State-dependent models of material handling systems in closed queueing networks

A comprehensive algorithmic analysis of finite state-dependent queueing models and exponentially distributed workstations is formulated and presented. The material handling system is modeled with finite state-dependent queueing network M/G/c/c models and the individual workstations are modeled with exponentially distributed single and multi-server M/M/c queueing models. The coupling of these queueing models is unique via the material handling structure. The performance modeling of the systems for series, merge, and split and other complex network topologies are included so as to demonstrate the type of topological network design that is possible with these incorporated material handling systems. Of some importance, it is shown that these integrated M/M/c and M/G/c/c networks have a product form when the population arriving at the M/G/c/c queues is controlled. Numerous experimental results demonstrate the efficacy of our approach for a variety of contexts and situations.     

Simulation studies of multiclass queueing networks

Multiclass queueing networks have been used to model communication and complex manufacturing systems. Recent results have shown that these networks can be unstable in the sense that the total number of jobs in the network explodes as time tends to infinity even if the traffic intensity at each station is less than unity. Simulation is used to demonstrate these unusual phenomena. Conjectures based on simulation are presented.     

Performance analysis of IEEE 802.11 DCF and 802.11e EDCA based on queueing networks

The authors propose a new analytical model based on BCMP closed queueing networks in order to evaluate the performance of IEEE 802.11 DCF MAC protocol when all nodes are in the transmission range of each other, that is, a single hop wireless ad hoc network. By the proposed model, some performance metrics such as saturation and non-saturation throughput, distributions of channel access delay and the number of packets in the MAC buffer are derived. An extension of the proposed model is used for the analysis of IEEE 802.11e EDCA and the same performance metrics are evaluated for this protocol. Analytical results on IEEE 802.11e prove that differentiation in service is possible and channel share for each service type may be well assigned by tuning the MAC protocol parameters. Simulation results show consistency with our analytical results.     

Approximation of single-class queueing networks with downtime-induced traffic variability

Queuing networks have been used with partial success for analytical modelling of manufacturing systems. In this paper, we consider a tandem system with high traffic variability caused by downtime events in the first queue. We propose improved approximation for departure variability in order to predict the waiting duration at the bottleneck queue located last in the line. We demonstrate that existing methods do not properly approximate such systems and provide some reasons and insights. Thus, a new decomposition method which employs the variability function principles is proposed. We differentiate between two components of the departure variability in multi-class systems: the ‘within-class effect’ – the variability caused by the class’ own inter-arrival and service time distributions – and the ‘between-class effect’ – the variability caused by interactions with other classes. Our analysis shows that the first effect can be approximated by existing multi-class decomposition methods, while the second effect requires a new development. Our proposed approximation for between-class effect is based on simulating a proper sub-system. The method enables modelling different policies of downtimes (e.g. FCFS, Priority). Numerical experiments show relative errors much smaller vs. existing procedures.     

An algorithm for sub-optimal routeing in series-parallel queueing networks

The optimal routeing problem of maximizing system throughput in series-parallel networks with finite buffers is studied in this paper. The problem is extremely difficult to solve since closed form expressions are not easily constructed for throughput in finite networks. A piece-wise linear upper bound on the throughput of a tandem network is used to develop a throughput approximation in seriesparallel networks. Based on this approximation we are able to specify a suboptimal range for routeing probabilities at each junction in the network as a function of the arrival rate to this junction. We also specify a unique value for the routeing probability at each junction, independent of the arrival rate to that junction. We then construct an O(N) algorithm to analyse general series-parallel networks with more than one junction and specify the sub-optimal routeing probabilities at each junction.     

The buffer allocation problem for general finite buffer queueing networks

The Buffer Allocation Problem (BAP) is a difficult stochastic, integer, nonlinear programming problem. In general, the objective function and constraints of the problem are not available in a closed form. An approximation formula for predicting the optimal buffer allocation is developed based upon a two-moment approximation formula involving the expressions for M/ M/1/ K systems. The closed-form expressions of the M/ M/1/ K and M/ G/1/ K systems are utilized for the BAP in series, merge, and splitting topologies of finite buffer queueing networks. Extensive computational results demonstrate the efficacy of the approach.     

Monotonicity of the throughput of a closed exponential queueing network in the number of jobs

Summary It is shown that the throughput of a closed exponential queueing network is nondecreasing in the number of jobs in the system if the service rate in each station is nondecreasing in the number of jobs in that queue. The line of proof seems to be extendable to a variety of networks without a product form equilibrium.

