Optimal scheduling in some multiqueue single-server systems

The authors address the problem of optimal scheduling in a multiqueue single-server (MQSS) model. An arriving customer joins queue j with probability 1/N, j=1,. . ., N. The server visits each queue for a random period of time whose duration is independent of the queue length. At the end of a visit period, either all customers of the attended queue leave the system (variant I), or only customers that were present in the queue upon the arrival of the server leave the system (variant II). A scheduling policy is a rule that selects the next queue to be visited by the server. When the controller has no information on the state of the system, it is shown that a cyclic policy minimizes the expected number of customers in the system. When the controller knows the number of customers in each queue, it is shown that the so-called most customers first (MCF) policy minimizes, in the sense of strong stochastic ordering, the vector of the number of customers in each queue whose components are arranged in decreasing order     

On reliability of binary systems in a random environment

The influence of random environments to technical systems reliability is studied. A Markov model of reliability of the system that operates in a random Markov environment is proposed. General relations for stationary and non-stationary Quality of Service (QoS) characteristics of such system are given. Numerical study and comparison for a cold backup system operating in stable and random two-state environments are performed.     

Erlang loss queueing system with batch arrivals operating in a random environment

We consider the BMAP/PH/N/0$\text{<italic>BMAP</italic>}/\text{<italic>PH</italic>}/N/0$ queueing system operating in a finite state space Markovian random environment. Disciplines of partial admission, complete rejection and complete admission are analyzed. The stationary distribution of the system states is calculated. The loss probability and other main performance measures of the system are derived. The Laplace–Stieltjes transform of the sojourn time distribution of accepted customers is obtained. Illustrative numerical examples are presented. They show effect of an admission strategy, a correlation in an arrival process, a variation of a service process. Poor quality of the loss probability approximation by means of more simple models utilization is illustrated.     

Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems

This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.     

有界丢包网络环境下不确定系统的预测控制

研究了有界丢包网络环境下的多包不确定系统的鲁棒预测控制．首先在构建无限时域性能代价函数时,不同于传统预测控制方法,只考虑成功数据传输序列,并由此提出了两种鲁棒预测控制方法：将无限时域控制作用参数化为一个状态反馈控制律;或参数化为一个自由控制作用接一个状态反馈控制律．与传统方法一样,采用性能代价函数作为Ｌｙａｐｕｎｏｖ函数证明了系统的闭环稳定性．仿真实例验证了此方法的有效性．     

On the rate of convergence to the stationary distribution in the single-server queuing systems

For a version of the single-server infinite-buffer queuing system which is much more general than M/G/1, the results on the rate of convergence to the stationary mode were reviewed in brief. New sufficient conditions guaranteeing the polynomial estimate of the rate of convergence were established using the “Markovization” method.     

具有双边随机时延和丢包的网络控制系统有限时间控制

针对双边丢包和双边时延的网络化控制系统的有限时间控制问题,通过引入时间偏移量的方法,将丢包转换为时延,从而形成多时延系统,并将时间延迟转换为系统状态延迟。基于全概率公式给出已知网络丢包率下连续丢包的概率公式,用Markov链表征网络时延的变化规律。以线性矩阵不等式的形式给出改进的有限时间时延相关稳定性判据,并通过数值仿真验证所提方法的有效性。     

Analysis and optimal design of systems operating in a random environment and having a rescue option

The paper presents a model for a system exposed to a random environment characterized by the Poisson shock processes. A subset of the system components ?_M is required for a mission completion. Failures of some components of this subset terminate a mission, whereas failures of other components are not terminal and allow for a rescue operation that is activated immediately upon failure. This operation is performed by a subset ?_R of the system components and succeeds if all components from ?_R survive all shocks occurring until its completion. The subsets ?_M and ?_R overlap. The duration of the rescue operation depends on the time of its activation. The components that are engaged only in the rescue operation remain in the warm standby mode during the primary mission. An approach for obtaining the mission success and the system survival probabilities is developed and an algorithm for the corresponding numerical computation is presented. An example analyzing the tradeoff between these two probabilities and illustrating optimization of the system protection design is given.     

On the optimality of myopic production controls for single-server,continuous-flow manufacturing systems

In this note, we consider a broad class of dynamic scheduling problems associated with a single-server, multiclass, continuous-flow manufacturing system. Using a general framework, we provide conditions under which the solution to these problems is the implementation of a class of production controls called myopic scheduling policies. The proof of optimality, which is intuitively appealing, applies to more general production models than existing proofs in the literature, which typically either use the maximum principle or solve the Hamilton-Jacobi-Bellman (HJB) equation. We also present several counter-examples that explicitly illustrate the potential limitations of myopic scheduling policies     

Multi-item partial backlogging inventory models over random planninghorizon in random fuzzy environment

