2,967 research outputs found

    Techniques for the Fast Simulation of Models of Highly dependable Systems

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    With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system

    On two modifications of E-r/E-s/1/m queuing system subject to disasters

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    The paper deals with modelling a finite single-server queuing system with the server subject to disasters. Inter-arrival times and service times are assumed to follow the Erlang distribution defined by the shape parameter r or s and the scale parameter rĪ» or sĪ¼ respectively. We consider two modifications of the model āˆ’ server failures are supposed to be operate-independent or operate-dependent. Server failures which have the character of so-called disasters cause interruption of customer service, emptying the system and balking incoming customers when the server is down. We assume that random variables relevant to server failures and repairs are exponentially distributed. The constructed mathematical model is solved using Matlab to obtain steady-state probabilities which we need to compute the performance measures. At the conclusion of the paper some results of executed experiments are shown.Web of Science12215814

    Busy period analysis of the level dependent PH/PH/1/K queue

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    In this paper, we study the transient behavior of a level dependent single server queuing system with a waiting room of finite size during the busy period. The focus is on the level dependent PH/PH/1/K queue. We derive in closed form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. We differentiate between two types of losses: the overflow losses that are due to a full queue and the losses due to an admission controller. For the M/PH/1/K, M/PH/1/K under a threshold policy, and PH/M/1/K queues, we determine simple expressions for their joint transforms

    Compositional Performance Modelling with the TIPPtool

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    Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations

    Exact transient analysis of a circulant queuing network

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    AbstractCirculant matrices possess unusual and interesting properties. These properties have been exploited to obtain the transient solution in closed form for a circulant queuing network that models a distributed query processing system. The sojourn time of a customer in the circulant queuing network is determined. A semi-Markov generalisation of this network is also studied

    Construction and Verification of Performance and Reliability Models

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    Over the last two decades formal methods have been extended towards performance and reliability evaluation. This paper tries to provide a rather intuitive explanation of the basic concepts and features in this area. Instead of striving for mathematical rigour, the intention is to give an illustrative introduction to the basics of stochastic models, to stochastic modelling using process algebra, and to model checking as a technique to analyse stochastic models

    A transient solution to the M/M/c queuing model equation with balking and catastrophes

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    In this paper, we consider a Markovian multi-server queuing system with balking and catastrophes. The probability generating function technique along with the Bessel function properites is used to obtain a transient solution to the queuing model. The transient probabilities for the number of customers in the system are obtained explicitly. The expressions for the time-dependent expected number of customers in the system are also obtained. Finally, applications of the model are also discussed

    Queuing for an infinite bus line and aging branching process

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    We study a queueing system with Poisson arrivals on a bus line indexed by integers. The buses move at constant speed to the right and the time of service per customer getting on the bus is fixed. The customers arriving at station i wait for a bus if this latter is less than d\_i stations before, where d\_i is non-decreasing. We determine the asymptotic behavior of a single bus and when two buses eventually coalesce almost surely by coupling arguments. Three regimes appear, two of which leading to a.s. coalescing of the buses.The approach relies on a connection with aged structured branching processes with immigration and varying environment. We need to prove a Kesten Stigum type theorem, i.e. the a.s. convergence of the successive size of the branching process normalized by its mean. The technics developed combines a spine approach for multitype branching process in varying environment and geometric ergodicity along the spine to control the increments of the normalized process
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