Consider two Markovian N-policy queueing models in discrete time, one with batch arrival, the other with batch service. In this paper the transient behaviour of both models is studied and the analogous continuous time results are achieved by a limiting process. The steady state solution for the model with batch arrival is derived. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Dissertação(mestrado)-Universidade Federal do Rio Grande, Programa de Pós-Graduação em Engenharia Oceânica, Escola de Engenharia, 2010. / Submitted by Lilian M. Silva (lilianmadeirasilva@hotmail.com) on 2013-04-25T18:45:30Z No. of bitstreams: 1 Uma metodologia para o dimensionamento de frota de rebocadores em terminais portuários uma aplicação ao porto do Rio Grande.pdf: 3651900 bytes, checksum: 1f13ba79f912ee9fc097d08ddfe86268 (MD5) / Approved for entry into archive by Cristiane Silva(cristiane_gomides@hotmail.com) on 2013-05-02T22:36:10Z (GMT) No. of bitstreams: 1 Uma metodologia para o dimensionamento de frota de rebocadores em terminais portuários uma aplicação ao porto do Rio Grande.pdf: 3651900 bytes, checksum: 1f13ba79f912ee9fc097d08ddfe86268 (MD5) / Made available in DSpace on 2013-05-02T22:36:10Z (GMT). No. of bitstreams: 1 Uma metodologia para o dimensionamento de frota de rebocadores em terminais portuários uma aplicação ao porto do Rio Grande.pdf: 3651900 bytes, checksum: 1f13ba79f912ee9fc097d08ddfe86268 (MD5) Previous issue date: 2010 / A operação portuária é um assunto relevante e fundamental para o desenvolvimento do país. Assim, com o intuito de contribuir na melhoria dos sistemas portuários, o presente trabalho aborda uma metodologia para o dimensionamento de frota de rebocadores em terminais portuários, utilizando uma modelagem probabilística para tentar maximizar os serviços oferecidos e, ao mesmo tempo, reduzir os custos incorridos neste sistema. Nesse trabalho é proposta e aplicada uma metodologia para dimensionar a frota de rebocadores para atender ao Porto do Rio Grande, de modo a obter economia e satisfação dos clientes, fazendo uso da técnica de Modelagem de Filas. Foram realizados estudos e análises com os dados de entrada e saída dos navios referente ao ano de 2007, juntamente com o número de operações e solicitações de rebocadores também referente ao mesmo ano. Foram usados dados fornecidos pelo setor de estatística da Superintendência do Porto do Rio Grande (SUPRG) e pela Praticagem da Barra. No processo de modelagem empregado, levando-se em conta dados históricos de chegadas de navios, foi ajustada uma distribuição de Poisson. A aplicação dessa metodologia leva à conclusão de que, para um período útil de 24 horas/dia de funcionamento do Porto, para os anos de 2010 a 2015, o tamanho de frota mais indicado para a situação em análise é de três rebocadores. Também é feita uma aplicação considerando-se apenas os anos de 2010 e 2015, adotando-se, para cada um destes anos, uma hipótese otimista e outra pessimista, além do período de funcionamento de 24 horas/dia. Os resultados mostram que são necessários 3 rebocadores no caso da hipótese otimista (tanto em 2010 como em 2015) e na hipótese pessimista de 2015. Agora, no caso da hipótese pessimista para o ano de 2010, dois rebocadores são suficientes. / The port operation is an important issue and critical to the development of the country. Thus, in order to contribute to the improvement of port systems, this paper discusses a methodology for sizing the fleet of tugs in port terminals, using a probabilistic modeling to try to maximize the services offered and at the same time reducing the costs this system. This paper suggests and applies a methodology to find the appropriate number of tugs to attend the Port of Rio Grande in order to achieve savings and customer satisfaction, making the use of the Technique of Modeling Queues. Extensive research and analysis were conducted with the entry and departure data of vessels for the year 2007, together with the number of operations and requests of tugs on the same year. It was used data provided by industry sector of the Superintendence of the Port of Rio Grande (SUPRG) and the Pilotage Bar. In the modeling process used, taking into account historical data on arrivals of vessels, it was fitted a Poisson distribution. The application of this methodology leads to the conclusion that for a period of 24 working hours / days of operation of the Port, for the years 2010 to 2015, the fleet size more indicated to the situation under consideration is three tugs. Also a simulation is done considering only the years 2010 and 2015, adopting, for each of these years, an optimistic and a more pessimistic assumption, and the operating period of 24 hours / day. The results show that three tugs are needed for the optimistic assumption (in both 2010 and 2015) and two tugs for the pessimist one 2015. Now, for the pessimistic assumption for the year 2010, two tugboats are sufficient.

