Predicting departure times in multi-stage queueing systems

We develop an approximation model for the state-dependent sojourn time distribution of customers or orders in a multi-stage, multi-server queueing system, when interarrival and service times can take on general distributions. The model can be used to make probabilistic statements about the departure time of a customer or order, given the number and location of customers currently in process or waiting, and these probabilities can be recomputed while waiting at any point during the sojourn time. The model uses phase-type distributions and a new method to estimate the remaining processing times of customers in service when the sojourn time distribution is computed.     

The scale factor: a new degree of freedom in phase-type approximation

This paper introduces a unified approach to phase-type approximation in which the discrete and the continuous phase-type models form a common model set. The models of this common set are assigned with a non-negative real parameter, the scale factor. The case when the scale factor is strictly positive results in discrete phase-type distributions and the scale factor represents the time elapsed in one step. If the scale factor is 0, the resulting class is the class of CPH distributions. Applying the above view, it is shown that there is no qualitative difference between the discrete and the CPH models. Based on this unified view of phase-type models one can choose the best phase-type approximation of a stochastic model by optimizing the scale factor.     

Sensitivity analysis of distributed parameter elements in high-speed circuit networks

This paper presents an analysis method, based on MacCormack's technique, for the evaluation of the time domain sensitivity of distributed parameter elements in high-speed circuit networks. Sensitivities can be calculated from electrical and physical parameters of the distributed parameter elements. The proposed method is a direct numerical method of time-space discretization and does not require complicated mathematical deductive process. Therefore, it is very convenient to program this method. It can be applied to sensitivity analysis of general transmission lines in linear or nonlinear circuit networks. The proposed method is second-order-accurate. Numerical experiment is presented to demonstrate its accuracy and efficiency.     

Sensitivity analysis of distributed parameter elements in high-speed circuit networks

This paper presents an analysis method, based on MacCormack＇s technique, for the evaluation of the time domain sensitivity of distributed parameter elements in high-speed circuit networks. Sensitivities can be calculated from electrical and physical parameters of the distributed parameter elements. The proposed method is a direct numerical method of time-space discretization and does not require complicated mathematical deductive process. Therefore, it is very convenient to program this method. It can be applied to sensitivity analysis of general transmission lines in linear or nonlinear circuit networks. The proposed method is second-order-accurate. Numerical experiment is presented to demonstrate its accuracy and efficiency.     

Waiting time distribution in a class of discrete-time cyclic service multi-queue systems

A new approximate method is developed for finding the waiting and sojourn time distributions in a class of multi-queue systems served in cyclic order at discrete intervals. An immediate application for such a model is in communication networks where a number of different traffic sources compete to access a group of transmission channels operating under a time-slotted sharing policy. This system maps naturally onto a model in which the inter-visit time has a probability mass function of phase-type. We derive a set of matrix equations with easily tractable iterative procedures for their solution and controllable accuracy in their numerical evaluation. We then validate the analytical model against simulation and discuss the validity of the assumptions. This methodology can be extended to several other polling strategies.     

Analysis of threshold-based batch-service queueing systems with batch arrivals and general service times

Most research concerning batch-service queueing systems has focussed on some specific aspect of the buffer content. Further, the customer delay has only been examined in the case of single arrivals. In this paper, we examine three facets of a threshold-based batch-service system with batch arrivals and general service times. First, we compute a fundamental formula from which an entire gamut of known as well as new results regarding the buffer content of batch-service queues can be extracted. Second, we produce accurate light- and heavy-traffic approximations for the buffer content. Third, we calculate various quantities with regard to the customer delay. This paper thus provides a whole spectrum of tools to evaluate the performance of batch-service systems.     

Mean message waiting times in symmetric multi-queue systems with cyclic service

A new performance analysis is provided for a cyclic service system consisting of statistically identical stations where at most one message is served for any station in a cycle. We assume that the time is slotted and that the number of message arrivals at each station in any slot is independent and generally distributed. The switch-over time and message service time (integral multiples of the slot size) are also generally distributed. For this system (called limited service system) we find the mean message waiting time explicitly. In the case of Poisson arrivals we show that our mean message waiting time is greater than that for the gated service system which is greater than that for the exhaustive service system. We also summarize the corresponding results for the three types of services in continuous-time systems.     

The distribution of network states during residence times in product form queueing networks

Product form queueing networks are so named because their equilibrium state probabilities have a simple product form. This simple form has lead to computationally efficient techniques for obtaining solutions of these networks. Recent work on the probability of network states at those instants when a customer completes service at a service center (departure instants) or arrives at a service center (arrival instants) has revealed a similar product form. The arrival instant result provides a simple, intuitive explanation of the Mean Value Analysis solution technique for product form networks with First-Come-First-Served service centers.In this paper we derive the distribution of network states seen by a particular customer while resident at a particular service center. This distribution too has a relatively simple product form. We use this information to explain in an intuitive way the MVA solution technique for a more general class of network, those containing load independent Processor Sharing and last-Come-First-Served-Preemptive-Resume service centers. It is hoped that, just as the intuitive explanation of the response time formula for FCFS centers has led to approximation techniques for non-separable FCFS centers, this new information may provide approximation techniques for non-separable centers with other scheduling disciplines such as preemptive and non-preemptive priority.     

