Coupled queues with customer impatience

Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state space grows exponentially with the number of queues involved. To cope with this inherent state space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space. (C) 2017 Elsevier B.V. All rights reserved

Development of a parametric-decomposition methodology for solving queueing networks with simultaneous resource possession under capacity restrictions

Motivated by applications in health care systems, this study focused on queueing network models with instances of simultaneous resource possession under capacity restrictions in different stages. Customers during service at certain nodes in the first-level or primary system may simultaneously need service from a second-level server. In this simultaneous resource possession situation, the time the customer spends waiting for the second-level server will impact the overall service time at first-level server and consequently the performance of the entire system. Closed queueing networks and fork/join approximations for one and two-stage systems were used to capture the capacity restriction effects in different sections of the primary system. An iterative algorithm was developed to incorporate the effect of the second-level server on the performance of the entire system. This study used a modular approach rooted in the parametric-decomposition method and two-moment approximations. Different systems showing the proposed building blocks and their combinations to solve more complex systems illustrated the application of the proposed modeling approach.To evaluate the performance prediction accuracy of the solution algorithms, the analytical results were compared to simulation estimates for several configurations with single and multi-server nodes, a wide range of service time variability, and different levels of capacity constraints. The analytical results tracked the simulation estimates well with errors less than 10% in more than 80% of the configurations simulated. Higher errors in the 15% to 20% range were observed for system with low capacity limits, high service time variability (SCV=2), and high demand (p=0.75) for the second-level server

SLA Calculus

For modeling Service-Oriented Architectures (SOAs) and validating worst-case performance guarantees a deterministic modeling method with efficient analysis is presented. Upper and lower bounds for delay and workload in systems are used to describe performance contracts. The SLA Calculus allows one to combine model descriptions for single systems and to derive bounds for reaction time and capacity of composed systems with analytic means. The intended, but not exclusive modeling domain for SLA Calculus are distributed software systems with reaction time constraints. SOAs are a system design paradigm that encapsulate software functions in service applications. Due to their standardized interfaces and accessibility via networks, large systems can be composed from smaller services and presented as services again. A well-known implementation of the service paradigm are Web Services that allow applications with components connected by the Internet. Own services and those rented from providers can be transparently combined by users. Performance guarantees for SOAs gain importance with more complex systems and applications in business environments When a service is rented by a customer the provider agrees upon a Service Level Agreement (SLA) with conditions concerning interface, pricing and performance. Service reaction time in form of delay is an important part in many SLAs and subject to performance models discussed in this work. With SLAs providers implicate a maximum delay for their products when the customer limits the workload to their systems. Hence customers expect the contracted service provider to deliver the performance figures unless the workload exceeds the SLA. Since contract penalties could apply, providers have a natural interest in dimensioning their service in regard to the SLA. Even for maximum workloads specified in the contracts the worst-case delay has to hold. Moreover, due to the compositional nature of Web Services, customers become providers themselves when they offer their service compositions to others. Again, worst-case performance bounds are of major interest here. Analyzing models of SOAs is an option to plan, dimension and validate service performance. For system modeling and analysis many methods exist. Queueing Systems and simulation are two well-known approaches in computer science. They provide average and thus long-term performance numbers quite easily using, probabilistic workload and service process descriptions. Deriving system behavior in worst-case situations for performance guarantees is elaborative and can be impossible for more complex systems. Receiving delay bounds usable in SLAs for SOAs by model analysis is still a research issue. A promising candidate to model SOA with SLAs is Network Calculus, an analytical method to derive performance bounds for network components. Given deterministic descriptions for arrival to and service in a network node hard bounds for network delay and the required buffer memory in routers are computed. A fine-granular separation between short- and long-term goals is possible. Network Calculus models also feature composition of elements and fast analytical analysis. When applied to SOAs with SLAs the problem arises that SLAs are not suitable as a system description and information source for Network Calculus models. Especially the internal service capacity is not exposed by SLAs, since providers consider them as a business secret. Without service process descriptions Network Calculus models cannot be analyzed. The SLA Calculus is presented as a solution to this problem. As a novel contribution for deterministic model analysis for SOAs, SLA Calculus is an extension to Network Calculus. Instead of service process descriptions, it uses information on latency to characterize a system. Delay of services is not a scalar analysis result anymore, it becomes a process over time that is bound with Network Calculus-style curves, the delay curves. Together with arrival curves the performance contracts in SLAs are formalized by so-called SLA Delay Properties (SDPs) as a description for the service performance in worst-case. Service composition can be modeled by serial and parallel combination of SDPs. The necessary theorems for the resulting worst-case bounds are given and proved. We will present a method to transfer these performance figures to the missing service process description again. Apart from basic theory we will also consider solutions for practical modeling situations. An algorithm to extract arrival and delay curves from measurements, enables the modeler to include already existing systems without given SLAs as model elements. Finally, we will sketch a selection method in form of an optimization problem for services to support the dynamic service selection in SOAs with a Service Broker. SLA Calculus model analysis will deliver deterministic upper and lower bounds for workload capacities and response times. For upper bounds the worst-case is assumed, thus bounds are pessimistic. The advantage of SLA Calculus is the ability to compute these bounds very fast and to give system modelers a quick overview on system characteristics considering extreme situations. In other modeling methods a lengthy transient analysis would be required. The strict perspective towards worst-case brought up another analysis target: Until now, relatively little attention was paid to contract conformance between subsequent services within service compositions. When services offer different workload capacities the arrival rate to the system needs to be adjusted to avoid bottlenecks. Additionally, for service compositions no response time contract can be guaranteed without internal buffering to enforce a common arrival rate. SLA Calculus unveils the necessary buffer delays and is able to bound them

A survey of parallel execution strategies for transitive closure and logic programs

An important feature of database technology of the nineties is the use of parallelism for speeding up the execution of complex queries. This technology is being tested in several experimental database architectures and a few commercial systems for conventional select-project-join queries. In particular, hash-based fragmentation is used to distribute data to disks under the control of different processors in order to perform selections and joins in parallel. With the development of new query languages, and in particular with the definition of transitive closure queries and of more general logic programming queries, the new dimension of recursion has been added to query processing. Recursive queries are complex; at the same time, their regular structure is particularly suited for parallel execution, and parallelism may give a high efficiency gain. We survey the approaches to parallel execution of recursive queries that have been presented in the recent literature. We observe that research on parallel execution of recursive queries is separated into two distinct subareas, one focused on the transitive closure of Relational Algebra expressions, the other one focused on optimization of more general Datalog queries. Though the subareas seem radically different because of the approach and formalism used, they have many common features. This is not surprising, because most typical Datalog queries can be solved by means of the transitive closure of simple algebraic expressions. We first analyze the relationship between the transitive closure of expressions in Relational Algebra and Datalog programs. We then review sequential methods for evaluating transitive closure, distinguishing iterative and direct methods. We address the parallelization of these methods, by discussing various forms of parallelization. Data fragmentation plays an important role in obtaining parallel execution; we describe hash-based and semantic fragmentation. Finally, we consider Datalog queries, and present general methods for parallel rule execution; we recognize the similarities between these methods and the methods reviewed previously, when the former are applied to linear Datalog queries. We also provide a quantitative analysis that shows the impact of the initial data distribution on the performance of methods

Analytical Approximations to Predict Performance Measures of Manufacturing Systems with Job Failures and Parallel Processing

Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others

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

Approximation methods for stochastic petri nets

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists