Closed Queueing Network Research Articles

Poisson 수요과정을 갖는 두 품목 콘윕시스템의 성능평가

In this study we consider a flow line CONWIP system in which two types of product are produced. The processing times of each product type at each station follow an independent exponential distribution and the demands for the finished products of each type arrive according to a Poisson process. The demands that are not satisfied instantaneously are either backordered or lost according to the number of unsatisfied demands that exist at their arrival instants. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts of each product type at each station, mean waiting times of backordered demands and the proportion of backordered demands. For the analysis of the proposed CONWIP system, we model the CONWIP system as a two class closed queueing network with a synchronization station and analyze the closed queueing network using a product-form approximation method for multiple classes developed by Baynat and Dallery. In the approximation method, each subsystem is analyzed using a matrix geometric method. Comparisons with simulation show that the approximation method provides fairly good results for all performance measures.

Pricing techniques for self regulation in Vehicle Sharing Systems

We study self regulation through pricing for Vehicle Sharing Systems (VSS). Without regulation VSS have poor performances. We want to improve the efficiency of VSS using pricing as incentive. We take as base model a Markovian formulation of a closed queuing network with finite buffer and time dependent service time. This model is unfortunately intractable for the size of instances we want to tackle. We discuss heuristics: a scenario approach, a fluid approximation, simplified stochastic models and asymptotic approximations. We compare these heuristics on toy cities.

Solving general multi-class closed queuing networks using parametric decomposition

This paper presents a new approach to evaluate the performance of general multi-class closed queuing networks. The approach uses parametric characterization of the traffic processes to derive two-moment approximations for performance measures at individual nodes. Based on these approximations, linkage equations are derived to establish the relationships between the various nodes in the network. These relationships result in a system of non-linear equations that is solved using an iterative procedure. Numerical studies comparing the performance of the approach with detailed simulations suggest that the approach yields fairly accurate estimates of performance measures without significant computational complexity.

Application of Closed Queuing Network to Computer System

Application of Closed Queuing Network to Computer System

Asymptotic analysis of the closed network with time-dependent service parameters and single-type messages

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

The stationary distribution invariance of states in a closed queueing network with temporarily non-active customers

A stationary functioning of a closed queueing network with temporarily non-active customers is analyzed. Non-active customers are located at network nodes in queues, being not serviced. For a customer, the feasibility of passing from its ordinary state to the temporarily non-active state (and backwards) is provided. Service times of customers at different nodes possess arbitrary distributions. Finally, the stationary distribution invariance of network states is established with respect to the functional form of customer service time distributions under fixed first-order moments.

An Estimated Delay Based Association Policy for Web Browsing in a Multirate WLAN

Station-Access Point (STA-AP) association is an important function in IEEE 802.11 Wireless LAN (WLAN) management. We obtain an association policy that can be implemented in centralized WLAN management devices, or in STAs, by taking into account explicitly two aspects of practical importance: (a) TCP-controlled short file downloads interspersed with read times (motivated by web browsing), and (b) different STAs associated with an Access Point (AP) at possibly different rates (depending on distance from the AP). Our approach is based on two steps. First, we consider an analytical model to obtain the aggregate AP throughput for long TCP-controlled file downloads when STAs are associated at k different rates r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , ..., r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ; this extends earlier work in the literature. Second, we present a 2-node closed queueing network model to approximate the expected average-sized file download time for a user who shares the AP with other users associated at a multiplicity of rates. These analytical results motivate the proposed association policy, called the Estimated Delay based Association (EDA) policy: Associate with the AP at which the expected file download time is the least. Simulations indicate that for a web-browsing type traffic scenario, EDA performs substantially better than other policies that have been proposed earlier. Crucially, the improved performance is sustained even in realistic evaluation scenarios, where the assumptions underpinning the analytical model do not hold. To the best of our knowledge, this is the first work that proposes an association policy tailored specifically for web browsing. Apart from this, our analytical results could be of independent interest.

