Gerard L. Reijns

Reliability Analysis of

k-out-of-n systems with cold standby units are typically studied for unit lifetime distributions that allow analytical tractability. Often, however, these distributions differ significantly from reality. In this paper, we present an analytical approach to compute the mean failure time for k -out-of-n systems with a single cold standby unit for the wide class of lifetime distributions that can be captured by the Pearson distribution. The method requires the first four statistical moments of the units lifetime distribution to be given, and computes the mean failure time using the Pearson distribution as an intermediate vehicle during the numerical integration. Experimental results for various instances of the Weibull distribution show that the numerical accuracy of the approach is high, with less than 0.5 percent error across a large range of k -out-of-n systems.

k

For the development of efficient parallel applications, fast but reliable performance predictions are essential. Many existing modelling formalisms are either not directly suited to model parallel applications, or too expensive. This paper describes several extensions and improvements to a previously introduced methodology, based on an extension of queueing networks. The set of machine model building blocks is extended, a new algorithm for the prediction of multiple-class parallel section completion times is introduced, and it is shown how programs containing conditional statements at the program level and memory hierarchies at the machine level are modelled. The concepts introduced in this paper are illustrated by a number of examples throughout the paper, and a case study comparing the predictions to measurements carried out on an actual parallel machine.<<ETX>>

-out-of-

Predicting the execution time of parallel programs involves computing the maximum or minimum of the execution times of the tasks involved in the parallel computation. We present a method to accurately compute the distribution of the largest (Max) and the smallest (Min) execution time of the composite of a number of parallel programming tasks, each having an independent, stochastic, arbitrary workload. The Max function applies to the general case that the composite task completes at the time its longest constituent task terminates. The Min function applies when the completion of its shortest task terminates the whole parallel process, such as in a parallel searching program. Both the Min and Max density function of a constituent task are characterized in terms of a Pearson distribution. Due to its accuracy, the presented method is especially of interest when the performance of time critical parallel applications must be derived. Both prediction methods are tested against three well-known distributions. Furthermore, the Max prediction method is also tested against a number of measured real-life data parallel programs with different degree of parallelism. The results show excellent accuracy of better than 1% with a very few exceptions in extreme situations.

n

In many practical engineering circumstances, systems reliability analysis is complicated by the fact that the failure time distributions of the constituent subsystems cannot be accurately modeled by standard distributions. In this paper, we present a low-cost, compositional approach based on the use of the first four statistical moments to characterize the failure time distributions of the constituent components, subsystems, and top-level system. The approach is based on the use of Pearson distributions as an intermediate analytical vehicle, in terms of which the constituent failure time distributions are approximated. The analysis technique is presented for -out-of- systems with identical subsystems, series systems with different subsystems, and systems exploiting standby redundancy. The moment-in-moment-out approach allows for the analysis of systems with arbitrary hierarchy, and arbitrary (unimodal) failure time distributions, provided the subsystems are independent such that the resulting failure time can be expressed in terms of sums or order statistics. The technique consistently exhibits very good accuracy (on average, much less than 1 percent error) at very modest computing cost.

Systems With Single Cold Standby Using Pearson Distributions

In this paper we briefly describe the operation of PACS(1), equipped with a central relational data base, which correlates patient identification data with the location where the related images can be found. A performance model of this PACS(1) with response times is presented in this paper. PACS(1) has also been built using as much as possible, standard software and standard protocols, to keep the development costs down. From the standards used we mention: TCP/IP, SQL, X Windows and FTP. The recent development of powerful workstations has now made it possible to eliminate the image servers in PACS(1) and integrate the functions of the image servers into the display stations. This rather simple and elegant design, called PACS(2), is presented in this paper together with a performance model. Although the development of PACS(2) has not yet been completed, we found that the presently available high power workstations are still somewhat too slow to execute, with the required response times, simultaneously the high speed communication functions and the display functions. Special purpose hardware, to implement the TCP/IP protocol functions, is introduced in the display workstation in order to reduce its workload and improve the response times.

