Queueing systems with service interruptions: An approximation model

We present a single queueing model which can be used to analyse queueing systems with service interruptions. The model is based on a diffusion approximation using an instantaneous return process which reflects the particular queueing system under consideration. Applications to queueing systems with preemptive resume priority and breakdowns are given in this paper as well as numerical results showing the accuracy of the approximation.     

On the analysis of exponential queuing systems with randomly changing arrival rates: Stability conditions and finite buffer scheme with a resume level

This paper considers a single server exponential queue with random fluctuations in the intensity of the arrival process. The motivation being the modelling of random changes in traffic patterns. This random intensity model does not obey the independence assumption made in queuing theory. Necessary and sufficient conditions for the stability or ergodicity of the queuing process are obtained via analytic techniques using Jury's stability criteria, often used to study discrete time control systems. The effect of such fluctuations is then studied for a finite resume level queue which is often used in flow control. Exact performance measures are computed and are compared with existing results.     

Waiting time in a preemptive resume system with compound-poisson input

A single-server queueing system withN priority classes, general service times, and preemptive resume discipline is investigated. The first two moments of the waiting time are calculated. The mathematical method uses the approximation of the waiting time by lower and upper bounds which converge to one another. These bounds are the solution of certain time-discrete queueing models.

     

Performance analysis of a non-preemptive priority queuing system subjected to a correlated Markovian interruption process

In this paper, we consider a discrete-time queuing system with head-of-line non-preemptive priority scheduling and a single server subjected to server interruptions. We model the server interruptions by a correlated Markovian on/off process with geometrically distributed on and off periods. Two classes of traffic are considered, namely high-priority and low-priority traffic. In the first part of the paper, we derive an expression for the functional equation describing the transient evolution of this priority queuing system. This functional equation is then manipulated and transformed into a mathematical tractable form. This allows us to derive the joint probability generating function (pgf) of the system contents. From this pgf, closed-form expressions for various performance measures, such as mean and variance of system contents and customer delay can be derived. Finally, we illustrate our solution technique with some numerical examples, whereby we demonstrate the negative effect of correlation in the interruption process on the performance of both classes. Some numerical results illustrating the impact of second-order characteristics of the arrival process on mean delays are also presented. The proposed approach which is purely based on pgfs is entirely analytical and enables the derivation of not only steady-state but transient performance measures, as well. The paper presents new insights into the performance analysis of discrete-time queues with service interruption and it also covers some previously published results as a special case.

Scope and purpose

In this contribution, we consider a practical queuing model, with HOL priority scheduling, two classes of traffic, and a server which is subjected to a correlated Markovian interruption process. We first derive a non-linear functional equation relating the joint pgf of the system state vector between two consecutive slots. Then we outline a solution technique to solve for this functional equation. This allows us to derive the joint pgf of the system contents of both classes, from which various performance measures related to mean system contents and customer delays are derived. We also demonstrate how the proposed approach allows for derivation of transient performance measures, as well. It should be noted that detailed coverage of the transient analysis of the system is beyond the scope of this paper.To our best knowledge, this is the first initiative that aims to explore the performance of queuing systems with priority scheduling when the shared server is subjected to service interruption. The paper also generalizes the results of Walraevens et al. (Analysis of a single-server ATM queue with priority scheduling, Computers & Operations Research 2003;30(12):1807–30) by incorporating service interruption into their original queuing model. By means of numerical results, the paper also demonstrates the effect of correlation in the service interruption process on the performance of both classes of customers. The impact of second-order characteristics of the arrival process on mean delays is also investigated.     

Analysis of a finite-capacity M/G/1 queue with a resume level

In order to model the buffer pool behavior in a data communication component, an M/G/1/K queue where input is shut down when the queue size (number of messages) attains K until it decreases to a specified level is analyzed. By use of semi-Markov process approach, the queue length distribution at an arbitrary time is found, and the resultant performance measures (utilization, loss probability, and mean response time) are computed.     

仿真排队系统的统计计算研究

通过C 语言来仿真排队系统，该系统的数学模型为M／M／m/模型。然后用统计计算的方法来分析和研究仿真得到的数据，从而得出该系统的统计分布规律。     

Processes with probabilities,priority and time

A probabilistic calculus, derived from Milner's SCCS, WSCCS is presented. We define a notion of bisimulation for probabilistic processes and show that it is a congruence. A simple equational characterisation is shown to be both sound and complete for finite processes. We present many examples including some extended ones. The larger examples show both the expressive power of WSCCS and the availability of simple proof methods for some complex systems.     

Dynamic repair priority for a transfer line with a finite buffer

We formulate a continuous-time Markov chain model of a transfer line in which there are two unreliable machines separated by a finite buffer. Due to limited repair resources, simultaneous repairs are not possible in cases where both machines fail, and therefore we develop a repair priority rule that depends on the number of work-pieces present in the buffer. Each machine is characterized by three exponentially distributed random variables: processing time, time to failure, and time to repair. We provide a stochastic model for finding an optimal repair priority rule and an efficient algorithm accompanied by easy-to-use Matlab software. An extensive numerical study is performed to test the sensitivity of the proposed dynamic repair priority rule. While in previous studies repair priority was given to the bottleneck machine, we show that there are situations in which priority should be given to the non-bottleneck machine. Finally, we identify conditions in which adding a second technician is economically advisable.     

