Studying the queue length in a single-server queuing system with unreliable server

The unreliable queuing system was studied in both the nonstationary and stationary modes. It was assumed that a Poisson flow of customers arrives to the system; the times of customer servicing and restoration of the server (servicing system) are random variables with arbitrary distributions; the flow of stable failures makes up the restoration process; the interfailure intervals are distributed hyperexponentially; and the waiting and sojourn times as well as the queue length are not limited.Translated from Avtomatika i Telemekhanika, No. 1, 2005, pp. 72–81.Original Russian Text Copyright © 2005 by Mikadze, Khocholava.This paper was recommended for publication by V.V. Rykov, a member of the Editorial Board     

一类排队服务系统的最优控制策略研究

建立一个双阈值排队服务模型, 用来协调顾客的等待时间和服务系统的运行成本. 采用一种精细的概率分解方法获得瞬态和稳态队长的概率分布性质; 再根据系统稳态性能指标, 建立系统营运利润函数, 并设计一种针对双离散变量函数的全局优化收索算法来研究最优控制策略; 进一步的数值实验揭示出双重阈值策略的优越性.     

Optimal policies for a controlled queueing system with removable server under a random vacation circumstance

In this paper, we consider two stochastic models for a controlled single-server M/G/1 queueing system under a random vacation circumstance. The relevant expected costs are formulated under two control strategies and approximated by means of a familiar diffusion approximation method. Numerical calculations are devoted to examine the accuracy of the proposed approximation method. The results show that the diffusion approximation method is reasonably good for the performance evaluation on the typical queueing control systems, especially, for the M/M/1 single-server queue.     

基于排队网络的网络服务器性能分析与优化

针对网络服务器在用户数量和状态相对复杂情况下无法对服务器性能进行有效分析的问题,提出了一种基于排队网络的服务器性能分析方法。该方法可以有效降低时间复杂度和空间复杂度,使服务器性能分析更加精确,效率更高。实验结果表明,利用该方法对服务器性能进行建模和分析,并根据分析结果对服务器程序进行优化,可以达到合理利用系统资源、提高服务器性能的要求。     

Performance analysis of a queuing system with facilities requiring post-processing

This paper considers a queuing system in which a fixed number of identical facilities (servers) are employed one at a time for providing individual customer service at the single service station with unit capacity and each facility undergoes a post-processing after serving its own customer. Customers arrive in a Poisson process, and the customer service time and the facility post-processing time distributions are all exponential. For the queuing system, two different cases, the loss system (finite buffer capacity) and the delay system (infinite buffer capacity), will be analyzed separately to exploit their approximate computation algorithms for the associated long-run system state distributions. The algorithms are then tested for efficiency and effectiveness with various numerical problems.     

An application of modern control theory to a time-dependent queuing system for optimal operation

‘ Bang-bang ’ optimal closed-loop service policy for a time dependent M/M/l queuing system is derived using optimal control theory. The policy is based on probabilistic (and not stochastic) behaviour of the queue. Computational results are obtained for an illustrative example with non-bang-bang service policy using the conjugate gradient algorithm with bounded control variables. It is interesting to note that the optimal service policy is not sensitive to the arrival rate but to the mean service cost of a customer.     

The MAP/PH/N multi-server queuing system with broadcasting service discipline and server heating

A multiserver queuing system with an infinite buffer is considered. The incoming customer is described by a Markovian input flow. The heating time of the servers and the time of the customer service have a phase type distribution. The heating of all the free servers starts at the customer’s arrival moment, and the customer receives the service by all these servers after the heating’s termination. The steady state distribution of the customers and their sojourn time in a system are found. The basic performance measures of the system are calculated. The results of the numerical experiments show the potential usability of the proposed service discipline in comparison with the classical one.     

Cost analysis of a finite capacity queue with server breakdowns and threshold-based recovery policy

This paper analyzes a repairable M/M/1/N queueing system under a threshold-based recovery policy. The threshold-based recovery policy means that the server breaks down only if there is at least one customer in the system, and the recovery can be performed when q (1 ≤ q ≤ N) or more customers are present. For this queueing system, a recursive method is applied to obtain steady-state solutions in neat closed-form expressions. We then develop some important system characteristics, such as the number of customers in the system, the probability that the server is busy, the effective arrival rate and the expected waiting time in the system, etc. A cost model is constructed to determine the optimal threshold value, the optimal system capacity and the optimal service rate at a minimum cost. In order to solve this optimization problem, the direct search method and Newton's method are employed. Sensitivity analysis is also conducted with various system parameters. Finally, we present some managerial insights through an application example.     

Sensitivity analysis of an optimal routing policy in an ad hoc wireless network

We examine the sensitivity of optimal routing policies in ad hoc wireless networks with respect to estimation errors in channel quality. We consider an ad hoc wireless network where the wireless links from each node to its neighbors are modeled by a probability distribution describing the local broadcast nature of wireless transmissions. These probability distributions are estimated in real-time. We investigate the impact of estimation errors on the performance of a set of proposed routing policies.     

Performance analysis of a discrete-time queuing system with a correlated train arrival process

In this paper, we present an exact transient and steady-state discrete-time queuing analysis of a statistical multiplexer with a finite number of input links and whose arrival process is correlated and consists of a train of a fixed number of fixed-length packets. The functional equation describing this queuing model is manipulated and transformed into a mathematical tractable form. This allows us to derive the transient probability generating function (pgf) of the buffer occupancy. From this transient pgf, time-dependent performance measures such as transient probability of empty buffer, transient mean of buffer occupancy and instantaneous packet overflow probabilities are derived. By applying the final-value theorem, the corresponding exact expressions for the steady-state pgf of the queue length and packet arrivals are derived. We also show how the transient analysis provides insights into the derivation of the system's busy period distribution. Closed-form expressions for the mean packet and message delays are also provided. The paper presents significant results on the transient and steady-state analysis of statistical multiplexers with N input links and correlated train arrivals.     