Tail probabilities of the delay in a batch-service queueing model with batch-size dependent service times and a timer mechanism

We deduce approximations for the tail probabilities of the customer delay in a discrete-time queueing model with batch arrivals and batch service. As in telecommunications systems transmission times are dependent on packet sizes, we consider a general dependency between the service time of a batch and the number of customers within it. The model also incorporates a timer mechanism to avoid excessive delays stemming from the requirement that a service can only be initiated when the number of present customers reaches or exceeds a service threshold. The service discipline is first-come, first-served (FCFS). We demonstrate in detail that our approximations are very useful for the purpose of assessing the order of magnitude of the tail probabilities of the customer delay, except in some special cases that we discuss extensively. We also illustrate that neglecting batch-size dependent service times or a timer mechanism can lead to a devastating assessment of the tail probabilities of the customer delay, which highlights the necessity to include these features in the model. The results from this paper can, for instance, be applied to assess the quality of service (QoS) of Voice over IP (VoIP) conversations, which is typically expressed in terms of the order of magnitude of the probability of packet loss due to excessive delays.     

分布式网络性能监测代理自适应部署研究

分布式网络性能监测的关键问题是如何在管理域中的适当位置放置适当数目的代理,才能达到提高监测效率,减小额外监测流量和响应时间的目的。本文提出的算法是在管理员改变网络拓扑结构或者网络节点或链路失效时被启动,能够针对网络的变化自动地进行局部监测代理分布的调整,使监测系统恢复到近似最优状态。该算法使本监测系统具有良好的可扩展性和适应能力,仿真实验证明了算法的可行性。     

Discriminatory processor sharing queues with stationary ergodic service times and the performance of TCP in overload

In a recent paper, Bonald and Roberts (2001) [6] studied non-persistent TCP connections in transient overload conditions, under the assumption that all connections have the same round-trip times. In this paper our goal is to develop theoretical tools that will enable us to relax this assumption and obtain explicit expressions for the rate of growth of the number of connections at the system, the rate at which TCP connections leave the system, as well as the time needed for the completion of a connection. To that end, we model the system as a discriminatory processor sharing (DPS) system which we analyze under very mild assumptions on the probability distributions related to different classes of arrivals: we only assume that the arrival rates of connections exist, and that the amount of information transmitted during a connection of a given type forms a stationary ergodic sequence. We then proceed to obtain explicit expressions for the growth rate of the number of connections at the DPS system for several specific probability distributions. We check through simulations the applicability of our queueing results for modeling TCP connections sharing a bottleneck.     

On the time lag of the effect of network position on service performance in software service networks

We examine whether a time lag exists before the network position of a software service affects its performance. Moreover, we analyze different time lags, using empirical data about software services and their usage for creating composite services. Our results show that software services in central positions (i.e., high betweenness centrality) attract users the most. The highest effect exhibits, if the time lag is 26–32 months. Our findings are relevant, as they can guide developers in marketing their software services and are expected to impact innovation studies regarding the importance of considering time lags and analyzing complementary knowledge.     

Sensitivity analysis of artificial neural networks for just-suspension speed prediction in solid-liquid mixing systems: Performance comparison of MLPNN and RBFNN

Just-suspension speed (Njs) is an important parameter for stirred tank design using a solid-liquid mixing system in the chemical process industry. However, current correlations for Njs suffer from uncertainty from limited experimental databases and limitations due to many parameters that play an important role in Njs determination. A comprehensive computation of the radial basis function neural network (RBFNN) was developed based on solid-liquid mixing experiments, which contain 935 datasets for the prediction of Njs. The Njs values were obtained experimentally using Zwietering correlation with different solid loading percentages, solid particle density, solid particle diameter, mixing solvent density, number of impeller blades, impeller diameter, impeller blade hub angle, impeller blade tip angle, the width of the impeller blade and the ratio of the clearance between the impeller and the bottom of the tank with the tank diameter. The RBFNN proved to have a much better ability to accurately predict the desired Njs compared to MLPNN even after decreasing the number of input variables from 11 to 8. Thus, the computational RBFNN model results will be useful for extending the application of a solid-liquid mixing system for estimating the just-suspension speed for stirred tank design.     

Characterizing the measures on the unit circle with exact quadrature formulas in the space of polynomials

In the present paper we characterize the measures on the unit circle for which there exists a quadrature formula with a fixed number of nodes and weights and such that it exactly integrates all the polynomials with complex coefficients. As an application we obtain quadrature rules for polynomial modifications of the Bernstein measures on [−1,1], having a fixed number of nodes and quadrature coefficients and such that they exactly integrate all the polynomials with real coefficients.     

