A note on stable flow-equivalent aggregation in closed networks

We introduce the Conditional Mean Value Analysis (CMVA) algorithm, an exact solution method for product-form load-dependent closed queueing networks that provides a numerically stable solution of models where the load-dependent Mean Value Analysis (MVA) is numerically unstable. Similarly to the MVA algorithm for constant-rate queues, CMVA performs operations in terms of mean quantities only, i.e., queue-lengths, throughput, response times. Numerical stability derives from a new version of the MVA arrival theorem for load-dependent models which is expressed in terms of mean queue-lengths instead of marginal probabilities. The formula is obtained by the analysis of the conditional state spaces which describe network equilibrium as seen by jobs during their residence times at queues. We also provide a generalization of CMVA to multiclass models that preserves the numerical stability property.     

Performance analysis in a re-entrant operation with combinational routing and yield probabilities

Queuing networks arising from multistage processes with probabilistic re-entrant lines are common in manufacturing environments. Probabilistic re-entrant operation is defined as lots entering the operation with different repeated cycle requirements. This paper extends our work [S. Kumar, M.K. Omar, Stochastic re-entrant line modeling for an environmental stress testing in a semiconductor assembly industry, Appl. Math. Comput. 173 (2006) 603–615.] and proposes a modified analytical method based on the mean value analysis (MVA) technique and considering a probabilistic re-entrant line with yield loss probabilities. Introducing probabilities consideration into the MVA approach will substantially increase the complexity of the modeling and results analysis. However, the contribution of this paper is the introduction of a solution methodology that can overcome such complexity and allow operational managers to compute performance measures such as total cycle time and the mean throughput.     

EVA-MVA及会计指标对股票收益解释能力的比较研究

本文以沪深两市659家上市公司三年的数据为基础,运用回归分析方法,研究在目前国内权益资本市场中,经济增加值、市场增加值及会计指标三大指标体系对股票收益的解释能力。结果表明,在结合经济增加值和市场增加值两大指标体系之后,对沪深两市的股票收益存有一定的解释能力,但与传统的会计指标体系相比,解释能力得到很大的提高;此外,经济增加值和市场增加值指标分别表现了自身的特点,起到了各自的作用,从而在一定程度上说明了经济增加值与市场增加值在国内有一定的适用性。     

Queueing network modelling of flexible manufacturing system using mean value analysis

In the present investigation, we develop queueing model for the performance prediction of flexible manufacturing systems (FMSs) with a multiple discrete material-handling devices (MHD). An iterative method has been suggested using mean value analysis (MVA) for the state-dependent routing. Two queueing network models are considered to determine the material-handling device interference. In the first one, we model the interference from the MHD by inflating the station service times but neglect queueing at the MHD. In another network, the queueing for the MHD is taken into consideration. The performance of FMS configuration is obtained by iterating between two networks. The suggested algorithms demonstrate better results than the algorithm used by earlier workers for single MHD. Some performance indices viz. throughput, mean service time, mean waiting time, etc. are obtained. Numerical results are provided to highlight the effect of the system parameters on performance indices, which are further evaluated by using neuro-fuzzy controller system to validate the tactability of soft computing approach.     

上市公司经营绩效评价方法的典型相关分析

本文介绍了上市公司经营绩效的传统评价方法和EVA、MVA方法,并对几种方法进行了比较,采用典型相关分析方法,以沪市180指标股的相关数据进行了实证研究。我们发现EVA类指标与传统财务评价指标的结论是相一致的,都是公司经营绩效的有效反映。     

A decomposition approximation method for multiclass BCMP queueing networks with multiple-server stations

Closed multiclass separable queueing networks can in principle be analyzed using exact computational algorithms. This, however, may not be feasible in the case of large networks. As a result, much work has been devoted to developing approximation techniques, most of which is based on heuristic extensions of the mean value analysis (MVA) algorithm. In this paper, we propose an alternative approximation method to analyze large separable networks. This method is based on an approximation method for non-separable networks recently proposed by Baynat and Dallery. We show how this method can be efficiently used to analyze large separable networks. It is especially of interest when dealing with networks having multiple-server stations. Numerical results show that this method has good accuracy.     

Workloads and waiting times in single-server systems with multiple customer classes

One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. Under certain restrictions, the work conservation property gives rise to a conservation law for mean waiting times, i.e., a linear relation between the mean waiting times of the various classes of customers. This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. For a large class of such systems with interruptions, a decomposition of the amount of work into two independent components is obtained; one of these components is the amount of work in the corresponding systemwithout interruptions. The work decomposition gives rise to a (pseudo)conservation law for mean waiting times, just as work conservation did for the system without interruptions.     