In this paper, some multi-item inventory models for deteriorating items are developed in a random planning horizon under inflation and time value money with space and budget constraints. The proposed models allow stock dependent consumption rate and partially backlogged shortages. Here the time horizon is a random variable with exponential distribution. The inventory parameters other than planning horizon are deterministic in one model and in the other, the deterioration and net value of the money are fuzzy, available budget and space are fuzzy and random fuzzy respectively. Fuzzy and random fuzzy constraints have been defuzzified using possibility and possibility–probability chance constraint techniques. The fuzzy objective function also has been defuzzified using possibility chance constraint against a goal. Both deterministic optimization problems are formulated for maximization of profit and solved using genetic algorithm (GA) and fuzzy simulation based genetic algorithm (FAGA). The models are illustrated with some numerical data. Results for different achievement levels are obtained and sensitivity analysis on expected profit function is also presented.Scope and purposeThe traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However for more sale, inventory should be maintained at a higher level. Of course, this would result in higher holding or procurement cost, etc. Also, in many real situations, during a shortage period, the longer the waiting time is, the smaller the backlogging rate would be. For instance, for fashionable commodities and high-tech products with short product life cycle, the willingness for a customer to wait for backlogging diminishes with the length of the waiting time. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But at present, the economic situation of most of the countries has been much deteriorated due to large scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any further. The purpose of this article is to maximize the expected profit of two inventory control systems in the random planning horizon.     

Comparing two functional programming systems

A technique is presented for comparing the performance of functional languages with different evaluation strategies running on different machines. A set of small benchmarks is used, and th execution times of these programs running in the functional language and in the implementation language of the functional system are compared. The ratio of these execution times measured how well the functional system used the resources of the underlying hardware and implementation language. Also two functional programming systems are described. One system is a graph reduction interpreter for lambda calculus. The other is a DEL-style intermediate instruction set architecture for FP. The benchmarks in FP and the performances of the two systems on these benchmarks are presented     

Reliability-based optimization under random vibration environment

A methodology of formulating the optimum design problem for structural systems with random parameters and subjected to random vibration as a mathematical programming problem is presented. The proposed method is applied to the optimum design of a cantilever beam with a tip mass and a truss structure supporting a water tank. The excitations are assumed to be Gaussian processes and the geometric and material properties are taken to be normally distributed random variables. The probabilistic constraints are specified for individual failure modes since it is easier to specify the reliability level for each failure mode keeping in view the consequences of failure in that particular mode. The time parameter appearing in the random vibration based constraints is eliminated by replacing the probabilities of failure by suitable upper bounds. The numerical results demonstrate the feasibility and effectiveness of applying the reliability-based design concepts to structures with random parameters and operating in random vibration environment.     

Buffer allocation in general single-server queueing networks

The optimal buffer allocation in queueing network systems is a difficult stochastic, non-linear, integer mathematical programming problem. Moreover, the objective function, the constraints or both are usually not available in closed form, making the problem even harder. A good approximation for the performance measures is thus essential for a successful buffer allocation algorithm. A recently published two-moment approximation formula to obtain the optimal buffer allocation in general service time single queues is examined in detail, based on which a new algorithm is proposed for the buffer allocation in single-server general service time queueing networks. Computational results and simulation results are shown to evaluate the efficacy of the approach in generating optimal buffer allocation patterns.     

Reliability of supply chains in a random environment

A supply chain is considered that operates in a random environment.The last is described by continuous-time finite irreducible Markov chain. Each state of the environment (the Markov chain) has its own probability of fatal failure as a result of the breakdown of the supply. There are algorithms for calculating the reliability of the chain (a probability of a successful supply) and the distribution function of the successful performance time presented in this paper. The numerical example illustrates the suggested approach.     

Partial realization of random systems

Consider a vector-valued stationary random process {Y_k}^∞_−∞, from which the estimates, R₀, R₁, …, R_N, of the covariance matrices EY_kY′_k−i, i=0, 1, 1, …, N, can be made.     

On identification of random systems

Motivated by identification problems in biological and social sciences, this paper considers the identification of systems having inherently random parameters. Identification algorithms are presented for a class of non-linear regression models and differential systems having random coefficients. The results reveal the significant conceptual and computational differences that exist between deterministic and random identification procedures.     

Service networks with multichannel nodes in a random environment

Service networks with multichannel nodes of semi-Markovian type are considered. The parameters of a source of demands depend on the state of the Markovian random environment. For the process of servicing demands, the conditions of existence of a stationary mode are found, and the properties of stationary distribution in terms of spectral characteristics of the routing matrix are investigated. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 167–172, January–February, 2000.     

Comparing partition and random testing via majorization and Schur functions

The comparison of partition and random sampling methods for software testing has received considerable attention in the literature. A standard criterion for comparisons between random and partition testing based on their expected efficacy in program debugging is the probability of detecting at least one failure causing input in the program's domain. We investigate the relative effectiveness of partition testing versus random testing through the powerful mathematical technique of majorization, which was introduced by Hardy et al. (1952). The tools of majorization and the concepts of Schur (convex and concave) functions (1923) enable us to derive general conditions under which partition testing is superior to random testing and, consequently, to give further insights into the value of partition testing strategies.