A simulation model with synchronization manufacturing stations

PurposeThe aim of this paper is to develop an efficient analytical procedure to evaluate performance of the most general pull production systems particularly when multiple‐part‐types are involved. The authors consider a kanban controlled production system that can be modelled as a closed queuing network with different product classes. The production line is decomposed into stages which consist of one or several stations and an output buffer. Each stage is associated with a given number of kanbans. The main idea of this analytical algorithm is to analyze each subnetwork individually using a product form approximation technique. The iterative procedure is used to find the unknown parameters.Design/methodology/approachThe authors design a multiclass queuing network that can be used to represent kanban controlled production systems. To solve this model, three procedures are used: decompose the original network into M subnetworks, convergence of unknown parameters in each subnetwork, and convergence of unknown parameters in the original network. The authors now describe these procedures separately.FindingsThe main contribution of this paper is the formulation of the problem of kanban controlled production systems with several part‐types. The methodology is based on approximate formula with decomposition and is applicable to more general manufacturing environments. The authors' method can be applied to both limited and unlimited demands. The analytical algorithm designed in this work has demonstrated excellent performance in analyzing kanban controlled production systems.Originality/valueThe methodology of this algorithm is based on approximate formula and is applicable to more general manufacturing environments.

Exact-Order Asymptotic Analysis for Closed Queueing Networks

In this paper we study the asymptotic behavior of a general class of product-form closed queueing networks as the population size grows large. We first characterize the asymptotic behavior of the normalization constant for the stationary distribution of the network in exact order. This result then enables us to establish the asymptotic behavior of the system performance metrics, which extends a number of well-known asymptotic results to exact order. We further derive new, computationally simple approximations for performance metrics that significantly improve upon existing approximations for large-scale networks. In addition to their direct use for the analysis of large networks, these new approximations are particularly useful for reformulating large-scale queueing network optimization problems into more easily solvable forms, which we demonstrate with an optimal capacity planning example.

Exact-Order Asymptotic Analysis for Closed Queueing Networks

In this paper we study the asymptotic behavior of a general class of product-form closed queueing networks as the population size grows large. We first characterize the asymptotic behavior of the normalization constant for the stationary distribution of the network in exact order. This result then enables us to establish the asymptotic behavior of the system performance metrics, which extends a number of well-known asymptotic results to exact order. We further derive new, computationally simple approximations for performance metrics that significantly improve upon existing approximations for large-scale networks. In addition to their direct use for the analysis of large networks, these new approximations are particularly useful for reformulating large-scale queueing network optimization problems into more easily solvable forms, which we demonstrate with an optimal capacity planning example.

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.

A closed queueing network approach to analyzing multi-vehicle material handling systems

This article models a multi-vehicle material handling system as a closed-loop queueing network with finite buffers and general service times, where the vehicles represent the jobs in the network. This type of network differs from other queueing systems, because the vehicles’ residence times on track segments (servers) depend on the number of jobs (vehicles) in circulation. A new iterative approximation algorithm is presented that estimates throughput capacity and decomposes the network consisting of S servers into S separate G/G/1 systems. Each subsystem is analyzed separately to estimate the work-in-process via a population constraint to ensure that the summation of the average buffer sizes across all servers equals the total number of vehicles. Numerical results show that the methodology proposed is accurate in a wide range of operating scenarios.

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.

The impact of transportation delays on repairshop capacity pooling and spare part inventories

In this paper, to serve different fleets of machines at different locations, we study whether repair shop pooling is more cost effective than having dedicated on-site repair shops for each fleet. When modeling the former alternative, we take transportation delays and related costs into account and represent it as a closed queueing network. This allows us to include on-site spare-part inventories that operate according to a continuous-review base-stock policy. We obtain the steady-state distribution of components at each location and the cost of the system with a pooled repair shop by applying the Mean-Value Analysis technique. Our numerical findings indicate that when transportation costs are reasonable, repair shop pooling is a better alternative.

Performance analysis of CONWIP systems with batch size constraints

Multi-product manufacturing systems operating under CONWIP control are often modeled as closed queuing networks with synchronization stations. Performance analysis of these systems can be challenging, especially when batch size constraints are explicitly considered. This research develops a new approach for evaluating the performance of these systems based on parametric characterizations and traffic process approximations. The approach explicitly models the effect of batch size constraints on the departure process and waiting times at the different stations in the network to derive new characterization equations. These equations are used to derive a set of linking equations that is solved using an iterative algorithm to obtain estimates of network performance. Numerical studies indicate that the proposed method is yields fairly accurate performance estimates and can be useful in evaluating tradeoffs that guide managerial decisions.