具有第二次多选择服务的M[X]/G/1排队系统

本文研究成批到达的具有第二次多选择服务的单服务员排队系统．顾客的到达形成一广义泊松过程，不同批的顾客按先到先服务的规则，而同一批的顾客按随机次序接受服务．两次服务的服务时间都是一般分布且相互独立．本文采用补充变量法，求得在瞬态和稳态情况下系统队长的概率母函数，然后又计算出顾客的平均队长和平均等待时间．     

Modelling a three-phase electric arc furnace: a comparative study of control strategies

The dynamic performance of a 135 tonne 35 MVA three-phase electric arc furnace is investigated. Three-phase models of an arc-impedance and arc-current-controlled furnace are developed by combining the results of an identification study with analytically derived models. It is shown that arc-current and arc-impedance control philosophies correspond to interacting and non-interacting control respectively. The two control strategies are compared to assess which results in the minimum accumulated power discrepancy under dynamic conditions, and a dual impedance/current-controlled regulator is proposed.     

An M/G/1 queue with second optional service

We study an M/G/1 queue with second optional service. Poisson arrivals with mean arrival rate (>0) all demand the first essential service, whereas only some of them demand the second optional service. The service times of the first essential service are assumed to follow a general (arbitrary) distribution with distribution function B(v) and that of the second optional service are exponential with mean service time 1/₂ (₂>0). The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly. Also the mean queue length and the mean waiting time have been found explicitly. The well-known Pollaczec–Khinchine formula and some other known results including M/D/1, M/E_k/1 and M/M/1 have been derived as particular cases.     

An analysis of p-median location problem: Effects of backup service level and demand assignment policy

Any solution to facility location problems will consider determining the best suitable locations with respect to certain criteria. Among different types of location problems, involving emergency service system (ESSs) are one of the most widely studied in the literature, and solutions to these problems will mostly aim to minimize the mean response time to demands. In practice, however, a demand may not be served from its nearest facility if that facility is engaged in serving other demands. This makes it a requirement to assign backup services so as to improve response time and service quality. The level of backup service is a key, strategic-level planning factor, and must be taken into consideration carefully. Moreover, in emergency service operations conducted in congested demand regions, demand assignment policy is another important factor that affects the system performance. Models failing to adopt sufficient levels of backup service and realistic demand assignment policies may significantly deteriorate the system performance.Considering the classic p-median problem (pMP) location model, this paper investigates the effects of backup service level, demand assignment policy, demand density, and number of facilities and their locations on the solution performance in terms of multiple metrics. For this purpose, we adopt a combined optimization and simulation approach. We will first modify the classic pMP to account for distances to backup services. Next, we employ a discrete event simulation to evaluate the performance of location schemes obtained from the deterministic mathematical model. Our results provide insights for decision-makers while planning ESS operations.     

Multi-dimensional vector assignment problems

We consider a special class of axial multi-dimensional assignment problems called multi-dimensional vector assignment (MVA) problems. An instance of the MVA problem is defined by $m$ disjoint sets, each of which contains the same number $n$ of $p$-dimensional vectors with nonnegative integral components, and a cost function defined on vectors. The cost of an $m$-tuple of vectors is defined as the cost of their component-wise maximum. The problem is now to partition the $m$ sets of vectors into $n$   $m$-tuples so that no two vectors from the same set are in the same $m$-tuple and so that the sum of the costs of the $m$-tuples is minimized. The main motivation comes from a yield optimization problem in semi-conductor manufacturing. We consider a particular class of polynomial-time heuristics for MVA, namely the sequential heuristics, and we study their approximation ratio. In particular, we show that when the cost function is monotone and subadditive, sequential heuristics have a finite approximation ratio for every fixed $m$. Moreover, we establish smaller approximation ratios when the cost function is submodular and, for a specific sequential heuristic, when the cost function is additive. We provide examples to illustrate the tightness of our analysis. Furthermore, we show that the MVA problem is APX-hard even for the case $m=3$ and for binary input vectors. Finally, we show that the problem can be solved in polynomial time in the special case of binary vectors with fixed dimension $p$.     