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Zusammenfassung Es wird gezeigt, daß der Durchsatz eines geschlossenen exponentiellen Warteschlangen-Netzwerks hinsichtlich der Anzahl der Aufträge im System nicht fällt, wenn die Bedienungsrate in jeder Station hinsichtlich der Anzahl der Aufträge in dieser Warteschlange nicht fällt. Die Beweisführung scheint erweiterbar auf eine Vielzahl von Netzwerken ohne Produktionsgleichgewicht.

     

An improved algorithm for optimizing a closed queueing network model of a flexible manufacturing system

Vinod and Solberg (1985) address an optimization problem within the framework of a closed queueing network model for a Flexible Manufacturing System (FMS). The above problem is referred to as the Optimal System Configuration Problem of an FMS. The optimization parameters in the problem are the number of machines at each workstation and the total number of jobs circulating in the system. In this paper we suggest a more efficient algorithm for the solution of the above-mentioned problem. Our algorithm is of an implicit enumeration nature and derives its efficiency from the exploitation of properties of the throughput function of a closed queueing network. The efficiency of the algorithm is demonstrated with the use of extensive computational results.     

Generalized queueing network analysis of integrated supply chains

Supply chain networks are formed from complex interactions between several companies whose aim is to produce and deliver goods to the customers at specified times and places. Computing the total lead time for customer orders entering such a complex network of companies is an important exercise. In this paper we present analytical models for evaluating the average lead times of make-to-order supply chains. In particular, we illustrate the use of generalized queueing networks to compute the mean and variance of the lead time. We present four interesting examples and develop queueing network models for them. The first two examples consider pipeline supply chains and compute the variance of lead time using queueing network approximations available in the literature. This analysis indicates that for the same percentage increase in variance, an increase at the downstream facility has a far more disastrous effect than the same increase at an upstream facility. Through another example, we illustrate the point that coordinated improvements at all the facilities is important and improvements at individual facilities may not always lead to improvements in the supply chain performance. The existing literature on approximate methods of analysis of forkjoin queueing systems assumes heavy traffic and requires tedious computations. We present here two tractable approximate analytical methods for lead time computation in a class of fork-join queueing systems. Our method is based on the results presented by Clarke in 1961. For the case where the 'joining' servers of the queueing system are of the type D/N/1, we present an easy to use approximate method and illustrate its use in evaluating decisions regarding logistics (for instance, who should own the logistics fleet-the manufacturer or the vendor?) and computing simple upper bounds for delivery reliability, that is the probability that customer desired due dates are met.     

An open queueing network for lead time analysis

In this paper we develop an open queueing network for a multi-product multi-machine job-shop in a make-to-order environment. The job-shop produces a variety of products which are characterized by individual general arrival rates and individual general production rates for the machines on their deterministic routings. By incorporating the machines into a general open queueing network, we obtain the average, variance and probability distribution of the individual product lead times, The open queueing network will be illustrated by application to a real-life example existing at Recticcl Bedding Hulshout. In addition to using a flexible and computational efficient approach, we methodologically reveal that the approximate queueing network is suitable lo rapidly provide an answer to managerial questions.     

Multi-class queueing models for performance analysis of computer systems

Queueing models, networks of queues in particular, have been found especially useful for estimating the performance of computer systems. Networks of queues with multiple customer classes provide a flexible framework for modelling computer systems, where a rich set of analytical results and techniques are available. When because of the complexity of the system being modelled the analytical results cannot be applied directly, they often point to fairly accurate approximation schemes. In this paper, we present a brief survey of some of the important results and techniques from the theory of multi-class queueing networks. We also present a case study to illustrate how these results and techniques are used in a real-life situation where many of the modelling constraints are violated.     

一种高效挖掘生物网络闭合频繁子图的算法

针对生物网络中频繁子图的挖掘问题,提出了一种基于FP-树结构的MaxFP算法.此算法以代谢路径作为研究对象,在适合于生物网络图简化模型的基础上,采用一种不产生候选集的改进FP-growth算法挖掘生物网络中的闭合频繁子图.此算法考虑了基于频繁项目集的算法应用于网络的缺陷,根据生物网络的特点对FP-growth算法进行了改进.实验证明,提出的MaxFP算法比基于Apriori的频繁模式挖掘算法运行速度快,不仅能挖掘出最大的频繁子图,且能找到更多具有生物意义的频繁子图.     