No description available.

The microservice architectural pattern refers to a system consisting of independently deployable services that communicate across networks. RabbitMQ is a popular message broker that can be used to make this communication possible. An alternative to this is Amazon Simple Queuing Service (SQS), which is a fully managed queuing service. By performing a literature- and case study, two systems with a microservice architecture are developed. One using RabbitMQ to communicate between the services, and the other using Amazon SQS. The systems are compared, with regards to message latency, ease of use and maintainability. The results show that RabbitMQ provides much lower message latency than Amazon SQS. Amazon SQS is however both easier to maintain and to use than RabbitMQ. / En mikrotjänstarkitektur syftar till ett system bestående av tjänster som kan driftsättas oberoende av varandra och som kommunicerar över nätverk. RabbitMQ är en populär meddelandemäklare som nyttjas för att möjliggöra ovan nämnd kommunikation. Ett alternativ till detta är Amazon Simple Queueing Service (SQS), vilket är en meddelandetjänst som helt och hållet förvaltas av Amazon. Genom att utföra en litteratur- och fallstudie utvecklas två system med en mikrotjänstarkitektur. Det ena nyttjar RabbitMQ för kommunikation mellan tjänster, medan det andra använder Amazon SQS. Båda systemen jämförs därefter med hänsyn till meddelandens fördröjning, användarvänlighet samt enkelhet att underhålla. Resultaten visar att meddelanden skickade genom RabbitMQ har mycket lägre fördröjning än de skickade genom Amazon SQS. Ur perspektiven användarvänlighet och enkelhet att underhålla är Amazon SQS ett mer fördelaktigt akternativ än RabbitMQ.

<p>U doktorskoj disertaciji rešavaju se sledeći problemi: problem opisivanja sistema masovnog opsluživanja kada teorija masovnog opsluživanja nailazi na ograničenja primene, problem predviđanja vremena čekanja, problem modelovanja odnosa na tržištu ekspres usluga kao izvora uticaja na redove čekanja, problem upravljanja brojem aktivnih kanala sistema masovnog opsluživanja i problem uticaja na subjektivno vreme čekanja. Primenom elemenata veštačke inteligencije i statističkih metoda razvijen je model za predviđanje parametra vremena čekanja u realnom vremenu pri jedinicama poštanske mreže za pružanje usluga korisnicima.</p> / <p>The dissertation provides answers to the following issues: the problem of describing the queueing system when the queueing theory encounters limitations in its use, predicting the waiting time, the problem of modeling relations in the market of express services as a source of influence on the queues, managing the number of active channels in the queueing systems and the impact on subjective waiting time. Through application of artificial intelligence and statistical methods, a model has been developed which in real time predicts the parameters of waiting time at the units of postal network that provide service to customers.</p>

