Utilizou-se neste trabalho um sistema de filas contendo três servidores exponenciais, heterogêneos, operando em paralelo. Trocas entre filas são permitidas após o usuário analisar dois aspectos: a diferença entre o tamanho das filas envolvidas na troca e o grau de vizinhança entre elas. O jockeying não é obrigatório, podendo os usuários optar por ele com uma probabilidade de ocorrência de acordo com os aspectos citados. Como resultado deste estudo foi obtida uma equação geral que representa o sistema. O sistema M/(M/1)3 com jockeying probabilístico tem uma ociosidade bem menor que o tradiconal M/Mi/3, alimentado por fila única. Outras características foram analisadas. / We consider a parallel queueing system with three exponential heterogeneous servers where is allowed jockey among queues with no obligation and the customers may choose for it with an occurrence probability after they have been analyzed two aspects: the difference between involved lines lenght in jockeying and the neighborhood degree among them. The effect of this study is a general equation which represents the system. The M/(M/1)3 system with probabilistc jockeying has a smaller idleness than the traditional M/Mi/3 fed from a single queue. We also analysed other characteristics.

Utilizou-se neste trabalho um sistema de filas contendo três servidores exponenciais, heterogêneos, operando em paralelo. Trocas entre filas são permitidas após o usuário analisar dois aspectos: a diferença entre o tamanho das filas envolvidas na troca e o grau de vizinhança entre elas. O jockeying não é obrigatório, podendo os usuários optar por ele com uma probabilidade de ocorrência de acordo com os aspectos citados. Como resultado deste estudo foi obtida uma equação geral que representa o sistema. O sistema M/(M/1)3 com jockeying probabilístico tem uma ociosidade bem menor que o tradiconal M/Mi/3, alimentado por fila única. Outras características foram analisadas. / We consider a parallel queueing system with three exponential heterogeneous servers where is allowed jockey among queues with no obligation and the customers may choose for it with an occurrence probability after they have been analyzed two aspects: the difference between involved lines lenght in jockeying and the neighborhood degree among them. The effect of this study is a general equation which represents the system. The M/(M/1)3 system with probabilistc jockeying has a smaller idleness than the traditional M/Mi/3 fed from a single queue. We also analysed other characteristics.

Long-range dependence in discrete and continuous time Markov chains over a countable state space is defined via embedded renewal processes brought about by visits to a fixed state. In the discrete time chain, solidarity properties are obtained and long-range dependence of functionals are examined. On the other hand, the study of LRD of continuous time chains is defined via the number of visits in a given time interval. Long-range dependence of Markov chains over a non-countable state space is also carried out through positive Harris chains. Embedded renewal processes in these chains exist via visits to sets of states called proper atoms. Examples of these chains are presented, with particular attention given to long-range dependent Markov chains in single-server queues, namely, the waiting times of GI/G/1 queues and queue lengths at departure epochs in M/G/1 queues. The presence of long-range dependence in these processes is dependent on the moment index of the lifetime distribution of the service times. The Hurst indexes are obtained under certain conditions on the distribution function of the service times and the structure of the correlations. These processes of waiting times and queue sizes are also examined in a range of M/P/2 queues via simulation (here, P denotes a Pareto distribution).

Consider a set of N i.i.d. random variables in [0, 1]. When the experimental values of the random variables are arranged in ascending order from smallest to largest, one has the order statistics of the set of random variables. In this note an O(N3) algorithm is developed for computing the probability that the order statistics vector lies in a given rectangle. The new algorithm is then applied to a problem of statistical inference in queues. Illustrative computational results are included.

Weber and Stidham (1987) used submodularity to establish transition monotonicity (a service completion at one station cannot reduce the service rate at another station) for Markovian queueing networks that meet certain regularity conditions and are controlled to minimize service and queueing costs. We give an extension of monotonicity to other directions in the state space, such as arrival transitions, and to arrival routing problems. The conditions used to establish monotonicity, which deal with the boundary of the state space, are easily verified for many queueing systems. We also show that, without service costs, transition-monotone controls can be described by simple control regions and switching functions, extending earlier results. The theory is applied to production/inventory systems with holding costs at each stage and finished goods backorder costs.

