Analysis Of Queueing Networks Research Articles

Analysis of cyclic queueing networks with parallelism and vacation

The aim of this paper is to improve the machine interference model with vacation to deal with more recent problems of the communication area. To this scope the model is extended to include parallelism in the vacation station. The underlying Markov process is analyzed and a state arrangement is found that yields an efficient matrix-analytic technique that substantially lowers down the time- and space-complexity of standard methods. A numerical example of the method effectiveness is presented, and an example of resource allocation is introduced that finds applications in the QoS management of wireless networks.

Performance approximation and design of pick-and-pass order picking systems

An approximation method based on G/G/m queuing network modeling using Whitt's queuing network analyzer to analyze pick-and-pass order picking systems is presented. The objective of this approximation method is to provide an instrument for obtaining rapid performance estimates (such as order lead time and station utilization) of an order picking system. The pick-and-pass system is decomposed into conveyor segments and pick stations. Conveyor segments have a constant processing time, whereas the service times at a pick station depend on the number of order lines in the order to be picked at the station, the storage policy at the station and the work practices. The proposed approximation method appears to be sufficiently accurate for practical purposes. It can be used to rapidly evaluate the effects of the storage methods in pick stations, the number of order pickers at stations, the size of pick stations, the arrival process of customer orders and the impact of batching and splitting orders on system performance.

Integration of queuing network and IDEF3 for business process analysis

PurposeThe purpose of this paper is to provide a framework and prototype software to use IDEF3 descriptions as a knowledge base from which a queuing network (QN) analysis is performed to compute system performance measures as part of quick response manufacturing. This intends to help domain experts obtain informative quantitative performance measures such as resource utilization, waiting time, and cycle time without relying on a time consuming simulation approach.Design/methodology/approachA general open queuing network is used to extract the related resource information from the process knowledge captured by IDEF3 method. The relational database is used to integrate the open QN and IDEF3, which also improves the knowledge reusability. In addition, the performance of the open queuing network analyzer (QNA) is compared to the simulation through case studies.FindingsThe domain experts usually do not own much technical modeling knowledge. However, through this integration, it is found that they could obtain several meaningful system performance measures without simulation. They could also perform the diverse “what if” scenario analyses with this prototype without difficulties. It is another finding that the system performance measures generated by the open QNA are reasonably close to the values obtained from simulation, articularly when the system utilization is low.Research limitations/implicationsThe open QN analysis used in this integration is not as generic as the simulation approach in terms of the modeling scope and capability. Hence, this integration supports only the exclusive OR (XOR) out of three junctions in IDEF3 grammars.Practical implicationsSome system analysis problems do not require a complex simulation modeling approach. Domain experts need a modeling tool to quickly obtain some system dynamics and insights. This integration framework suffices those requirements.Originality/valueThis paper describes the first attempt to generate informative system performance measures from the IDEF3 model using the open QN. It also offers practical help to the domain experts working in the system analysis area.

A multi-class queuing network analysis methodology for improving hospital emergency department performance

This paper derives an open queuing network model of an emergency department (ED) design intended to increase the capacity of an ED to treat patients. The methodology captures hospital-specific differences in patient acuity mix, arrival patterns and volumes, and efficiencies of processes in a single common computational model. A spreadsheet implementation of the resulting queuing equations is used by managers, in real time, to size ED areas using waiting time and overflow probability as quality of service targets. Non-homogeneous arrival patterns, non-exponential service time distributions, and multiple patient types are all incorporated. The methodology has been applied to a fleet of hospitals for validation. Results from one of them are used to demonstrate the methodology. Scope and purpose Population growth, closure of emergency departments (EDs) nearby, or seasonal peak variation can cause ED patient wait times to increase dramatically. Prolonged waits induce patients to leave the ED before receiving treatment, creating a public health problem. The purpose of this paper is to introduce a new paradigm of ED care that reduces “walk-aways”, and increases ED access, through an operational research method that customizes to any hospital through the use of hospital-specific data elements.

