Priority based scheduling disciplines are widely used by existing computer operating systems. However, the mathematical analysis and modelling of these systems present great difficulties since priority schedulling is not compatible with exact product form solutions of queueing network models (QNM's). It is therefore, necessary to employ credible approximate techniques for solving QNM's with priority classes. The principle of maximum entropy (ME) is a method of inference for estimating a probability distribution given prior information in the form of expected values. This principle is applied, based on marginal utilisation, mean queue length and idle state probability constraints, to characterise new product-form approximations for general open and closed QNM's with priority (preemptive-resume, non-preemtive head-of-line) and non-priority (first-come-first-served, processor-sharing, last-come-first-served with, or without preemtion) servers. The ME solutions are interpreted in terms of a decomposition of the original network into individual stable GIG11 queueing stations with assumed renewal arrival processes. These solutions are implemented by making use of the generalised exponential (GE) distributional model to approximate the interarrival-time and service-time distributions in the network. As a consequence the ME queue length distribution of the stable GE/GEzl priority queue, subject to mean value constraints obtained via classical queueing theory on bulk queues, is used as a 'building block' together with corresponding universal approximate flow formulae for the analysis of general QNM's with priorities. The credibility of the ME method is demonstrated with illustrative numerical examples and favourable comparisons against exact, simulation and other approximate methods are made.

Priority based scheduling disciplines are widely used by existing computer operating systems. However, the mathematical analysis and modelling of these systems present great difficulties since priority schedulling is not compatible with exact product form solutions of queueing network models (QNM's). It is therefore, necessary to employ credible approximate techniques for solving QNM's with priority classes. The principle of maximum entropy (ME) is a method of inference for estimating a probability distribution given prior information in the form of expected values. This principle is applied, based on marginal utilisation, mean queue length and idle state probability constraints, to characterise new product-form approximations for general open and closed QNM's with priority (preemptive-resume, non-preemtive head-of-line) and non-priority (first-come-first-served, processor-sharing, last-come-first-served with, or without preemtion) servers. The ME solutions are interpreted in terms of a decomposition of the original network into individual stable GIG11 queueing stations with assumed renewal arrival processes. These solutions are implemented by making use of the generalised exponential (GE) distributional model to approximate the interarrival-time and service-time distributions in the network. As a consequence the ME queue length distribution of the stable GE/GEzl priority queue, subject to mean value constraints obtained via classical queueing theory on bulk queues, is used as a 'building block' together with corresponding universal approximate flow formulae for the analysis of general QNM's with priorities. The credibility of the ME method is demonstrated with illustrative numerical examples and favourable comparisons against exact, simulation and other approximate methods are made. / Algerian government

Målet med denna studie var att studera olika aspekter av den prioritetsordning som används för att prioritera elanvändare i svenska elnät i händelse av nationell-, regional eller lokal elbrist. Studien redogör för hur prioriteringar av olika elanvändare går till och hur nyttan av olika elnät förändras utifrån en beslutsfattares egna preferenser, vidare redovisas hur samverkan mellan olika elnät påverkar den totala nyttan som varje invånare i ett samhäller erbjuds. Objekten i ett samhälle som förekommer på ett elnät delas in i åtta prioriteringsklasser beroende av objektets funktion. Området för denna studie har varit beslutsanalys. Studien har genomförts med hjälp av resultat från tidigare studier och teorier kring beslutsanalys, med detta som grund har en simulering genomförts för att påvisa hur nyttan av ett elnät ändras då förutsättningarna ändras. Förutsättningarna har varit; total kapacitet av elektricitet till samhället, avstånd mellan samhällen och de olika objektens efterfrågan av elektricitet. Studiens resultat har påvisat att ellinjer med objekt av hög prioriteringsklass ska prioriteras före ellinjer med objekt av låg prioriteringsklass. Vidare har studien visat att det kan finnas elnät i ett samhälle vars nytta skulle kunna vara större än de elnät som förespråkas av prioritetsordningen, och att dessa kan vara disjunkta. Detta för att prioriteringsordningen ska prioritera det elnät med högprioriterade objekt, inte nödvändigtvis det elnät med störst nytta. Studie har därmed resulterat i att elnät bör prioriteras efter dess nytta och att en beslutsfattare bör vara medveten om elbristens storlek, avstånd mellan samhällen och varje objekts efterfrågan av kapacitet för att kunna fatta ett bra beslut. Gällande samverkan mellan elnät visade studien på att detta kan genomföras om avståndet mellan samhällena inte var för stort. / The aim of this study was to study the Styrel concept as an approach to identify electricity users and prioritize them in the event of a power shortage on a power grid. The study has examined and investigated how the priorities of different electricity users go to, how the benefits of manual disconnection change according to the decision makers' different priorities and how interaction between different local networks affects total utility. The features of a community on a local area, also called objects, are divided into eight priority classes depending on the function of the objects. The area for this study has been decision management. The study has been conducted using results from previous studies and theories on decision analysis as the basis for constructing a simulator that simulates how the power of a power failure changes for a local area dependent on the extent of the electricity supply (capacity). The study's findings have shown that prioritization of electricity supply line with higher priority classes should be prioritized than an electricity supply line with lower priority classes. This is also the result of previous studies. On the other hand, the study has shown that the fixed asset for an electricity supply line with lower priority objects is higher than an electricity supply line with higher priority objects, but with less benefit, priority should be given to the electricity supply line of higher priority objects. This study has thus resulted in the fact that electricity supply lines should be prioritized after the benefit if a decision maker is aware of the extent of the deficiency. Current collaboration between local networks showed that this could be dependent on the factors: distance, risk profile of decision makers and change of benefit through collaboration.