Modeling Stochastic Lead Times in Multi-Echelon Systems

In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well defined, which is especially a problem for simulation modeling. In this paper, we use results from queuing theory to define a set of simple lead time processes guaranteeing that (a) orders do not cross and (b) prespecified means and variances of all lead times in the multiechelon system are attained

Performance Evaluation for Hybrid Architectures

In this dissertation we discuss methologies for estimating the performance of applications on hybrid architectures, systems that include various types of computing resources (e.g. traditional general-purpose processors, chip multiprocessors, reconfigurable hardware). A common use of hybrid architectures will be to deploy coarse pipeline stages of application on suitable compute units with communication path for transferring data. The first problem we focus on relates to the sizing the data queues between the different processing elements of an hybrid system. Much of the discussion centers on our analytical models that can be used to derive performance metrics of interest such as, throughput and stalling probability for networks of processing elements with finite data buffering between them. We then discuss to the reliability of performance models. There we start by presenting scenarios where our analytical model is reliable, and introduce tests that can detect their inapplicability. As we transition into the question of reliability of performance models, we access the accuracy and applicability of various evaluation methods. We present results from our experiments to show the need for measuring and accounting for operating system effects in architectural modeling and estimation

Dynamical Modeling of Cloud Applications for Runtime Performance Management

Cloud computing has quickly grown to become an essential component in many modern-day software applications. It allows consumers, such as a provider of some web service, to quickly and on demand obtain the necessary computational resources to run their applications. It is desirable for these service providers to keep the running cost of their cloud application low while adhering to various performance constraints. This is made difficult due to the dynamics imposed by, e.g., resource contentions or changing arrival rate of users, and the fact that there exist multiple ways of influencing the performance of a running cloud application. To facilitate decision making in this environment, performance models can be introduced that relate the workload and different actions to important performance metrics.In this thesis, such performance models of cloud applications are studied. In particular, we focus on modeling using queueing theory and on the fluid model for approximating the often intractable dynamics of the queue lengths. First, existing results on how the fluid model can be obtained from the mean-field approximation of a closed queueing network are simplified and extended to allow for mixed networks. The queues are allowed to follow the processor sharing or delay disciplines, and can have multiple classes with phase-type service times. An improvement to this fluid model is then presented to increase accuracy when the \emph{system size}, i.e., number of servers, initial population, and arrival rate, is small. Furthermore, a closed-form approximation of the response time CDF is presented. The methods are tested in a series of simulation experiments and shown to be accurate. This mean-field fluid model is then used to derive a general fluid model for microservices with interservice delays. The model is shown to be completely extractable at runtime in a distributed fashion. It is further evaluated on a simple microservice application and found to accurately predict important performance metrics in most cases. Furthermore, a method is devised to reduce the cost of a running application by tuning load balancing parameters between replicas. The method is built on gradient stepping by applying automatic differentiation to the fluid model. This allows for arbitrarily defined cost functions and constraints, most notably including different response time percentiles. The method is tested on a simple application distributed over multiple computing clusters and is shown to reduce costs while adhering to percentile constraints. Finally, modeling of request cloning is studied using the novel concept of synchronized service. This allows certain forms of cloning over servers, each modeled with a single queue, to be equivalently expressed as one single queue. The concept is very general regarding the involved queueing discipline and distributions, but instead introduces new, less realistic assumptions. How the equivalent queue model is affected by relaxing these assumptions is studied considering the processor sharing discipline, and an extension to enable modeling of speculative execution is made. In a simulation campaign, it is shown that these relaxations only has a minor effect in certain cases

Queueing models for cable access networks

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Queueing models for cable access networks

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Extensions to the dynamic requirements planning model

"April 1998."Includes bibliographical references (p. 32).by John Ruark

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

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277

Integrated Analytical Performance Evaluation Models of Warehouses

Warehouse design process is a complex process with numerous alternatives at all design stages, with focus on throughput capacity, inventory size and material handling equipment requirements. Enumerating all feasible solutions that satisfy the throughput and storage capacity requirements is not practical. Analytical models play a key role in the preliminary design stages in identifying several good initial warehouse configurations. This research effort pertains to the development of integrated analytical models that address capacity/congestion and inventory issues simultaneously in warehouse systems.The first part of the dissertation focuses on the development of a queueing network model of the "shared-server system," which is an inventory store with a server performing both storage and retrieval operations. First, we modeled the shared-server system using Continuous Time Markov Chains (CTMC) under exponential assumptions. We then developed an approximate queueing network model for general arrivals and general service time distribution, and designed a solution procedure based on the parametric-decomposition method. Later, we extended these models to include multi-server cases.The second part of the dissertation focuses on the development of a queueing-inventory (QI) model of an order-picking system. The configuration of the unit-load that is stored (pallets) is different from that which is retrieved (cases). We developed a single stage QI model with batch processing to represent the material movement in and out of the forward inventory store. We then extended these models to include multi-server cases.The last part of the dissertation focuses on the development of an integrated model that demonstrates the applicability of these key building blocks (the shared-server system and the order-picking system) in developing an end-to-end model of the warehouse system. Extensive numerical experiments indicate that the proposed analytical models can be solved in a computationally efficient manner and are accurate for a wide range of parameter values when compared with simulation estimates.Industrial Engineering & Managemen