An analytical simulator for deploying IP telephony

AbstractDeploying IP telephony or voice over IP (VoIP) is a major and challenging task. This paper describes an analytical design and planning simulator to assess the readiness of existing IP networks for the deployment of VoIP. The analytical simulator utilizes techniques used for network flows and queuing network analysis to compute two key performance bounds for VoIP: delay and bandwidth. The simulator is GUI‐based and has an interface with drag‐and‐drop features to easily construct any generic network topology. The simulator has an engine that automates and implements the analytical techniques. The engine determines the number of VoIP calls that can be sustained by the constructed network while satisfying VoIP QoS requirements and leaving adequate capacity for future growth. As a case study, the paper illustrates how the simulator can be utilized to assess the readiness to deploy VoIP for a typical network of a small enterprise. We have made the analytical simulator publicly available in order to improve and ease the process of VoIP deployment. Copyright © 2008 John Wiley & Sons, Ltd.

Queuing network models for delay analysis of multihop wireless ad hoc networks

In this paper we analyze the average end-to-end delay and maximum achievable per-node throughput in random access multihop wireless ad hoc networks with stationary nodes. We present an analytical model that takes into account the number of nodes, the random packet arrival process, the extent of locality of traffic, and the back off and collision avoidance mechanisms of random access MAC. We model random access multihop wireless networks as open G/ G/1 queuing networks and use the diffusion approximation in order to evaluate closed form expressions for the average end-to-end delay. The mean service time of nodes is evaluated and used to obtain the maximum achievable per-node throughput. The analytical results obtained here from the queuing network analysis are discussed with regard to similarities and differences from the well established information-theoretic results on throughput and delay scaling laws in ad hoc networks. We also investigate the extent of deviation of delay and throughput in a real world network from the analytical results presented in this paper. We conduct extensive simulations in order to verify the analytical results and also compare them against NS-2 simulations.

Queueing network analysis on dynamic lot streaming

Lot streaming is a technique used to split a production lot into several smaller transfer batches. In this way, processing a product in a multistage serial production system by overlapping production between stages is available. As a result, production can be accelerated. In this paper, a modified N - policy M / G / 1 queueing system with a non-reliable server is proposed. With the relevant parameters of this queueing system, the problem of lot streaming in dynamic situations can be solved. To obtain the optimal transfer batch size, a cost objective function including transport cost, repair cost, turning cost, and holding cost is formulated. Further, in order to illustrate the usefulness of the proposed methods, numerical examples are solved. On the basis of the results of these examples, some important conclusions are drawn.

An efficient algorithm for the exact analysis of multiclass queueing networks with large population sizes

We introduce an efficient algorithm for the exact analysis of closed multiclass product-form queueing network models with large population sizes. We adopt a novel approach, based on linear systems of equations, which significantly reduces the cost of computing normalizing constants. With the proposed algorithm, the analysis of a model with N circulating jobs of multiple classes requires essentially the solution of N linear systems with order independent of population sizes.A distinguishing feature of our approach is that we can immediately apply theorems, solution techniques, and decompositions for linear systems to queueing network analysis. Following this idea, we propose a block triangular form of the linear system that further reduces the requirements, in terms of both time and storage, of an exact analysis. An example illustrates the efficiency of the resulting algorithm in presence of large populations.

A multi-stage stochastic methodology for whole hospital bed planning under peak loading

We propose a multi-stage stochastic methodology to balance inpatient bed unit utilisations in an entire hospital. It minimises blocking of beds from upstream units, within given constraints on bed reallocation, while considering multiple patient types. Queuing network analysis and optimisation are used to achieve balanced targets of bed unit utilisation while building hospital staff involvement. Discrete event simulation is then used to maximise flow through the system including nonhomogeneous effects of daily and hourly peak loading, nonexponential lengths of stay, and blocking behaviour. A 400 plus bed major hospital is analysed with the methodology and results are validated against field data.

Analytic approach for deploying desktop videoconferencing

The deployment of desktop videoconferencing, also known as video and voice over IP (VVoIP), over existing IP networks is gaining popularity. Such a deployment has become a major and challenging task for data network researchers and designers. An analytic approach for deploying videoconferencing is presented. The approach utilises queueing network analysis and investigates two key performance bounds for videoconferencing: delay and bandwidth. The approach can be used to assess the support and readiness of an existing IP network. Prior to the purchase and deployment of desktop videoconferencing equipment, the approach predicts the number of videoconferencing sessions or calls that can be sustained by an existing network while satisfying QoS requirements of all network services and leaving adequate capacity for future growth. As a case study, we apply our approach to a typical network of a small enterprise. In addition, we use OPNET network simulator to verify and validate our analysis. Results obtained from analysis and simulation are in line and give a close match.