Structured priority queueing systems with applications to packet-radio networks

In this paper we investigate a certain class of systems containing dependent discrete time queues. This class of systems consists of N nodes transmitting packets to each other or to the outside of the system over a common shared channel, and is characterized by the fact that access to the channel is assigned according to priorities that are preassigned to the nodes. To each node a given probability distribution is attached, that indicates the probabilities that a packet transmitted by the node is forwarded to one of the other nodes or to the outside of the system.

Using extensively the fact that the joint generating function of the queue lengths distribution is an analytic function in a certain domain, we obtain an expression for this joint generating function. From the latter any moment of the queue lengths and also average time delays can be obtained.

The main motivation for investigating the class of systems of this paper is its applicability to several packet-radio networks. We give two examples: The first is a certain access scheme for a network where all nodes can hear each other, and the second is a three-node tandem packet-raido network.     

An optimal replacement policy for repairable cold standby system with priority in use

In this article, a cold standby repairable system consisting of two nonidentical components and one repairman is studied. It is assumed that component 2 after a repair is “as good as new” while component 1 after a repair is not, but component 1 is given priority in use. Under these assumptions, by using the geometric process repair model, we consider a replacement policy N based on the number of failures of component 1 under which the system is replaced when the number of failures of component 1 reaches N. Our problem is to determine an optimal policy N* such that the long-run average cost per unit time (i.e. the average cost rate) of the system is minimized. The explicit expression of the average cost rate of the system is derived and the corresponding optimal replacement policy N* can be determined numerically. Finally, a special system with Weibull-distributed working time and repair time of component 1 is given to illustrate the theoretical results in this article.     

An approximation technique for central server queueing models with a priority dispatching rule

An approximation technique to solve central server queueing models with a priority dispatching rule is described in this paper. This technique reduces the problem size by aggregating I/O activities and combining different classes into a smaller number of classes, so that the reduced problem can be solved numerical examples considered, throughputs and mean CPU queue sizes calculated by the approximation differ from simulation results by less than 15 percent.     

Optimizing a multiserver queuing system with a variable number of servers

A multiserver Poisson queuing system with losses, with a variable number of servers, and an additive quality functional is investigated. All major characteristic of the system are obtained in an explicit form. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 92–101, July–August 2007.     

Polyhedral Surface Modeling with a Diffusion System

This paper presents a method of generating polyhedral surfaces by using a diffusion system that calculates the positional and normal vectors on their vertices. The system generates smooth shapes that satisfy the minimum norm property, and can be extended to imitate the shape controls of curvature continuous surfaces with bias and tension parameters. The shape of a surface is determined by the stable state of nonlinear and local calculations between vertices, and is easily controlled by adding constraints on arbitrary vertices. Such bottom-up calculation of surfaces enhances flexibility in the interactive design of complicated free-form shapes.     

Stationary characteristics of a single-channel queuing system with one waiting space

A semi-Markovian model of a queuing system, with a discrete-continuous phase space of states is developed. Its main stationary characteristics are determined. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 51–62, September–October 2006.     

Ergodicity condition for a system with queuing and servicing of objects with a complicated structure

A single-channel queuing system with a Poisson incoming flow of objects is considered. Each object consists of several spaced requests. A simple ergodicity condition is established. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 8–12, September–October 2007.     

Stability condition for m/d/l retrial queuing system with a limited waiting time

A stability condition is derived for a queueing system with a Poisson input with parameter λ and constant service time τ. If the virtual waiting time is less than a constant a, then the demand can be serviced; otherwise, it is repeated in exponentially distributed time or is lost with a probability q >- 0. Translated from Kibemetika i Sisternnyi Anaiii. No. 2, pp. 184–186, March–April, 2000.     

一类动态互联复杂系统的稳定性分析

通过引入动态图及动态邻接矩阵相关理论,对具有动态互联信息结构约束的复杂系统进行描述和建模,并引入ＬｏｔｋａＶｏｌｔｅｒｒａ方程作为该系统的动态互联信息结构模型．根据李雅普诺夫方法,对系统的动态互联模型进行了详细分析,研究了非负定限内联结平衡的设定及其渐近稳定条件,进而研究了整个系统的稳定条件．最后得到了该类动态互联复杂系统联结稳定及整个系统稳定的相关结论．     

Experience with remote procedure calls in a real-time control system

This paper describes several years' practical experience with remote procedure calls as a primary tool for application software in a large and complex distributed real-time process control system. We motivate the use of remote procedure calls as an effective technique for the use of local area networks, describe our implementation and discuss its advantages and disadvantages.