Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia

On some queueing systems with server vacations, extended vacations, breakdowns, delayed repairs and stand-bys

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This research investigates a batch arrival queueing system with a Bernoulli scheduled vacation and random system breakdowns. It is assumed that the repair process does not start immediately after the breakdown. Consequently there maybe a delay in starting repairs. After every service completion the server may go on an optional vacation. When the original vacation is completed the server has the option to go on an extended vacation. It is assumed that the system is equipped with a stand-by server to serve the customers during the vacation period of the main server as well as during the repair process. The service times, vacation times, repair times, delay times and extended vacation times are assumed to follow different general distributions while the breakdown times and the service times of the stand-by server follow an exponential distribution. By introducing a supplementary variable we are able to obtain steady state results in an explicit closed form in terms of the probability generating functions. Some important performance measures including; the average length of the queue, the average number of customers in the system, the mean response time, and the value of the traffic intensity are presented. The professional MathCad 2001 software has been used to illustrate the numerical results in this study

An Application of Matrix Analytic Methods to Queueing Models with Polling

We review what it means to model a queueing system, and highlight several components of interest which govern the behaviour of customers, as well as the server(s) who tend to them. Our primary focus is on polling systems, which involve one or more servers who must serve multiple queues of customers according to their service policy, which is made up of an overall polling order, and a service discipline defined at each queue. The most common polling orders and service disciplines are discussed, and some examples are given to demonstrate their use. Classic matrix analytic method theory is built up and illustrated on models of increasing complexity, to provide context for the analyses of later chapters. The original research contained within this thesis is divided into two halves, finite population maintenance models and infinite population cyclic polling models. In the first half, we investigate a 2-class maintenance system with a single server, expressed as a polling model. In Chapter 2, the model we study considers a total of C machines which are at risk of failing when working. Depending on the failure that a machine experiences, it is sorted into either the class-1 or class-2 queue where it awaits service among other machines suffering from similar failures. The possible service policies that are considered include exhaustive, non-preemptive priority, and preemptive resume priority. In Chapter 3, this model is generalized to allow for a maintenance float of f spare machines that can be turned on to replace a failed machine. Additionally, the possible server behaviours are greatly generalized. In both chapters, among other topics, we discuss the optimization of server behaviour as well as the limiting number of working machines as we let C go to infinity. As these are systems with a finite population (for a given C and f), their steady-state distributions can be solved for using the algorithm for level-dependent quasi-birth-and-death processes without loss of accuracy. When a class of customers are impatient, the algorithms covered in this thesis require their queue length to be truncated in order for us to approximate the steady-state distribution for all but the simplest model. In Chapter 4, we model a 2-queue polling system with impatient customers and k_i-limited service disciplines. Finite buffers are assumed for both queues, such that if a customer arrives to find their queue full then they are blocked and lost forever. Finite buffers are a way to interpret a necessary truncation level, since we can simply assume that it is impossible to observe the removed states. However, if we are interested in approximating an infinite buffer system, this inconsistency will bias the steady-state probabilities if blocking probabilities are not negligible. In Chapter 5, we introduce the Unobserved Waiting Customer approximation as a way to reduce this natural biasing that is incurred when approximating an infinite buffer system. Among the queues considered within this chapter is a N-queue system with exhaustive service and customers who may or may not be impatient. In Chapter 6, we extend this approximation to allow for reneging rates that depend on a customer's place in their queue. This is applied to a N-queue polling system which generalizes the model of Chapter 4

Sabisu kiritsu o koryoshita GI/GI/1 machi gyoretsu shisutemu no kakusan kinjiho ni kansuru kenkyu

制度:新 ; 報告番号:甲3539号 ; 学位の種類:博士(工学) ; 授与年月日:2012/2/25 ; 早大学位記番号:新587

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Resource Management in Computing Systems