Instability in stochastic and fluid queueing networks

The fluid model has proven to be one of the most effective tools for the analysis of stochastic queueing networks, specifically for the analysis of stability. It is known that stability of a fluid model implies positive (Harris) recurrence (stability) of a corresponding stochastic queueing network, and weak stability implies rate stability of a corresponding stochastic network. These results have been established both for cases of specific scheduling policies and for the class of all nonidling policies. However, only partial converse results have been established and in certain cases converse statements do not hold. In this paper we close one of the existing gaps. For the case of networks with two stations, we prove that if the fluid model is not weakly stable under the class of all nonidling policies, then a corresponding queueing network is not rate stable under the class of all nonidling policies. We establish the result by building a particular nonidling scheduling policy which makes the associated stochastic process transient. An important corollary of our result is that the condition ρ*≤1, which was proven in [Oper. Res. 48 (2000) 721–744] to be the exact condition for global weak stability of the fluid model, is also the exact global rate stability condition for an associated queueing network. Here ρ* is a certain computable parameter of the network involving virtual station and push start conditions.

Taking Account of Correlations Between Streams in Queueing Network Approximations

In this paper we describe a new variation on QNA, the Queueing Network Analyzer (Whitt [38]). QNA calculates approximate congestion measures for a network of queues. The variant proposed here allows us to relax QNA's assumption that certain counts of events in the network are uncorrelated. Following QNA, the network is approximated in terms of three basic operations on streams, namely, queueing, splitting and superposition, and random quantities of interest are characterized approximately by two moments. The approach differs from QNA in that instead of expressing the network operations as transformations applied to two-moment characterizations of the inputs, it expresses these operations as regression relations between counts in the output streams and the input streams. In essence, we substitute approximate regression relationships between random variables for QNA's approximate moment relationships. This device allows us to enhance QNA's moment relationships with information about correlations between the streams. We compare the performance of the proposed approach with QNA on a simple feed-forward network to demonstrate the need for taking account of correlation. We also discuss some of the limitations of this approach, particularly its difficulty in handling feedback, and give some ideas to improve accuracy.

Batch size modeling in a multi-item, discrete manufacturing system via an open queuing network

An open Queuing Network Analyzer (QNA) is often used in areas such as communication systems and discrete parts manufacturing systems. It uses the parametric decomposition method to approximately calculate the performance measures. The core of the method involves solving two systems of linear equations to calculate the first two moments of the effective arrival rate and service time. In this paper, we consider the effects of batch size on the parametric decomposition procedure of the QNA and modify the two sets of linear equations accordingly. The concept of a relative batch size is proposed for the purpose of modeling the effects of batch size. Experimental results are shown to illustrate the effectiveness of the method.

Configuration of distributed message converter systems

Finding a configuration of a distributed system satisfying performance goals is a complex search problem that involves many design parameters, like hardware selection, job distribution and process configuration. Performance models are a powerful tool to analyze potential system configurations, however, their evaluation is expensive, such that only a limited number of possible configurations can be evaluated. In this paper we present a systematic method to find a satisfactory configuration with feasible effort, based on a two-step approach. First, performing a queuing network analysis a hardware configuration is determined and then a software configuration is incrementally optimized by simulating Layered Queuing Network models. We applied this method to the design of performant EDI converter systems in the financial domain, where increasing message volumes need to be handled due to the growing importance of B2B interaction.

Queuing network analysis approach for estimating the sizes of the time buffers in Theory of Constraints-controlled production systems

The present paper describes an open queuing network modelling approach to estimate the size of the time buffers in production systems controlled by the Theory of Constraints philosophy. Workstations in the production network are modelled as GI/G/m queues and a queuing network analysis multiproduct open queuing network modelling method is used to estimate the average flow time to the time buffer origin and the standard deviation of flow time. Using these two values together with an assumption of normally distributed flow times and a chosen service level, the final time buffer length is determined. The queuing network analysis method has been modified to enable the modelling of production networks with machine failures, batch service and varying transfer batch sizes. The modelling approach has also been incorporated in a computerized tool that uses product specific information such as bill-of-material and routing data, and production network information such as resource data to estimate the sizes and location of the necessary time buffers for each product. Simulation experiments indicate that the procedure is sufficiently accurate to provide an initial quick estimate of the needed time buffer lengths at the design stage of the line.