A probabilistic approach to parallel system performance modelling

A Picture Archive and Communication System (PACS) as it is to be used in a Hospital will consist of a number of workstations, data acquisition stations and output stations, connected to a central storage facility. In this paper the architecture of the central storage facility is studied, and an implementation is proposed. Simulation studies have been performed on the proposed implementations, showing their feasibility. The simulation studies show that the central storage facility can store over 500 sets on a daily basis, while simultaneously handling the review and output activity associated with such a production. On the average, each set is assumed to consist of 3 images of 4 Mbyte each. Simulation results are presented for a number of alternative systems. Special attention is given to the implications of prefetching on the protocols to be used in the PACS system. It is shown that prefetching, in particular in combination with a pipelined system, can yield significant performance benefits. We believe that prefetching of images is a prerequisite for good system performance. The implementation assumes that a high-speed communication protocol is used to interconnect the PACS components. The paper will not go into details on the network considerations. The central storage facility is designed using a general purpose System/370 machine, with the peripherals commonly used for such machines. This implies that it can be realized with currently available equipment. Several alternative implementations using interconnected workstation based systems are suggested.

Predicting the execution times of parallel-independent programs using Pearson distributions

In cooperation with BAZIS (Support Group Hospital Information Systems at Leiden, The Netherlands), we started the design of a Picture Archiving and Communications System (PACS) a few years ago that contains a centralized image data base. By means of system modeling and measuring some performance parameters, we have discovered that such a system cannot provide the required response times. This is mainly because of equipment communication interfaces that are not fast enough and have a throughput that does not generally exceed 16 Mbits/second. By providing a parallel operating image buffer system, the problems related to the limited speed of the communication interfaces can be overcome. Moreover, by splitting the network into a number of subnets connected to each other by means of “bridges,” the communications load can be locally reduced, improving in this manner the response times. Our PACS contains a supervisor and one relational data base that relates patient data with image locations. A significant part of the report is concerned with the design of the high speed American College of Radiology-National Electronic Manufacturing Association transmission control protocol/internet protocol (ACR-NEMA TCP/IP) communications interface. The use of such an interface eliminates the need for a Network Interface Unit, reducing in this manner communication delays and complexity. We have developed and have in operation for experimental purposes a small-scale PACS, consisting of a number of workstations, a relational data base and image buffers, all connected to a network that uses the ACR-NEMA TCP/IP protocols. This experimental PACS is used to provide input data to a PACS performance model, to validate this model, and to investigate alternative system configurations.

Reliability Analysis of Hierarchical Systems Using Statistical Moments

The desirability of an integrated (digital) communication system for medical images is widely accepted. In the USA and in Europe several experimental projects are in progress to realise (a part of) such a system. Among these is the IMAGIS project in the Netherlands. From the conclusions of the preliminary studies performed, some requirements can be formulated such a system should meet in order to be accepted by its users. 1. The storage resolution of the images should match the maximum resolution of the presently acquired digital images. This determines the amount of data and therefore the storage requirements. 2. The desired images should be there when needed. This time constraint determines the speed requirements to be imposed on the system. As compared to current standards, very large storage capacities and very fast communication media are needed to meet these requirements. By employing cacheing techniques and suitable data compression schemes for the storage and by carefully choosing the network protocols, bare capacity demands can be alleviated. A communication network is needed to make the imaging system available over a larger area. As the network is very likely to become a major bottleneck for system performance, effects of variation of various attributes have to be carefully studied and analysed. After interesting results had been obtained (although preliminary) using a simulation model for a layered storage structure, it was decided to apply simulation also to this problem. Effects of network topology, access protocols and buffering strategies will be tested. Changes in performance resulting from changes in various network parameters will be studied. Results of this study at its present state are presented.

Efficient distributed PACS

A multstatic frequency-modulated continuous wave (FMCW) radar system is under development for use in the control system of autonomous vehicles. The aim of the system, named Colarado, is the 3D location of obstacles in the surrounding environment. In this paper a laboratory prototype system version, the demonstrator, is described and current results are presented.

A design for a Picture Archiving Communication System central storage facility

A laboratory picture archiving and communications system for hospitals (PACS) was built which consists of a network, image acquisition stations, viewing stations, a relational database and an image storage system. Acceptable response times have been obtained by using a hierarchical image storage system and by applying pre-fetching of image data at two levels. Response times provided by a performance model are compared with measured values obtained from the real system. To keep the cost down, our PACS has been built using standard software and standard protocols wherever possible.<<ETX>>