Resource management is an essential building block of any modern computer and communication network. In this thesis, the results of our research in the following two tracks are summarized in four papers. The first track includes three papers and covers modeling, prediction and control for multi-tier computing systems. In the first paper, a NARX-based multi-step-ahead response time predictor for single server queuing systems is presented which can be applied to CPU-constrained computing systems. The second paper introduces a NARX-based multi-step-ahead query response time predictor for database servers. Both mentioned predictors can predict the dynamics of response times in the whole operation range particularly in high load scenarios without changes having to be applied to the current protocols and operating systems. In the third paper, queuing theory is used to model the dynamics of a database server. Several heuristics are presented to tune the parameters of the proposed model to the measured data from the database. Furthermore, an admission controller is presented, and its parameters are tuned to control the response time of queries which are sent to the database to stay below a predefined reference value.The second track includes one paper, covering a problem formulation and optimal solution for a content replication problem in Telecom operator's content delivery networks (Telco-CDNs). The problem is formulated in the form of an integer programming problem trying to minimize the communication delay and cost according to several constraints such as limited content replication budget, limited storage size and limited downlink bandwidth of each regional content server. The solution of this problem is a performance bound for any distributed content replication algorithm which addresses the same problem

On some queueing systems with server vacations, extended vacations, breakdowns, delayed repairs and stand-bys

This research investigates a batch arrival queueing system with a Bernoulli scheduled vacation and random system breakdowns. It is assumed that the repair process does not start immediately after the breakdown. Consequently there maybe a delay in starting repairs. After every service completion the server may go on an optional vacation. When the original vacation is completed the server has the option to go on an extended vacation. It is assumed that the system is equipped with a stand-by server to serve the customers during the vacation period of the main server as well as during the repair process. The service times, vacation times, repair times, delay times and extended vacation times are assumed to follow different general distributions while the breakdown times and the service times of the stand-by server follow an exponential distribution. By introducing a supplementary variable we are able to obtain steady state results in an explicit closed form in terms of the probability generating functions. Some important performance measures including; the average length of the queue, the average number of customers in the system, the mean response time, and the value of the traffic intensity are presented. The professional MathCad 2001 software has been used to illustrate the numerical results in this study.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Simulating The Impact of Emissions Control on Economic Productivity Using Particle Systems and Puff Dispersion Model

A simulation platform is developed for quantifying the change in productivity of an economy under passive and active emission control mechanisms. The program uses object-oriented programming to code a collection of objects resembling typical stakeholders in an economy. These objects include firms, markets, transportation hubs, and boids which are distributed over a 2D surface. Firms are connected using a modified Prim’s Minimum spanning tree algorithm, followed by implementation of an all-pair shortest path Floyd Warshall algorithm for navigation purposes. Firms use a non-linear production function for transformation of land, labor, and capital inputs to finished product. A GA-Vehicle Routing Problem with multiple pickups and drop-offs is implemented for efficient delivery of commodities across multiple nodes in the economy. Boids are autonomous agents which perform several functions in the economy including labor, consumption, renting, saving, and investing. Each boid is programmed with several microeconomic functions including intertemporal choice models, Hicksian and Marshallian demand function, and labor-leisure model. The simulation uses a Puff Dispersion model to simulate the advection and diffusion of emissions from point and mobile sources in the economy. A dose-response function is implemented to quantify depreciation of a Boid’s health upon contact with these emissions. The impact of emissions control on productivity and air quality is examined through a series of passive and active emission control scenarios. Passive control examines the impact of various shutdown times on economic productivity and rate of emissions exposure experienced by boids. The active control strategy examines the effects of acceptable levels of emissions exposure on economic productivity. The key findings on 7 different scenarios of passive and active emissions controls indicate that rate of productivity and consumption in an economy declines with increased scrutiny of emissions from point sources. In terms of exposure rates, the point sources may not be the primary source of average exposure rates, however they significantly impact the maximum exposure rate experienced by a boid. Tightening of emissions control also negatively impacts the transportation sector by reducing the asset utilization rate as well as reducing the total volume of goods transported across the economy