Reducing cycle times in production networks with batching stations

Batching is an important system behaviour wherein several entities in a network are combined into a single entity in all further network flow. Total cycle time can be dramatically affected by an improper choice of batch sizes. In this paper, continuous-time Markov chains are used to represent the states corresponding to three common types of batching stations: single product batching stations with one-at-a-time arrivals, single product batching stations with bulk arrival distribution, and multiple product batching stations with one-at-a-time arrivals where a common batch-processing size is used. The associated Chapman-Kolmogorov equations are solved producing surprisingly simple steady-state predictions for the batch station's steady-state behaviour in each case. Although the resulting formulas are useful alone, they are used to produce a supplement to queueing network analysis (QNA) that we call QNA[B]. The formulas are orders of magnitude more efficient computationally than conducting the corresponding simulation studies. They are validated by comparing discrete event simulation to QNA[B] in the redesign of an existing real-world electronic circuit board repair facility using design of experiments. The recommended process design for that system (the number of servers at the bottleneck station(s) and the batch size(s) at the batch-processing step(s)) cuts the current cycle time by approximately 70%.

Weak instability in stochastic and fluid queueing networks

The fluid model has proven to be one of the most effective tools for the analysis of stochastic queueing networks, specifically for the analysis of stability. It is known that stability of a fluid model implies positive (Harris) recurrence (stability) of a corresponding stochastic queueing network, and weak stability implies rate stability of a corresponding stochastic network. These results have been established both for cases of specific scheduling policies and for the class of all work conserving policies.However, only partial converse results have been established and in certain cases converse statements do not hold. In this paper we close one of the existing gaps. For the case of networks with two stations we prove that if the fluid model is not weakly stable under the class of all work conserving policies, then any corresponding queueing network is not rate stable under the class of all work conserving policies. We establish the result by building a particular work conserving scheduling policy which makes any corresponding stochastic process transient. An important corollary of our result is that the condition of the form ρ* < 1, which was proven in [7) to be the exact condition for global weak stability of the fluid model, is also the exact global rate stability condition for any corresponding queueing network. Here ρ* is a certain computable parameter of the network involving virtual station and push start conditions.

Queueing network analysis: concepts, terminology, and methods

Queueing network analysis can be a valuable tool to analyze network models. However, the vast number and diverse nature of the tools available to analyze a problem can often leave the uninitiated frustrated or bewildered––awash in concepts, terminology, and methods not encountered elsewhere. As a primer for queueing network analysis, this paper emphasizes essential concepts and terminology. Selection of analytical methods based on the type of queueing network is discussed. Analytical methods are demonstrated using numerous examples and references for further study into advanced analysis are included throughout.

Translating overall production goals into distributed flow control parameters for semiconductor manufacturing

As manufacturing systems are often operated under distributed control, translating overall production goals, such as system output rate and cycle time, into local flow control targets for internal operations, such as work-in-process (WIP) levels and part release intervals, has been a significant and challenging research topic. This paper studies the problem for semiconductor wafer fabrication plants, where there are multiple part types, failure-prone machines, and deterministic reentrant process flows. Such a system is first modeled as a failure-free and reentrant open queuing network with an aggregated part type. By exploiting a decomposition-based approximation, a backward queuing network analysis (BQNA) is designed to derive flow control parameters in terms of means and variations of input processes for each machine group. These derived control parameters can be utilized to obtain managerially tangible requirements for cycle times and WIP levels and to create guidelines for distributed flow control leading to the desired overall production goals. Comparisons with simulation results for two example wafer fabrication models demonstrate the accuracy and computational efficiency of BQNA and its potential for real applications.

An adaptive importance sampling approach for the transient analysis of markovian queueing networks

AbstractWe present a new method for the efficient estimation of rare events and smart probabilities in Markovian queueing networks. The method uses importance sampling to modify the probability distribution of the events to be observed. In contrast to most other importance sampling approaches, transient instead of steady state analysis is considered and the change of the measure is computed adaptively. The whole approach is based on the combination of discrete event simulation and randomization, a technique to transform a continuous time Markov chain into a discrete time chain and an associated Poisson process. By means of randomization it is possible to derive a simple model describing me relation between me occurrence of the rare event and the probability of different transition types. This model can be used to compute adaptively the change of transition probabilities to make the rare event less rare depending on the observed behavior in some replications and the time horizon of transient analysis. If the time horizon increases, the method is extended by introducing regeneration points in the analysis. By means of small examples it is shown that the method yields satisfactory results even for more complex queueing networks for which optimal or approximatively optimal importance sampling parameters are not known from the theory.