Symmetric queues served in cyclic order

Consider a symmetrical system of n queues served in cyclic order by a single server. It is shown that the stationary number of customers in the system is distributed as the sum of three independent random variables, one being the stationary number of customers in a standard M/G/1 queue. This fact is used to establish an upper bound for the mean waiting time for the case where at most k customers are served at each queue per visit by the server. This approach is also used to rederive the mean waiting times for the cases of exhaustive service, gated service, and serve at most one customer at each queue per visit by the server.     

Analyzing the finite buffer batch arrival queue under Markovian service process: GIX/MSP/1/N

We consider a batch arrival finite buffer single server queue with inter-batch arrival times are generally distributed and arrivals occur in batches of random size. The service process is correlated and its structure is presented through Markovian service process (MSP). The model is analyzed for two possible customer rejection strategies: partial batch rejection and total batch rejection policy. We obtain steady-state distribution at pre-arrival and arbitrary epochs along with some important performance measures, like probabilities of blocking the first, an arbitrary, and the last customer of a batch, average number of customers in the system, and the mean waiting times in the system. Some numerical results have been presented graphically to show the effect of model parameters on the performance measures. The model has potential application in the area of computer networks, telecommunication systems, manufacturing system design, etc.      

QoS-Guided Bandwidth Management in Differentiated Time Scales

This paper presents an integrated approach to QoS-guided network bandwidth allocation where each traffic flow requires a sufficient bandwidth allocation to support its mean traffic rate and to meet a delay requirement. Under the assumption that the peak rate of each traffic flow is decreasing with the time interval within which the rate is measured, we derive an analytical relationship between the delay bound and the bandwidth requirement for each individual flow. Then, based on a Gaussian aggregate traffic model, we show that two key controllable parameters, the coefficient of variation and the provision for variation for the aggregate traffic flow, determine all three fundamental QoS attributes (throughput, delay, and loss). We illustrate by examples that these results can be used to design admission policies. We demonstrate also quantitatively a remarkable QoS advantage of larger channel bandwidth in a statistical multiplexing environment. The analytical contributions are expected to be generally useful in QoS-guided bandwidth management in broadband networks.     

Moment inequalities for the discrete-time bulk service queue

For the discrete-time bulk service queueing model, the mean and variance of the steady-state queue length can be expressed in terms of moments of the arrival distribution and series of the zeros of a characteristic equation. In this paper we investigate the behaviour of these series. In particular, we derive bounds on the series, from which bounds on the mean and variance of the queue length follow. We pay considerable attention to the case in which the arrivals follow a Poisson distribution. For this case, additional properties of the series are proved leading to even sharper bounds. The Poisson case serves as a pilot study for a broader range of distributions.     

Threshold start-up control policy for polling systems

A threshold start-up policy is appealing for manufacturing (service) facilities that incur a cost for keeping the machine (server) on, as well as for each restart of the server from its dormant state. Analysis of single product (customer) systems operating under such a policy, also known as the N-policy, has been available for some time. This article develops mathematical analysis for multiproduct systems operating under a cyclic exhaustive or globally gated service regime and a threshold start-up rule. It pays particular attention to modeling switchover (setup) times. The analysis extends/unifies existing literature on polling models by obtaining as special cases, the continuously roving server and patient server polling models on the one hand, and the standard M/G/1 queue with N-policy, on the other hand. We provide a computationally efficient algorithm for finding aggregate performance measures, such as the mean waiting time for each customer type and the mean unfinished work in system. We show that the search for the optimal threshold level can be restricted to a finite set of possibilities. This revised version was published online in June 2006 with corrections to the Cover Date.     

一类批量服务排队系统的求解

给出一类特殊的批量服务排队系统-公交系统的稳态概率分布的求解过程，并在此基础上给出这类服务系统平均队长的算法，中给出具体例子说明计算过程。     

Analysis of the queue-length distribution for the discrete-time batch-service Geo/G/1/K queue

In this paper, we consider a discrete-time finite-capacity queue with Bernoulli arrivals and batch services. In this queue, the single server has a variable service capacity and serves the customers only when the number of customers in system is at least a certain threshold value. For this queue, we first obtain the queue-length distribution just after a service completion, using the embedded Markov chain technique. Then we establish a relationship between the queue-length distribution just after a service completion and that at a random epoch, using elementary ‘rate-in = rate-out’ arguments. Based on this relationship, we obtain the queue-length distribution at a random (as well as at an arrival) epoch, from which important performance measures of practical interest, such as the mean queue length, the mean waiting time, and the loss probability, are also obtained. Sample numerical examples are presented at the end.