Impact of class clustering in a multiclass FCFS queue with order-dependent service times

In multi-class queueing systems, customers of different classes can enter the system. When studying such systems, it is traditionally assumed that the different classes of customers occur randomly and independently in the arrival stream of customers in the system. This is often in contrast to the actual situation. Therefore, we study a multi-class system with so-called class clustering in the customer arrival stream, i.e., (Markovian) correlation occurs in the classes of consecutive customers. The system under investigation consists of one server that is able to serve two classes of customers. In addition, the service-time distribution of a customer depends on the equality or non-equality of its class with the class of the previous customer. This latter feature occurs frequently in practice. For instance, execution of the same task again can lead to both faster or slower processing times. The first case can occur when the execution of a different task entails resetting a machine, or loading new data, et cetera. The opposite situation appears, for instance, when execution of the same task requires postprocessing (such as cooling down or reinitialization of a machine). We deduce the probability generating function (pgf) of the system content, from which we can extract various performance measures, among which the mean values of the system content and the customer delay. We demonstrate that class clustering has a tremendous impact on the system performance, which highlights the necessity to include it in the performance assessment of any system in which it occurs.     

Aggregation in sensor networks with a user-provided quality of service goal

Significant research has been devoted to aggregation in sensor networks with the purpose of optimizing its performance. Existing research has mostly concentrated on maximizing network lifetime within a user-given error bound. In general, the greater the error bound, the longer the lifetime. However, in some situations, it may not be realistic for the user to provide an error bound. Instead, the user may want to provide a quality of service (QoS) goal that has a combined objective of lifetime and error. Indeed, the error tolerable by the user may depend on how long the sensor network can last. This paper presents an aggregation protocol and related algorithms for reaching such a QoS goal. The key idea is to periodically modify a filter threshold for each sensor in a way that is optimal within the user objective, the key technical method being to translate the problem into a mathematical programming formulation with constraints coming from various sources, such as the user, the sensor network, and the data characteristics. Extensive experiments demonstrate the high accuracy, high flexibility and low overhead of this QoS-based optimization approach.     

低复杂度重构在分布式实时数据密集型Web服务架构中的应用

针对下一代分布式实时系统在重构时实时性要求较高的问题,本文提出了一种降低系统图复杂度并在有限时间内重构的方法。首先,利用服务组合确保重构在有限时间内实现;然后,通过路径选择算法和路径发送算法对图进行实时剪裁;最后,引入图构建算法消除具有更多非可调度路径的服务实现来降低图的复杂度。在iLAND服务重构和组合组件内部验证了本文方法,实验结果表明,本文方法能够显著减少解空间,大大减少了重构过程的计算时间。     

Simulation for passage times in closed, multiclass networks of queues with unrestricted priorities

Regenerative simulation for passage times in networks of queues with priorities among job classes (and one or more job types) can be based on observation of a fully augmented job stack process which maintains the position of each of the jobs in a linear ‘job stack’, an enumeration of the jobs by service center and job class. In this paper we develop an estimation procedure for passage times through a subnetwork of queues. Observed passage times for all the jobs enter into the construction of point and interval estimates. The confidence intervals obtained using this estimation procedure are shorter than those obtained from simulation using a marked job.     

Point of presence design in Internet protocol networks with performance guarantees

In this paper, we propose a model for the point of presence (POP) design problem in Internet protocol (IP) networks with performance guarantees, where a POP is a node composed of several interconnected co-located backbone routers within a central office. This problem consists of selecting the number of routers and their types, selecting the interface card types, connecting the access and the backbone links to the ports and selecting the link types between the co-located routers. Furthermore, the model considers the routing of the IP traffic. The performance guarantees we refer to are bandwidth guarantees between the routers for the normal state of the POP and also for all failure scenarios of interest to the network planner. A tabu search heuristic to find solutions for real-size instances of the problem is proposed. Finally, we present a systematic set of experiments designed to assess the performance of the proposed heuristic.     

Analysis of file download time in peer-to-peer networks with stochastic and time-varying service capacities

The service capacities of a source peer at different times in a peer-to-peer (P2P) network exhibit temporal correlation. Unfortunately, there is no analytical result which clearly characterizes the expected download time from a source peer with stochastic and time-varying service capacity. The main contribution of this paper is to analyze the expected file download time in P2P networks with stochastic and time-varying service capacities. The service capacity of a source peer is treated as a stochastic process. Analytical results which characterize the expected download time from a source peer with stochastic and time-varying service capacity are derived for the autoregressive model of order 1. Simulation results are presented to validate our analytical results. Numerical data are given to show the impact of the degree of correlation and the strength of noise on the expected file download time. For any chunk allocation method, an analytical result of the expected parallel download time from a source peer with stochastic and time-varying service capacity is derived. It is shown that the algorithm which chooses chunk sizes proportional to the expected service capacities has better performance than the algorithm which chooses equal chunk sizes. It is also shown that multiple source peers do reduce the parallel download time significantly.