Analysis Of Queueing Networks Research Articles

Cluster analysis and workload classification

Clustering techniques are widely recommended tools for workload classification. The k-means algorithm is widely accepted as the "standard" technique of detecting workload classes automatically from measurement data. This paper examines validity of the obtained workload classes, when the current system and workload is analyzed by a queueing network model and mean value analysis. Our results, based on one week's accounting data of a VAX 8600, indicate that the results of queueing network analysis are not stable when the classes of workload are constructed through the k-means algorithm. Therefore, we cannot recommended that the most widely used clustering technique should be used in any workload characterization study without careful validation.

Performance and traffic analysis of a network-based distributed system

In this paper we study the performance of a distributed computing system that consists of a number of clients and a server, interconnected by a carrier-sense multiple-access with collision detection (CSMA/CD) LAN. Each client represents a single-user discless workstation, or an intelligent terminal, and generates application workload using either a conventional Unix file system or the Network File System (NFS). To characterize the application workload we perform a series of measurement experiments in a controlled environment. During each experiment the traffic on the network, and the activity on the various system resources are monitored. The measurements obtained from the experiments are used to parameterize a queueing network model of the system, which is then used to project the performance of the system under various load conditions, to identify system bottlenecks, and to compare design alternatives. The results obtained from the queueing network analysis are used to determine the maximum number of clients that can be supported by the system without violating system performance requirements.

Decomposable score function estimators for sensitivity analysis and optimization of queueing networks

This paper surveys some recent results and presents some new results on the so-called decomposable and truncated score functions (DSF and TSF) estimators for performance evaluation, sensitivity analysis and optimization of open non-Markovian (non-product) queueing networks. The idea behind the TSF estimators is based on truncation of the score function process, while the idea behind the DSF estimators is to decompose the queueing network into smaller units, calledmodules, such that each module contains several connected queues, and then approximate the unknown quantities by treating these modules as if they were completely independent. In other words, in the DSF estimators we use frequently occurrentlocal regenerative cycles at eachindividual module instead oftrue but seldom occurrentglobal ones of theentire system. Although the local cycles at each module interact with their neighbors, our numerical studies show that typically the contribution from the neighbors is quite small and thus DSF estimators approximate the unknown quantities rather well, in the sense that their bias is reasonably small and the variance is much smaller than that of the standard score function estimators. Both DSF and TSF estimators were implemented in a simulation package, called thequeueing network stabilizer and optimizer (QNSO). This package is suitable for performance evaluation, sensitivity analysis and optimization of general open non-Markovian queueing networks with respect to the parameter vector of an exponential family of distributions.

A new method of performance sensitivity analysis for non-Markovian queueing networks

The paper develops a new method of calculating and estimating the sensitivities of a class of performance measures with respect to a parameter of the service or interarrival time distributions in queueing networks. The distribution functions may be of a general form. The study is based on perturbation analysis of queueing networks. A new concept, the realization factor of a perturbation, is introduced for the network studied. The properties of realization factors are discussed, and a set of linear differential equations specifying the realization factors are derived. The sensitivity of the steady-state performance with respect to a parameter can be expressed in a simple form using realization factors. Based on this, the sensitivity can be estimated by applying a perturbation analysis algorithm to a sample path of the system. We show that the derivative of the performance measure with respect to a parameter based on a single sample path converges with probability one to the derivative of the steady-state performance as the length of the sample path goes to infinity. The results provide a new analytical method of calculating performance sensitivities and justifies the application of perturbation analysis algorithms to non-Markovian queueing networks.

Comparative evaluation of approximate methods for modelling of network systems

The paper discloses the results of a comparative evaluation of several approximate methods of queueing network analysis concerning their accuracy, fields of validity and computational consumptions; the comparison is being carried out with varying values of network parameters.

Strong consistency of infinitesimal perturbation analysis for tandem queueing networks

Strong consistency of infinitesimal perturbation analysis for the sojourn times in a class of tandem queueing networks is proved. Service times at the queues are correlated, and they are affine functions of the variable parameters. Differentiability of the average sojourn times is not assumed, but proved. The analysis is not based on assumptions of regenerative cycles of the networks but on stability and ergodicity of the queueing processes involved. The proof of strong consistency is based on a set of abstract conditions, described in terms of properties of the sample performance functions. These conditions are first shown to be sufficient for strong consistency, and then their validity for the networks in question is proved.

A line-balancing strategy for designing flexible assembly systems

We present a rough-cut analysis tool that quickly determines a few potential cost-effective designs at the initial design stage of flexible assembly systems (FASs) prior to a detailed analysis such as simulation. It uses quantitative methods for selecting and configuring the components of an FAS suitable for medium to high volumes of several similar products. The system is organized as a series of assembly stations linked with an automated material-handling system moving parts in a unidirectional flow. Each station consists of a single machine or of identical parallel machines. The methods exploit the ability of flexible hardware to switch almost instantaneously from product to product. Our approach is particularly suitable where the product mix is expected to be stable, since we combine the hardware-configuration phase with the task-allocation phase. For the required volume of products, we use integer programming to select the number of stations and the number of machines at each station and to allocate tasks to stations. We use queueing network analysis, which takes into account the mean and variance of processing times among different products to determine the necessary capacity of the material-handling system. We iterate between the two analyses to find the combined solution with the lowest costs. Work-in-process costs are also included in the analysis. Computational results are presented.

