staggered patient scheduling and appointment system and to have serious intervention and control on the dual practice, to ensure a smooth clinic process and to reduce waiting times