Sensitivity analysis for optimal shape design problems

Various methods for performing the sensitivity analysis in solving optimal shape design problems are outlined. The methods are illustrated in detail in the finite setting of a unilateral boundary value problem of the Dirichlet-Signorini type. The methods are compared in several numerical examples.     

Sensitivity analysis for an optimal control problem

This note considers an optimal control problem where the maximand, right-hand side of the system's equations and the constraints are concave and differentiable. The question asked is: What happens when there is a shift or a change in the parameters of the problem? Inequalities indicating the relation of the direction of change in the optimal choices as well as in the maximand to the direction of change in the parameters are derived under alternative hypothesis about the dependence of the problem on the parameters.     

Detecting correlation between server resources for system management

Efficient system management requires continuous knowledge about the state of system and application resources that are typically represented through time series obtained by monitors. Capacity planning studies, forecasting, state aggregation, anomaly and event detection would be facilitated by evidence of data correlations. Unfortunately, the high variability characterizing most monitored time series affects the accuracy and robustness of existing correlation solutions. This paper proposes an innovative approach that is especially tailored to detect linear and non-linear correlation between time series characterized by high variability. We compare the proposed solution and existing algorithms in terms of accuracy and robustness for several synthetic and real settings characterized by low and high variability, linear and non-linear correlation. The results show that our proposal guarantees analogous performance for low variable time series, and improves state of the art in finding correlations in highly variable domains that are of interest for the application context.     

服务器系统智能管理平台的设计

为有效提高集群服务器系统的可靠性、可用性、可扩展性,满足各种应用的需求,采用软硬件结合的设计思想,设计了独立于业务平面的智能管理平台.采用集中管理、分级控制的方法,通过设计两级管理控制器和管理总线,同时定义通用的管理接口协议和数据格式,实现对服务器系统中集群服务器、磁盘阵列、电源等的管理监控和动态配置,为故障判断、定位、隔离和在线维护等提供支持,从而提高资源的利用效率和系统的可靠性.     

基于单片机的排队管理系统设计

针对多业务排队管理系统对于算法可靠性和灵活性的要求,介绍了基于单片机的排队管理系统的硬件构成和算法实现.采用MCS-51单片机作为核心处理器,通过外扩相应的硬件资源实现了多业务排队算法.系统既可以满足多业务排队管理算法的可靠运行,又使成本降到了较低的水平.算法的改进以及硬件设计的独特之处弥补了传统排队管理系统只能办理单一业务的缺陷.系统为业务员以及客户提供了相应的显示屏,从而提高了系统运行的可视化程度.应用结果表明该算法以及硬件电路的设计均能够满足多业务排队管理系统的要求,并具有可移植性.     

Extended optimal replacement policy for a two-unit system with failure rate interaction and external shocks

This study presents an extended replacement policy for a two-unit system which is subjected to shocks and exhibits failure rate from interaction. The external shocks that affect the system are of two types. A type I shock causes a minor failure of unit-A and the damage that is caused by such a failure affects unit-B, whereas a type II shock causes a total failure of the system (catastrophic failure). All unit-A failures can be recovered by making minimal repairs. The system also exhibits the interaction between the failure rates of units: a failure of any unit-A causes an internal shock that increases the failure rate of unit-B, whereas a failure of a unit-B causes instantaneous failure of unit-A. The goal of this study is to derive the long-run cost per unit time of replacement by introducing relative costs as a factor in determining optimality; then, the optimal replacement period, T*, and the optimal number of unit-A failures, n*, which minimise that cost can be determined. A numerical example illustrates the method.     

A bivariate optimal imperfect preventive maintenance policy for a used system with two-type shocks

This article studies an optimal imperfect preventive maintenance policy based on a cumulative damage model for a used system with initial variable damage. The used system is subject to shocks occurring to a non-homogeneous Poisson process, and suffers one of two types of shocks with stochastic probability: type-I shock (minor) yields a random amount of additive damage of the system, or type-II shock (catastrophic) causes the system to fail. A bivariate preventive maintenance schedule (n, T) is presented in which the system undergoes preventive maintenance at a planned time T and the nth type-I shock, or corrective maintenance at any type-II shock and the total damage exceeds a threshold level, whichever occurs first. The optimal preventive maintenance schedule which minimizes the expected cost rate is derived analytically and discussed numerically.     

A multi-criteria optimal replacement policy for a system subject to shocks

A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As these shocks occur, the system experiences one of two types of failures: a type-I failure (minor), rectified by a minimal repair; or a type-II failure (catastrophic) that calls for a replacement. In this study, we consider a multi-criteria replacement policy based on system age, nature of failure, and entire repair-cost history. Under such a policy, the system is replaced at planned life time T, or at the nth type-I failure, or at the kth type-I failure (k < n) at which the accumulated repair cost exceeds the pre-determined limit, or at the first type-II failure, whichever occurs first. An optimal policy over the control parameters is studied analytically by showing its existence, uniqueness, and structural properties. This model is a generalization of several existing models in the literature. Some numerical examples are presented to show several useful insights.     

服务器系统管理的自律计算模型

利用时序模型算法和事件分类匹配算法对服务器系统多个节点的事件和系统参数进行分析与预测,结合策略库技术, 构建了一个服务器系统管理的自律计算模型。该模型能够根据已知的操作环境自我配置,在各种灾难发生前自我保护,发生后自我修复,并且可以自我优化。