The QNET method for two-moment analysis of open queueing networks

Consider an open network of single-server stations, each with a first-in-first-out discipline. The network may be populated by various customer types, each with its own routing and service requirements. Routing may be either deterministic or stochastic, and the interarrival and service time distributions may be arbitrary. In this paper a general method for steady-state performance analysis is described and illustrated. This analytical method, called QNET, uses both first and second moment information, and it is motivated by heavy traffic theory. However, our numerical examples show that QNET compares favorably with W. Whitt's Queueing Network Analyzer (QNA) and with other approximation schemes, even under conditions of light or moderate loading. In the QNET method one first replaces the original queueing network by what we call an approximating Brownian system model, and then one computes the stationary distribution of the Brownian model. The second step amounts to solving a certain highly structured partial differential equation problem; a promising general approach to the numerical solution of that PDE problem is described by Harrison and Dai [8] in a companion paper. Thus far the numerical solution technique has been implemented only for two-station networks, and it is clear that the computational burden will grow rapidly as the number of stations increases. Thus we also describe and investigate a cruder approach to two-moment network analysis, called ΠNET, which is based on a product form approximation, or decomposition approximation, to the stationary distribution of the Brownian system model. In very broad terms, ΠNET is comparable to QNA in its level of sophistication, whereas QNET captures more subtle system interactions. In our numerical examples the performance of ΠNET and QNA is similar; the performance of QNET is generally better, sometimes much better.

Approximate analysis of general open queuing networks with restricted capacity

We consider an open queuing network having general service time distributions. The total number of customers simultaneously present in the network connot exceed a given value, called the capacity of the network. Customers arriving while the network is full are forced to wait in an external queue. We present an approximate analysis of such queuing networks. We first derive an equivalent closed queuing network model. This closed model is analyzed using an approximate product-form solution technique. The performance parameters of the original open model are then easily derived. We compare this method with the classical aggregation technique.

An approximate analysis of open tandem queueing networks with blocking and general service times

An approximation algorithm is presented for open tandem queueing networks with finite buffers and with general service times. The algorithm decomposes the system into individual queues with revised arrival and service processes and revised queue capacity. Then, each queue is analyzed in isolation. The service process is revised to reflect the additional delay a unit might undergo due to blocking. Unlike previous algorithms, the arrival process to each decomposed queue is described by a C 2 distribution. The parameters of the service and the arrival processes are computed approximately using an iterative scheme. The approximation procedure yields the steady-state queue-length distribution of each queue. From this, other more commonly sought performance measures, such as mean queue-length, probability that a queue is empty, throughput, etc., can be easily computed. Comparisons of the approximate results with simulation results showed that the proposed algorithm has a good error-level.

A queueing network analysis of a health center

This paper shows how a queueing network model helped to uncover the causes of delay in a health center appointment clinic. Patients, clerks, technicians, doctors and nurses agreed that the clerical registration area was the major bottleneck in the system. Our first reaction was to simulate the system with special attention on the complex registration procedure. Time constraints on data collection and program development led us to a queueing network model and QNA, a software tool for analyzing queueing networks developed by Whitt. The queueing analysis showed the registration area was not the bottleneck and we conjectured that delays were due to scheduling problems. A preliminary trial in the clinic of a modified appointment system showed promise with a 20 minute reduction in average time in the system (based on a small sample). Although there were significant differences between features of the real system and assumptions in the queueing network model, the queueing network model yielded insight into the operation of the appointment clinic.

Aggregation approximations for sensitivity analysis of multi-class queueing networks

Two methods are presented for estimating performance derivatives from simulation of multi-class queueing networks for sensitivity analysis. The methods use approximate subnetwork aggregation to reduce the problem to a single-class derivative estimation problem with which a modified infinitesimal perturbation analysis algorithm is used. The modified algorithm treats a subnetwork as though it had been aggregated, but is actually applied to the original (non-aggregated) network. The two approaches to aggregation considered represent two extensions of the idea of a Norton equivalent to non-product-form networks, one based on an exact result, the other heuristic. These are of interest beyond the particular application considered here.

Analysis of cyclic queueing networks with finite buffers and blocking before service

We consider cyclic queueing networks with exponential servers and finite buffers. The blocking mechanism we consider is blocking-before-service, i.e., a server is allowed to start processing a job only if a space is available in the next queue. We present an approximate technique for analyzing such networks based on a decomposition approach. We first consider the case where at least one buffer has an infinite capacity. The network is decomposed into a set of M/M/1 x/ K queues. An iterative algorithm for calculating the performance parameters is proposed. This technique is then extended to the case where all queues have finite capacity. Numerical experiments show that this technique provides a fairly good estimate of the throughput and the average queue lengths.