Weber and Stidham (1987) used submodularity to establish transition monotonicity (a service completion at one station cannot reduce the service rate at another station) for Markovian queueing networks that meet certain regularity conditions and are controlled to minimize service and queueing costs. We give an extension of monotonicity to other directions in the state space, such as arrival transitions, and to arrival routing problems. The conditions used to establish monotonicity, which deal with the boundary of the state space, are easily verified for many queueing systems. We also show that, without service costs, transition-monotone controls can be described by simple control regions and switching functions, extending earlier results. The theory is applied to production/inventory systems with holding costs at each stage and finished goods backorder costs.

The furious pace of Moore's Law is driving computer architecture into a realm where the the speed of light is the dominant factor in system latencies. The number of clock cycles to span a chip are increasing, while the number of bits that can be accessed within a clock cycle is decreasing. Hence, it is becoming more difficult to hide latency. One alternative solution is to reduce latency by migrating threads and data, but the overhead of existing implementations has previously made migration an unserviceable solution so far. I present an architecture, implementation, and mechanisms that reduces the overhead of migration to the point where migration is a viable supplement to other latency hiding mechanisms, such as multithreading. The architecture is abstract, and presents programmers with a simple, uniform fine-grained multithreaded parallel programming model with implicit memory management. In other words, the spatial nature and implementation details (such as the number of processors) of a parallel machine are entirely hidden from the programmer. Compiler writers are encouraged to devise programming languages for the machine that guide a programmer to express their ideas in terms of objects, since objects exhibit an inherent physical locality of data and code. The machine implementation can then leverage this locality to automatically distribute data and threads across the physical machine by using a set of high performance migration mechanisms. An implementation of this architecture could migrate a null thread in 66 cycles -- over a factor of 1000 improvement over previous work. Performance also scales well; the time required to move a typical thread is only 4 to 5 times that of a null thread. Data migration performance is similar, and scales linearly with data block size. Since the performance of the migration mechanism is on par with that of an L2 cache, the implementation simulated in my work has no data caches and relies instead on multithreading and the migration mechanism to hide and reduce access latencies.

We discuss queueing systems subject to total disasters. If the time intervals between successive disasters are i.i.d. random variables independent of arrival and service process and arrivals form a Poisson process, then the transient and the asymptotic analysis of such models may be based on Feller's Second Renewal Theorem. Several examples are given: the limiting behavior of M/G/1 in case of exponential disasters and its special cases M/M/1, M/M/1/K and M/M/infinity. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Motivated by applications in multimedia streaming and in energy systems, we study duality relations in fi nite queues. Dual of a queue is de fined to be a queue in which the arrival and service processes are interchanged. In other words, dual of the G1/G2/1/K queue is the G2/G1/1/K queue, a queue in which the inter-arrival times have the same distribution as the service times of the primal queue and vice versa. Similarly, dual of a fluid flow queue with cumulative input C(t) and available processing S(t) is a fluid queue with cumulative input S(t) and available processing C(t). We are primarily interested in finding relations between the overflow and underflow of the primal and dual queues. Then, using existing results in the literature regarding the probability of loss and the stationary probability of queue being full, we can obtain estimates on the probability of starvation and the probability of the queue being empty. The probability of starvation corresponds to the probability that a queue becomes empty, i.e., the end of a busy period. We study the relations between arrival and departure Palm distributions and their relations to stationary distributions. We consider both the case of point process inputs as well as fluid inputs. We obtain inequalities between the probability of the queue being empty and the probability of the queue being full for both the time stationary and Palm distributions by interchanging arrival and service processes. In the fluid queue case, we show that there is an equality between arrival and departure distributions that leads to an equality between the probability of starvation in the primal queue and the probability of overflow in the dual queue. The techniques are based on monotonicity arguments and coupling. The usefulness of the bounds is illustrated via numerical results.

As systems have grown bigger and bigger with time message brokers have become popular to help build better and more flexible designed systems. A message broker provides communication between services in a system while still keeping the components independent from one another. This thesis evaluates end-to-end latency and throughput of two of the most popular message broker software. The first message broker is Apache Kafka which uses a commit log to write all messages to disk and a message batching to optimize throughput. The second message broker is RabbitMQ which implements the standardized Advanced MessageQueuing Protocol and, contrary to Kafka, primarily stores messages in the main memory. The throughput and message latency of both brokers were tested by integrating them both in an established system with micro-services and sending messages from one service to another through the message brokers. Results showed that RabbitMQ reached the highest recorded throughput while sendinga large amount of data, and it also reached lower latency on individual messages sent without any queue build up. Kafka had more throughput and lower latency under smaller loads of data, but needs further configuration to become more effective as the default settings are limiting under heavy loads.