A zero-or-one law in aggregated closed queueing networks

For a closed queueing network with single-server nodes, we prove that if the total number of requests, the number of servers in one of the nodes, and service rates in all other nodes are made n times as large, then the stationary number of requests in the multiserver node divided by n converges in probability as n ? ? to a positive constant, determined by parameters of the original network, with geometric convergence rate. Single-server nodes in the constructed network can be interpreted as repair nodes, the multiserver node as a set of workplaces, and requests as elements in a redundancy-with-repair model.

Exact analysis of performance models by the Method of Moments

Performance evaluation of distributed systems and service-oriented architectures is often based on stochastic models, such as closed queueing networks which are commonly solved by the Mean Value Analysis (MVA) algorithm. However, the MVA is unable to solve models with hundreds or thousands of users accessing services of multiple classes, a configuration that is often useful to predict the performance of real-world applications. This paper introduces the Method of Moments (MoM), the first exact algorithm for solving closed queueing networks with large population sizes. Compared to the MVA algorithm, which is based on a recursive evaluation of mean queue-lengths, MoM defines a recursion on higher-order moments of queue-lengths that is solved at each step by a linear system of equations. This approach dramatically decreases the costs of an exact analysis compared to the MVA approach. We prove that MoM requires log-quadratic time and log-linear space in the total population size, whereas MVA complexity expressions grow combinatorially as the product of class populations. This extends the feasibility of exact methods to a much larger family of multiclass performance models than those that can be solved by the MVA algorithm.

A multi-class closed queueing maintenance network model with a parts inventory system

The system we address is a maintenance network of repairable items where a set of bases is supported by a centrally located repair depot and a consumable replacement parts inventory system. If an item fails, a replacement part must be obtained at the parts inventory system before the failed item enters the repair depot. The ordering policy for the parts is the (S,Q) inventory policy. An approximation method for this system is developed to obtain performance measures such as steady-state probabilities of the number of items at each site and the expected backorders at the parts inventory system. The proposed system is modelled as a multi-class closed queueing network with a synchronization station and analyzed using a product-form approximation method. Particularly, the product-form approximation method is adapted so that the computational effort on estimating the parameters of the equivalent multi-class network is minimized. In analyzing a sub-network, a recursive method is used to solve balance equations by exploiting the special structure of the Markov chain. Numerical tests show that the approximation method provides fairly good estimation of the performance measures of interests.

An analysis of queuing network simulation using GPU-based hardware acceleration

Queuing networks are used widely in computer simulation studies. Examples of queuing networks can be found in areas such as the supply chains, manufacturing work flow, and internet routing. If the networks are fairly small in size and complexity, it is possible to create discrete event simulations of the networks without incurring significant delays in analyzing the system. However, as the networks grow in size, such analysis can be time consuming, and thus require more expensive parallel processing computers or clusters. We have constructed a set of tools that allow the analyst to simulate queuing networks in parallel, using the fairly inexpensive and commonly available graphics processing units (GPUs) found in most recent computing platforms. We present an analysis of a GPU-based algorithm, describing benefits and issues with the GPU approach. The algorithm clusters events, achieving speedup at the expense of an approximation error which grows as the cluster size increases. We were able to achieve 10-x speedup using our approach with a small error in a specific implementation of a synthetic closed queuing network simulation. This error can be mitigated, based on error analysis trends, obtaining reasonably accurate output statistics. The experimental results of the mobile ad hoc network simulation show that errors occur only in the time-dependent output statistics.

Optimal Routing in Closed Queueing Networks with State Dependent Queues

Optimal routing in closed queueing networks with state dependent queues is the focus of this paper. We seek a methodology and algorithm to efficiently solve the routing probabilities in closed systems. These systems may include multi-server exponential and general service finite capacity state dependent models as well as multi-chain systems. The state dependent models included within this paper extend the range of possible system applications with our algorithm to include transportation and material handling conveyor systems, pedestrian, and vehicular routing applications. Sometimes the networks will be purely state dependent M/G/c/c queues, while other times, there will be a mixture of M/M/c and M/G/c/c queues. These state dependent M/G/c/c queues are finite queues, while the workstations are infinite buffer queues. Because these networks have been shown to have a product form and the objective function in single chain networks is concave, we can achieve an optimal seeking algorithm. Numerous experiments are shown to illustrate the efficacy of the approach.