Since the field of computer networks has rapidly grown in the last two decades, congestion control of traffic loads within networks has become a high priority. Congestion occurs in network routers when the number of incoming packets exceeds the available network resources, such as buffer space and bandwidth allocation. This may result in a poor network performance with reference to average packet queueing delay, packet loss rate and throughput. To enhance the performance when the network becomes congested, several different active queue management (AQM) methods have been proposed and some of these are discussed in this thesis. Specifically, these AQM methods are surveyed in detail and their strengths and limitations are highlighted. A comparison is conducted between five known AQM methods, Random Early Detection (RED), Gentle Random Early Detection (GRED), Adaptive Random Early Detection (ARED), Dynamic Random Early Drop (DRED) and BLUE, based on several performance measures, including mean queue length, throughput, average queueing delay, overflow packet loss probability, packet dropping probability and the total of overflow loss and dropping probabilities for packets, with the aim of identifying which AQM method gives the most satisfactory results of the performance measures. This thesis presents a new AQM approach based on the RED algorithm that determines and controls the congested router buffers in an early stage. This approach is called Dynamic RED (REDD), which stabilises the average queue length between minimum and maximum threshold positions at a certain level called the target level to prevent building up the queues in the router buffers. A comparison is made between the proposed REDD, RED and ARED approaches regarding the above performance measures. Moreover, three methods based on RED and fuzzy logic are proposed to control the congested router buffers incipiently. These methods are named REDD1, REDD2, and REDD3 and their performances are also compared with RED using the above performance measures to identify which method achieves the most satisfactory results. Furthermore, a set of discrete-time queue analytical models are developed based on the following approaches: RED, GRED, DRED and BLUE, to detect the congestion at router buffers in an early stage. The proposed analytical models use the instantaneous queue length as a congestion measure to capture short term changes in the input and prevent packet loss due to overflow. The proposed analytical models are experimentally compared with their corresponding AQM simulations with reference to the above performance measures to identify which approach gives the most satisfactory results. The simulations for RED, GRED, ARED, DRED, BLUE, REDD, REDD1, REDD2 and REDD3 are run ten times, each time with a change of seed and the results of each run are used to obtain mean values, variance, standard deviation and 95% confidence intervals. The performance measures are calculated based on data collected only after the system has reached a steady state. After extensive experimentation, the results show that the proposed REDD, REDD1, REDD2 and REDD3 algorithms and some of the proposed analytical models such as DRED-Alpha, RED and GRED models offer somewhat better results of mean queue length and average queueing delay than these achieved by RED and its variants when the values of packet arrival probability are greater than the value of packet departure probability, i.e. in a congestion situation. This suggests that when traffic is largely of a non bursty nature, instantaneous queue length might be a better congestion measure to use rather than the average queue length as in the more traditional models.

Le présent travail porte sur l’estimation d’un système en temps discret dont l’évolution est décrite par une chaîne semi-markovienne (CSM) d’espace d’état fini. Nous présentons le principe d’invariance sous forme multidimensionnelle pour le noyau semi-markovien (NSM), ainsi que diverses mesures du processus. Ensuite, nous étudions l’estimation non-paramétrique de la loi stationnaire de la CSM, en considérant deux estimateurs différents, et nous montrons qu’ils ont le même comportement asymptotique. La probabilité de la première entrée est également introduite. Nous proposons un estimateur et nous étudions ses propriétés asymptotiques : la convergence forte et la normalité asymptotique.D’autre part, nous nous concentrons sur l’étude de la fiabilité des systèmes semi-markoviens. Nous définissons la fiabilité sur intervalle d’un système dont la fiabilité et la disponibilité sont des cas particuliers et nous étudions les propriétés asymptotiques d’un estimateur proposé. De plus, nous présentons une comparaison de l’estimation des différentes mesures de fiabilité fondées sur deux estimateurs du NSM, en réalisant une trajectoire unique et des observations multiples indépendantes. Ce travail fournit aussi des résultats dans le cas semi-markovien à temps discret avec espace d’état général. Nous évaluons l’approximation de moyenne et de diffusion des chaînes de renouvellement markovien. Enfin, nous nous sommes aussi intéressés à une autre classe des processus pour laquelle nous obtenons des résultats dans le cadre des files d’attente. Nous étudions l’approximation de moyenne pour le modèle d’Engset en temps continu et nous appliquons ce résultat aux files d’attente avec ré-essais. / The present work concerns the estimation of a discrete-time system whose evolution is governed by a semi-Markov chain (SMC) with finitely many states. We present the invariance principle in a multidimensional form for the semi-Markov kernel (SMK) and some associated measures of the process. Afterwards, we study the nonparametric estimation of the stationary distribution of the SMC, considering two different estimators, and we prove that they hold the same asymptotic behavior. We introduce also the first hitting probability. We propose an estimator and study its asymptotic properties : the strong consistency and the asymptotic normality. On the other hand, we focus on the study of the dependability of semi-Markovsystems. We introduce the interval reliability whose special cases are the reliability and the availability measures and we study the asymptotic properties of a proposed estimator. Moreover, we present a comparison of nonparametric estimation for various reliability measures based on two estimators of the SMK, realizing a unique trajectory and multiple independent observations.Furthermore, this work provides results on the discrete-time semi-Markov case with general state space. We evaluate the average and diffusion approximation of Markov renewal chains. Finally, we are also interested in another class of processes for which we obtain results in the framework of queueing systems. We establish the average approximationfor the Engset model in continuous time and we apply this result to retrial queues.