MEM for arbitrary queueing networks with multiple general servers and repetitive-service blocking

The analytic method for entropy maximisation, subject to marginal mean value constraints, is applied to characterise new product-form approximations for arbitrary FCFS (first-come-first-served) queueing networks with multiple server queues and general interarrival and service times under repetitive-service blocking involving both fixed and random destinations. For open queueing networks the maximum entropy solution suggests a decomposition into individual finite capacity multiple server queues with a censored arrival process and revised service-times. For closed queueing networks the product-form solution of open networks is initially modified to satisfy constraints on population and flow conservation and is in turn truncated and efficiently implemented via a convolution type recursive procedure with time complexity of O( M 2 L 2), where M is the number of queues and L is the fixed population of the network. The FCFS GE/GE/ c/ K; N censored queue with GE (generalised exponential) interarrival-time and service-time distributions, c ( c ≧ 1) multiple servers, minimum queue length, K ( K ⩾ 0) and finite capacity, N ( K < N < + ∞), is exactly analysed in the context of maximum entropy and used as a ‘building block’ for the approximate analysis of general queueing networks. Validation examples are presented for assessing the numerical accuracy of the maximum entropy method (MEM) and favourable comparisons against simulation results are made.

Planning the Workpiece Populations in Flexible Manufacturing Systems by Means of Approximate Performance Analysis

The solution of a particular synthesis problem is dealt with in this paper. With reference to a multiclass closed queueing network with deterministic service times, we consider the problem of determining the populations in the network in order to achieve a fixed set of production rates. The general expression of the required workpiece populations is found by making use of the relationships characterizing the equilibrium point of an approximate performance analysis method called QNA (Queueing Network Analyzer).

Approximations for Product Departures from a Single-Server Station with Batch Processing in Multi-Product Queues

In this paper we consider a single-server station processing jobs belonging to multiple product classes. The processing at the station is in batches of fixed size, r. Job arrivals in different product classes are independent of the arrivals in other classes. The arrivals within each product class and the service times are assumed to have general, independent and identical distributions. Based on approximate analyses, we present an estimate for the mean number of jobs and provide two complementary characterizations of the product departure streams. We present methods to compute the squared coefficient of variation of the departure intervals and the probability distribution of the lot sizes of product departures. The computational results reported in this paper demonstrate that the accuracy of the approximations is acceptable in most applications. Based on these results, we identify conditions under which the estimates can be expected to perform well. The methods developed in this paper complement the decomposition approach for open queueing networks proposed by Shanthikumar and Buzacott (Shanthikumar, J. G., J. A. Buzacott. 1981. Open queueing network models of job shops. Internat. J. Production Res. 19(3) 255–266.) and Whitt (Whitt, W. 1983. The queueing network analyzer. Bell System Tech. J. 62(9) 2779–2815.) and permit analysis of networks with some types of batch processing.

A computationally efficient approximation algorithm for feed-forward open queueing networks with blocking

We present a computationally efficient version of an algorithm reported by Altiok and Perros [2] for the analysis of feed-forward open exponential queueing networks with blocking. The proposed algorithm has minimal time and space requirements, and it has the same accuracy as the original algorithm.

Approximate throughput analysis of cyclic queueing networks with finite buffers

An approximation method for obtaining the throughput of cyclic queueing networks with blocking as a function of the number of customers in it is presented. The approximation method was developed for two different blocking mechanisms. It was also extended to the case of the central server model with blocking. Validation tests show that the algorithm is fairly accurate. >

Dependence in packet queues

The burstiness of the total arrival process has been previously characterized in packet network performance models by the dependence among successive interarrival times. It is shown that associated dependence among successive service times and between service times and interarrival times also can be important for packet queues involving variable packet lengths. These dependence effects are demonstrated analytically by considering a multiclass single-server queue with batch-Poisson arrival processes. For this model and more realistic models of packet queues, insight is gained from heavy-traffic limit theorems. This study indicates that all three kinds of dependence should be considered in the analysis and measurement of packet queues involving variables packet lengths. Specific measurements are proposed for real systems and simulations. This study also indicates how to predict expected packet delays under heavy loads. Finally, this study is important for understanding the limitations of procedures such as the queuing network analyzer (QNA) for approximately describing the performance of queuing networks using the techniques of aggregation and decomposition.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Approximate analysis of load dependent general queueing networks

A method for obtaining approximate solutions to load-dependent closed queueing networks containing general service-time distributions and first-come-first-served scheduling disciplines is presented. The technique demonstrated is an extension of the well-known method of R. Marie (1979). A formula for the conditional throughputs is derived. After each iteration a check is performed to guarantee that the results obtained are within a tolerance level epsilon . These iterations are repeated whenever invalid results are detected. On the average, the solutions obtained vary by less than 5% from their respective exact and simulation results. >