Dual boundary element analysis of closed cracks

A two-dimensional boundary element method for analysis of closed or partially closed cracks under normal and frictional forces is developed. The single domain dual formulation is used. As a contact problem is non-linear due to the friction phenomena at the crack interface and also because of the boundary conditions which may change during the loading, it is formulated in an incremental and iterative fashion. The stress intensity factors are calculated with the J-integral method. Also crack growth is considered. Several benchmark cases have been analysed to verify the results given by the method. The stress intensity factors and crack paths calculated are similar to those given in the literature. © 1997 John Wiley & Sons, Ltd.     

A closed form formula for the normalized throughput of unbuffered multistage interconnection networks

Abstract

The normalized throughput of an unbuffered multistage interconnection network (MIN) under the uniform traffic model can be computed iteratively [6] or recursively [7]. However, the asymptotic performance of such networks as the number of stages increases cannot be determined using these procedures. A closed form formula for the normalized throughput of unbuffered MINs is presented in this paper. The new formula is proved by mathematical induction on the number of stages. The major advantage of the closed form formula is that the asymptotic performance of unbuffered square MINs can be easily determined. The formula is generalized to unbuffered MINs in the presence of nonidentical input rates and non‐square switch size.     

The part mix and routing mix problem in FMS: a coupling between an LP model and a closed queueing network

In the near future many companies will face the problem of the optimal use of newly installed manufacturing technology (e.g. a flexible manufacturing system or FMS). Very often this will involve decisions on what parts to produce using the new system (the part mix problem) and how to produce these parts (the routing mix problem). We show that traditional operational research tools such as linear programming and queueing network theory are well suited to tackle these problems. In particular, LP models are combined with queueing network models in an iterative procedure. As such the strengths of both techniques can be exploited in making optimal use of the part mix and routing mix flexibility of the FMS.     

Reliability analysis of cluster-based ad-hoc networks

The mobile ad-hoc wireless network (MAWN) is a new and emerging network scheme that is being employed in a variety of applications. The MAWN varies from traditional networks because it is a self-forming and dynamic network. The MAWN is free of infrastructure and, as such, only the mobile nodes comprise the network. Pairs of nodes communicate either directly or through other nodes. To do so, each node acts, in turn, as a source, destination, and relay of messages. The virtue of a MAWN is the flexibility this provides; however, the challenge for reliability analyses is also brought about by this unique feature. The variability and volatility of the MAWN configuration makes typical reliability methods (e.g. reliability block diagram) inappropriate because no single structure or configuration represents all manifestations of a MAWN. For this reason, new methods are being developed to analyze the reliability of this new networking technology. New published methods adapt to this feature by treating the configuration probabilistically or by inclusion of embedded mobility models. This paper joins both methods together and expands upon these works by modifying the problem formulation to address the reliability analysis of a cluster-based MAWN. The cluster-based MAWN is deployed in applications with constraints on networking resources such as bandwidth and energy. This paper presents the problem's formulation, a discussion of applicable reliability metrics for the MAWN, and illustration of a Monte Carlo simulation method through the analysis of several example networks.     

Fleet sizing of automated guided vehicles: a linear programming approach based on closed queuing networks

We use multi-class closed queuing networks to model operations of automated guided vehicles in a manufacturing or distribution environment. We approximate the dynamics of the system using the first moment balance equations of the embedded stochastic chain representing the network under the steady-state conditions. These moments account for loaded and empty-travel times, as well as times when vehicles are being loaded/unloaded or waiting to be dispatched. We model the steady-state behaviour of the closed queuing network by a linear program whose optimal value is the estimate of the required fleet-size. The result of the analytical model is compared with those of the simulation studies for a set of numerical examples. The comparison shows that the analytical model provides a good estimate for the required number of vehicles.     

Finite waiting space bulk queueing systems

Summary This paper extends earlier work on the stationary queue length distribution of a bulk service system with finite waiting space by considering two queueing systems. The first system incorporates the feature of batch arrivals with group service; it has compound Poisson input, general service times and a single server with variable batch capacity. The second system has individually arriving customers with Erlangian interarrival time distribution, general service times and a single server with variable batch capacity.The financial support of the National Research Council of Canada, under Research Grants No. 3-644-189-60; NRC-A5639 and No. 3-641-189-10; NRC-A2796, is acknowledged.