No presente trabalho, estudamos alguns sistemas de partículas interagentes que podem ser vistos como modelos simples de fluxo de tráfego, a saber: O Processo de Hammersley-Aldous-Diaconis e o Processo de Exclusão. Exploramos suas representações como modelos de crescimento no plano. Ênfase é dada aos casos em que há mais de um tipo de partícula, aos processos multiclasses e às suas relações com modelos de filas. Analogia entre os modelos é usada para provar os resultados. Por fim, damos uma nova prova para o cálculo da variância assintótica reescalonada do fluxo de partículas de segunda classe no processo de Hammersley multiclasse em equilíbrio. / In the present work we study the following interacting particle systems which can be seen as simple models of traffic flow: The Hammersley-Aldous-Diaconis Process and the Exclusion Process. We explore the related growth models in the plane. Focus is given to cases where there are more than one kind of particles, to the multitype processes and to their relations with queue models. Analogy between the models is used to prove the results. At last, we give a new proof for the calculation of the asimptotic flux of second class particles in the Multiclass Hammersley process in equilibrium.

O modelo de fila M/M/n+G pode ser usado para descrever o comportamento de uma Central de Atendimento. Nesse modelo as chegadas são Poisson com taxa lambda, o atendimento é exponencialmente distribuído com taxa mi, há n atendentes e os tempos de paciência dos clientes têm distribuição geral. A espera do usuário em fila não pode ultrapassar um tempo (paciência) que tem distribuição G e, se isto ocorrer, ele abandona o sistema. Mandelbaum e Zeltyn [2004] mostraram que existe uma relação linear entre o tempo médio de permanência na fila e a probabilidade de abandono nesses modelos quando a paciência é exponencialmente distribuída. No presente trabalho, estudamos essa relação no caso de distribuiçãao de paciência do tipo mista (com partes discreta e contínua), em que buscamos representar a reação dos usuários às mensagens gravadas reproduzidas periodicamente para aqueles que estão esperando atendimento. Utilizamos duas distribuições de paciência: Exponencial Mista e Uniforme Mista e percebemos que não há uma relação linear entre o tempo médio de espera na fila e a probabilidade de abandono. Observamos que para uma mesma taxa de chegada, o tempo médio de espera na fila é menor para a distribuição de paciência mista quando comparada com a Exponencial ou Uniforme de mesmos parâmetros. Analisamos o que ocorre com essa relação quando alteramos a distribuição do atendimento e percebemos que ela é mais afetada pela média e pelo coeficiente de variação do que pela particular distribuição escolhida para o tempo de serviço. / The M/M/n+G queueing model can be used to describe the behavior of a Call Center. This model has Poisson arrivals with rate lambda, service times are exponentially distributed with rate mi, n agents and the client´s patience time has general distribution. The waiting in line could not exceed a time (patience) which has distribution G, and if it occurs, the client leaves the system. In this models, Mandelbaum and Zeltyn [2004] showed that there is a linear relationship between average waiting time in queue and the probability of abandonment if the distribution of patience is Exponencial. In this work, we study this relationship in the case of patience with mixed distribution (which has discret and continuous parts). Through mixed distributions we try to represent the user´s reaction to recorded messages reproduced periodically when they are waiting for service. We have used Mixed Exponencial and Mixed Uniform distributions and, in both of them, there is not a linear relationship between average waiting time in queue and the probability of abandonment. We observe that for the same arrival rate, the average waiting time in line for mixed distribution is smaller than Exponencial or Uniform distributions with the same parameters. Also, we study the effect on waiting time and abandonment of different distributions of service and we observe that it is more affected by the coeficient of variation and average that by the particular distribution chosen for service.

Este trabalho estuda medidas de desempenho aproximadas em centrais de atendimento, apresentadas pelo modelo M/G/s/r+G. As aproximações são calculadas a partir do modelo M/M/s/r+M(n). Os resultados foram extendidos para o caso de mais de um tipo de cliente, apresentado pelo modelo M/Mi/s/r+Mi(n). Para dois casos particulares com 2 tipos de clientes, as aproximações citadas foram avaliadas numericamente e comparadas com os resultados de referência obtidos através de simulação. Os resultados aproximados comprovam que a aproximação é bastante satisfatória. / We study approximations for performance measures of call centers, represented by M/G/s/r+G queueing model. We use the measures computed in the M/M/s/r+M(n) queueing model. The results were extended for more then one type of customer, represented by M/Mi/s/r+Mi(n) queueing model. For two particular cases with two types of customers, the mentioned approaches were numerically evaluated and compared with the results of reference obtained by simulation. The approximate results show that the approach is quite satisfactory.