A class of multi-server queueing systems with unreliable servers: Models and application.

Where queueing systems with unreliable servers are concerned, most research that has been done focuses on one-server systems or systems with a Poisson arrival process and exponential service time. However, in some situations we need to consider non-exponential service time or service rate changes with the number of available servers. These are the queueing systems that are discussed in this thesis, none of which has ever been discussed in the literature. Since the phase type distribution is more general than the exponential distribution and captures most features of a general distribution, the phase type distributed service time is considered in unreliable queueing systems such as M/PH/n and M/PH/n/c. For the M/PH/n queueing system with unreliable servers, the mathematical model, stability condition analysis, stationary distribution calculation, computer programs and examples are all presented. For the M/PH/n/c queueing system with server failures, a finite birth-and-death mathematical model is built and the stationary distribution and performance evaluation measurements are calculated. Computer programs are developed and an example is given to demonstrate the application of this queueing system. (Abstract shortened by UMI.)Dept. of Industrial and Manufacturing Systems Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .Y375. Source: Masters Abstracts International, Volume: 43-01, page: 0295. Adviser: Attahiru S. Alfa. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004

Příspěvek k modelování nespolehlivých M/M/1/M systémů hromadné obsluhy

In the queueing theory we usually assume that a server breakdown can not occur (see for example in [1], [2], [3] or [4]). In other words a utility server works without failures. But in practice this assumption is not correct, the server is often a technical device and every technical device can be broken. During the breakdown the server can not work which means that the consideration of server failures has got an effect on performance measures of studied queueing system. We can say that queueing models with unreliable servers are more closely to a reality than models with reliable servers. On the other hand unreliable queueing models are more complicated. This paper presents two models of Markov queueing systems with an unreliable server.V teorii hromadné obsluhy obvykle předpokládáme, že nemůže nastat porucha obslužné linky. Jinými slovy obslužná linka pracuje bez poruch. Ale v praxi není tento předpoklad správný, obslužná linka je často technické zařízení a každé technické zařízení se může porouchat. Během poruchy obslužná linka nemůže pracovat, což znamená, že uvažování poruch obslužné linky má vliv na provozní charakteristiky studovaného systému hromadné obsluhy. Můžeme tedy říct, že modely nespolehlivých systémů hromadné obsluhy jsou mnohem blíže realitě než modely spolehlivých systémů. Na druhou stranu jsou modely nespolehlivých systémů složitější. Tento článek předkládá dva modely Markovských systémů hromadné obsluhy s nespolehlivou linkou

Asymptotic Analysis Of Markov Queueing Network With Unreliable Systems

The closed exponentional queueing network with unreliable systems with the large number of messages is investigated. We have received the systems of differential equations for average number of messages and serviceable channels of network systems

Analysis of the finite-source multiclass priority queue with an unreliable server and setup time

In this article, we study a queueing system serving multiple classes of customers. Each class has a finite-calling population. The customers are served according to the preemptive-resume priority policy. We assume general distributions for the service times. For each priority class, we derive the steady-state system size distributions at departure/arrival and arbitrary time epochs. We introduce the residual augmented process completion times conditioned on the number of customers in the system to obtain the system time distribution. We then extend the model by assuming that the server is subject to operation-independent failures upon which a repair process with random duration starts immediately. We also demonstrate how setup times, which may be required before resuming interrupted service or picking up a new customer, can be incorporated in the model

Loss systems in a random environment

We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove an if-and-only-if-condition for a product form steady state distribution of the joint queueing-environment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, e.g. from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, e.g. of queueing-inventory processes. We investigate further classical loss systems, where due to finite waiting room loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise. We further investigate the embedded Markov chains at departure epochs and show that the behaviour of the embedded Markov chain is often considerably different from that of the continuous time Markov process. This is different from the behaviour of the standard M/G/1, where the steady state of the embedded Markov chain and the continuous time process coincide. For exponential queueing systems we show that there is a product form equilibrium of the embedded Markov chain under rather general conditions. For systems with non-exponential service times more restrictive constraints are needed, which we prove by a counter example where the environment represents an inventory attached to an M/D/1 queue. Such integrated queueing-inventory systems are dealt with in the literature previously, and are revisited here in detail

Propagation of epistemic uncertainty in queueing models with unreliable server using chaos expansions

In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary distribution of the model, which is a function of uncertain parameters. Polynomial chaos provide an efficient alternative to more traditional Monte Carlo simulations for modelling the propagation of uncertainty arising from those parameters. Furthermore, Polynomial chaos expansion affords a natural framework for computing Sobol' indices. Such indices give reliable information on the relative importance of each uncertain entry parameters. Numerical results show the benefit of using Polynomial Chaos over standard Monte-Carlo simulations, when considering statistical moments and Sobol' indices as output quantities

Minimizing the Age of Information in Wireless Networks with Stochastic Arrivals

We consider a wireless network with a base station serving multiple traffic streams to different destinations. Packets from each stream arrive to the base station according to a stochastic process and are enqueued in a separate (per stream) queue. The queueing discipline controls which packet within each queue is available for transmission. The base station decides, at every time t, which stream to serve to the corresponding destination. The goal of scheduling decisions is to keep the information at the destinations fresh. Information freshness is captured by the Age of Information (AoI) metric. In this paper, we derive a lower bound on the AoI performance achievable by any given network operating under any queueing discipline. Then, we consider three common queueing disciplines and develop both an Optimal Stationary Randomized policy and a Max-Weight policy under each discipline. Our approach allows us to evaluate the combined impact of the stochastic arrivals, queueing discipline and scheduling policy on AoI. We evaluate the AoI performance both analytically and using simulations. Numerical results show that the performance of the Max-Weight policy is close to the analytical lower bound