Mathematical model of wireless network as a cyclic random access queueing system

Выполнено исследование математической модели беспроводной сети передачи данных в виде циклической системы с повторными вызовами, на вход которой поступают два стационарных пуассоновских потока заявок, продолжительности обслуживания которых имеют экспоненциальную функцию распределения. Применяя метод асимптотического анализа, найдено предельное стационарное распределение вероятностей числа заявок в исследуемой математической модели сети передачи данных

A survey of the machine interference problem

This paper surveys the research published on the machine interference problem since the 1985 review by Stecke & Aronson. After introducing the basic model, we discuss the literature along several dimensions. We then note how research has evolved since the 1985 review, including a trend towards the modelling of stochastic (rather than deterministic) systems and the corresponding use of more advanced queuing methods for analysis. We conclude with some suggestions for areas holding particular promise for future studies.Natural Sciences and Engineering Research Council (NSERC) Discovery Grant 238294-200

Investigating the mean response time in finite-source retrial queues using the algorithm by Gaver, Jacobs, and Latouche

In this paper, we discuss the maximum of the mean response time that appears in finite-source retrial queues with orbital search when the arrival rate is varied. We show that explicit closed-form equations of the mean response time can be derived by exploiting the block-structure of the finite Markov chain underlying the model and using an efficient computational algorithm proposed by Gaver, Jacobs, and Latouche. However, we also show that already for the discussed relatively simple model, the resulting equation is rather complex which hampers further evaluation

Graph Based Processing

Η παρούσα εργασία εξερευνεί την αρχιτεκτονική εξυπηρετητών. Μία ανάλυση διαφορετικών αρχιτεκτονικών σχεδιασμών αποκαλύπτει τους λόγους για τα διαφορετικά χαρακτηριστικά εκτέλεσης που αναδεικνύουν. Προτείνεται μία νεα αρχιτεκτονική, ο γράφος υπολογισμού (process graph), που στοχεύει να αποτελέσει ένα πλαίσιο ανάπτυξης υπηρεσιών και γενικευμένων υπολογισμών. Ο γράφος υπολογισμού, μαζί με πιθανές υλοποιήσεις του, στοχεύει στην αντιμετώπιση προβλημάτων επιδόσεων των υπαρχόντων αρχιτεκτονικών, καθώς και στη διευκόλυνση ανάπτυξης διαχειρίσιμων υπηρεσιών. Μέσω ανάλυσης και επαλήθευσης, υποστηρίζω ότι τα πιθανά πλεονεκτήματα που παρουσιάζονται ισχύουν και ότι ο γράφος υπολογισμού είναι ικανός να είναι ανταγωνιστικός με σύγχρονες αρχιτεκτονικές εξυπηρετητών.This thesis explores the software architecture of servers. An analysis of different architectural designs reveals the reasons for the different execution characteristics that they exhibit. A new computation abstraction is proposed, the process graph, that aims to be a framework to develop services and generic computations. The process graph, along with its potential implementations, aims to address performance problems with other architectures, as well as facilitate the easy development of maintainable services. Through analysis and evaluation, I argue that the potential benefits that are presented are valid and the process graph has the potential to be competitive with existing state of the art server architectures

Single server retrial queueing models.

Most retrial queueing research assumes that each retrial customer has its own orbit, and the retrial customers retry to enter service independently of each other. A small selection of papers assume that the retrial customers themselves form a queue, and only one customer from the retrial queue can attempt to enter at any given time. Retrial queues with exponential retrial times have been extensively studied, but little attention has been paid to retrial queues with general retrial times. In this thesis, we consider four retrial queueing models of the type in which the retrial customers form their own queue. Model I is a type of M/G/1 retrial queue with general retrial times and server subject to breakdowns and repairs. In addition, we allow the customer in service to leave the service position and keep retrying for service until the server has been repaired. After repair, the server is not allowed to begin service on other customers until the current customer (in service) returns from its temporary absence. We say that the server is in reserved mode, when the current customer is absent and the server has already been repaired. We define the server to be blocked if the server is busy, under repair or in reserved mode. In Model II, we consider a single unreliable server retrial queue with general retrial times and balking customers. If an arriving primary customer finds the server blocked, the customer either enters a retrial queue with probability p or leaves the system with probability 1 - p. An unsuccessful arriving customer from the retrial queue either returns to its position at the head of the retrial queue with probability q or leaves the system with the probability 1 - q. If the server fails, the customer in service either remains in service with probability r or enters a retrial service orbit with probability 1 - r and keeps returning until the server is repaired. We give a formal description for these two retrial queueing models, with examples. The stability of the system is analyzed by using an embedded Markov chain. We get a necessary and sufficient condition for the ergodicity of the embedded Markov chain. By employing the method of supplementary variables, we describe the state of the system at each point in time. A system of partial differential equations related to the models is derived from a stochastic analysis of the model. The steady state distribution of the system is obtained by means of probability generating functions. In steady state, some performance measures of the system are reported, the distribution of some important performance characteristics in the waiting process are investigated, and the busy period is discussed. In addition, some numerical results are given. Model III consists of a single-server retrial queue with two primary sources and both a retrial queue and retrial orbits. Some results are obtained using matrix analytic methods. Also simulation results are obtained. Model IV consists of a single server system in which the retrial customers form a queue. The service times are discrete. A stability condition and performance measures are presented.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .W87. Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3883. Thesis (Ph.D.)--University of Windsor (Canada), 2006