Stochastic PERT and CAST Logic Approach for Computer Support of Complex Operation Planning

Antkiewicz, Ryszard; Gąsecki, Arkadiusz; Najgebauer, Andrzej; Pierzchała, Dariusz; Tarapata, Zbigniew

doi:10.1007/978-3-642-13568-2_12

Cited by 5 publications

(5 citation statements)

References 4 publications

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“…is an H n -square-integrable martingale. By the construction of the filtration H n in (B.16) and the definition of H n, 1 i , H n,1…”

Section: Discussionmentioning

confidence: 99%

“…(iii) We emphasize the interesting structure of the variances ofX k andŶ k and their covariances, k = 1, ..., K. Recall that for G/GI/∞ queues [37], the steady-state variance formula of the number of jobs in the system is given as the sum of two terms, the mean and the coefficient (c 2 a − 1) multiplying an integral associated with the service time distribution; for example, when E[η 1 k ] < ∞, the variance of the steady-state number of tasks in the k th service station is…”

Section: Theorem 34 (Gaussian Propertymentioning

confidence: 99%

“…Introduction Fork-join networks consist of a set of service stations that serve job requests simultaneously and sequentially according to pre-designated deterministic precedence constraints. Such networks have many applications in manufacturing and telecommunications [5,7,8,24,35,36,56,55,66,67,49,50,62,41], patient flow analysis in healthcare [31,3,4,71,72], parallel computing [60,65,64,68,42], military deployment operations [34,70,1], and law enforcement systems [38]. Two types of synchronization constraints are of particular interest.…”

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confidence: 99%

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Gaussian Limits for a Fork-Join Network with Nonexchangeable Synchronization in Heavy Traffic

Pang

2016

Mathematics of OR

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We study a fork-join network of stations with multiple servers and non-exchangeable synchronization in heavy traffic under the FCFS discipline. Tasks are only synchronized if all the tasks associated with the same job are completed. Service times of parallel tasks of each job can be correlated. We consider the number of tasks in each waiting buffer for synchronization, jointly with the number of tasks in each parallel service station and the number of synchronized jobs. We develop a new approach to show a functional central limit theorem for these processes in the quality-driven regime, under general assumptions on the arrival and service processes. Specifically, we represent these processes as functionals of a sequential empirical process driven by the sequence of service vectors for each job's parallel tasks. All the limiting processes are functionals of two independent processes-the limiting arrival process and a generalized Kiefer process driven by the service vector of each job. We characterize the transient and stationary distributions of the limiting processes.

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“…is an H n -square-integrable martingale. By the construction of the filtration H n in (B.16) and the definition of H n, 1 i , H n,1…”

Section: Discussionmentioning

confidence: 99%

Section: Theorem 34 (Gaussian Propertymentioning

confidence: 99%

mentioning

confidence: 99%

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Gaussian Limits for a Fork-Join Network with Nonexchangeable Synchronization in Heavy Traffic

Pang

2016

Mathematics of OR

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“…This is one of the forms of the decision trees (e.g. stochastic PERT [2]). It can be used for risk analysis during planning of hazardous materials transport, risk assessment for LNG terminals [1], risk analysis of chemical industry [5].…”

Section: Event Tree Analysermentioning

confidence: 99%

CBRN Risk Analysis Using the Analytical Tools of the WAZkA System

Antkiewicz

Tarapata

Pierzchała

et al. 2019

IFIP Advances in Information and Communication Technology

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The paper presents the set of analytical tools for CBRN risk analysis. They are modules of WAZkA system, which is IT system supporting the analysis of contamination risks and alarming in Poland. The Event Tree is a graphical representation of a chronological sequence of events, substantial from the point of view of functioning of the object, which occur after a given event that initiates such sequence. Events Tree Analyser tool, which implements Event Tree, was built according to client-server architecture and apart from web browser it does not require any additional user-installed software. If the Event Tree is associated with an initiating event that has its location, the prototype of WAZkA system allows the calculation of the so-called Loss Table . Each row in the Loss Table corresponds to a single effect in the event tree (leaf of the tree). Having threat zones from simulation experiment (e.g. Aloha software), a specialized expert algorithm is launched, which calculates the potential human losses in each zone and inputs them in the Loss Table . Finally, the Common Operational Picture. Visualization module is used to visualize results of simulation and analyses.

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“…This is one of the forms of the decision trees (e.g. stochastic PERT [1]). It can be used during e.g.…”

Section: The Concept Of Wazka Systemmentioning

confidence: 99%

A Computer System for CBRN Contamination Threats Analysis Support, Prediction Their Effects and Alarming the Population: Polish Case Study

et al. 2017

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Abstract. The article outlines a concept for the system supporting analyses of threats related to contamination and alarming (WAZkA), for the purpose of the National System for Detection of Contamination and Alarming .UDMRZ\ 6\VWHP :\NU\ZDQLD 6NDĪHĔ L $ODUPRZDQLD .6:SiA) in Poland. Additionally, the article presents the point of designing such system, its concept and components. The main objective of WAZkA is to support the following processes of the KSWSiA: information exchange between the system elements and coordination of the system operations, as well as to prepare assessment and expert analyses, needed by the decision-making bodies, with respect to risk emergency situations during natural disasters, technical failures or other events resulting in biological, chemical or radioactive contamination. The selected modules included in the WAZkA system: Event Tree Analyzer, visualization module (COP) and emulators of the threats monitoring systems, were described as well as the idea of using the system for the purpose of training, including the designed emulators of the risk monitoring systems together with the scenario editor. The Event Tree Anlyzer is a graphical representation of a chronological sequence of events, significant from the point of view of the functioning of the object, which occur after a given event that initiates such sequence. COP is the GIS tool, which allows to present an operating situation on the basis of background maps. The application offers a possibility of enriching the presented operating situation with the risk data provided in the form of NATO ADat-P3 (CBRN) reports. Emulators of the threats monitoring systems allow to generate, in an artificial and user-controlled manner, data on risks, which "pretend" to be real data obtained from the monitoring systems. The above approach significantly facilitates the organization of training and learning about rare situations or situations that have never occurred, but that are potentially dangerous.

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Stochastic PERT and CAST Logic Approach for Computer Support of Complex Operation Planning

Cited by 5 publications

References 4 publications

Gaussian Limits for a Fork-Join Network with Nonexchangeable Synchronization in Heavy Traffic

Gaussian Limits for a Fork-Join Network with Nonexchangeable Synchronization in Heavy Traffic

CBRN Risk Analysis Using the Analytical Tools of the WAZkA System

A Computer System for CBRN Contamination Threats Analysis Support, Prediction Their Effects and Alarming the Population: Polish Case Study

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