Analysis Of Queueing Networks Research Articles

Enabling Communication in Developing Regions

AbstractThe lack of communication facilities in developing countries is a constraint to social, political and economic empowerment of the people. However, advances in technology promise to deliver voice, video and data communication services, that are urgently needed, under a common packet switched communication network. Using Zambia as a case study, the cost effectiveness of three design scenarios which involve a hybrid of radio and microwave, radio and satellite, and radio and optic fibre were evaluated. The communication links in each scenario were modeled as E1 trunks. The cost of establishing these links was determined. Each scenario was then subjected to generic input traffic patterns using a multiclass queueing network analysis model to determine its effectiveness. Our findings show that the scenario involving the microwave links as inter‐regional links has the lowest cost. The second is the scenario involving satellite inter‐regional links and the most expensive is the scenario involving optic fibre inter‐regional links. Furthermore, the microwave‐radio hybrid scenario was found to have the smallest cost‐effectiveness ratio of 17.9 followed by the optic fibre‐radio scenario with 20.3 and finally the satellite‐radio scenario with 892.9. These results effectively imply that the microwave‐radio hybrid scenario is a better option for developing countries.

Performance Evaluation of Flexible Manufacturing Systems with Finite Local Buffers: Fixed and Dynamic Routings

This article evaluates the performance of flexible manufacturing systems with finite local buffers and fixed or dynamic routing rules, and addresses the optimal design or system configuration problem of maximizing the system throughput. The costs include machine cost, part (or pallet) cost, and local buffers cost. First, the system throughputs and their behaviors are considered with both queueing network analysis and simulation, and it is shown for a fixed routing model that the system throughput in the case of finite local buffers is greater than in the case of infinite local buffers. For a fixed versus dynamic routing rule, it is also found that the throughput in the former case can be close to the one in the latter case by changing the setting parameters. Next, the design problems of maximizing the system throughput are considered numerically for fixed and dynamic routing cases. Then, it is seen that better combination of design variables is a class of the monotonicity in local buffers, service rates, and routing probabilities.

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.

The design of robotic dairy barns using closed queueing networks

In this paper we present a closed queueing network model for a robotic milking barn. We use an approximative mean-value algorithm to evaluate important performance criteria such as the number of cows waiting, their waiting time and the utilization of the facilities in the barn. It is shown how the results from the queueing network analysis can support the discussion about the optimal design of the robotic barn.

Experiments with improved approximate mean value analysis algorithms

Approximate mean value analysis (MVA) is a popular technique for analyzing queueing networks because of the efficiency and accuracy that it affords. In this paper, we present a new software package, called the improved approximate mean value analysis library (IAMVAL), which can be easily integrated into existing commercial and research queueing network analysis packages. The IAMVAL packages include two new approximate MVA algorithms, the queue line (QL) algorithm and the fraction line (FL) algorithm, for analyzing multiple class separable queueing networks. The QL algorithm is always more accurate than, and yet has approximately the same computational efficiency as, the Bard–Schweitzer proportional estimation (PE) algorithm, which is currently the most widely used approximate MVA algorithm. The FL algorithm has the same computational cost and, in noncongested separable queueing networks where queue lengths are quite small, yields more accurate solutions than both the QL and PE algorithms.

Call/mobility processing capacity of the personal communication exchange

We analyze the call processing capacity of a personal communication exchange (PCX) for various call types (local, outgoing, incoming and transit calls). We also analyze the mobility processing capacity of the PCX for mobility functions (handover and location registration). The call/mobility processing capacities are calculated by simulation on a queueing network model. The delay times in the processing of call and mobility functions are also calculated by simulation and queueing network analyzer (QNA) for comparison between the two methods. We focus our analysis on the PCX system with distributed call/mobility processing structure, which has been under development in Korea. The numerical computations show that the results from the simulation and QNA are in closer agreement when the utilization rate (the faction of time a processor is busy) of processor handling the mobility functions becomes lower. It is estimated that the call processing capacity of the PCX is 421,280 busy hour complete call (BHC) which is equivalent to 150,700 subscribers of 1.6 BHC. The handover and location registration processing capacities are calculated to be 26,000 transactions/hour and 406,000 transactions/hour, respectively.

Queuing network analysis for waterways with artificial neural networks

An Artificial Neural Network (ANN) model has been developed for analyzing traffic in an inland waterway network. The main purpose of this paper is to determine how well such a relatively fast model for analyzing a queuing network could substitute for far more expensive simulation. Its substitutability for simulation is judged by relative discrepancies in predicting tow delays between the ANN and simulation models. This model is developed by integrating five distinct ANN submodels that predict tow headway variances at (1) merge points, (2) branching (i.e., diverging) points, (3) lock exits, and (4) link outflow points (e.g., at ports, junctions, or lock entrances), plus (5) tow queuing delays at locks. Preliminary results are shown for those five submodels and for the integrated network analysis model. Eventually, such a network analyzer should be useful for designing, selecting, sequencing, and scheduling lock improvement projects, for controlling lock operations, for system maintenance planning, and for other applications where many combinations of network characteristics must be evaluated. More generally, this method of decomposing complex queuing networks into elements that can be analyzed with ANNs and then recombined provides a promising approach for analyzing other queuing networks (e.g., in transportation, communication, computing, and production systems).

Implementation of Monte Carlo integration for the analysis of product-form queueing networks

MonteQueue is a new public-domain software package which rapidly solves large and small multiclass product-form queueing networks with multiple- and single-server stations over a wide range of traffic conditions. MonteQueue obtains estimates of performance measures by applying importance sampling to sum and integral representations of the network's normalization constants. This paper discusses the implementation issues and surveys of the theoretical properties of the four importance sampling techniques included in MonteQueue. It also presents new numerical data which compare the performance of the four techniques.

Analysis of balanced fork-join queueing networks

This paper presents an analysis of closed, balanced, fork-join queueing networks with exponential service time distributions. The fork-join queue is mapped onto two non-parallel networks, namely, a serial-join model and a state-dependent model. Using these models, it is proven that the proportion of the number of jobs in the different subsystems of the fork-join queueing network remains constant, irrespective of the multiprogramming level. This property of balanced fork-join networks is used to compute quick, inexpensive bounds for arbitrary fork-join networks.

Adaptive input control for job-shop type production systems with varying demands using inverse queueing network analysis

This paper describes the application of inverse queueing network analysis (IQNA) to a work-in-process (WIP) controlling problem of the job-shop type production system where the product mix varies periodically. We represent the continuously changing production system by a series of steady-state models which reflect its conditions for the respective periods. The WIP level which suboptimizes multiple evaluation functions defined for each period is obtained successively by using IQNA. The computational results of a sample problem on a hypothetical semiconductor manufacturing line are shown and compared with the simulation results under optimized conditions. The main cause of making the difference between the results of analysis and simulation is indicated by comparing the results of two kinds of simulation experiments, i.e. “ordinary simulation” and “compulsory simulation” the latter of which is closer by nature to the analysis. Finally, the method for reducing the difference is provided based on the indication.

Approximate analysis for queueing networks with finite capacity and customer loss

An approximation procedure is proposed for the analysis of general queueing networks with finite capacity. A customer arriving to a node with fully occupied buffer is lost. Throughput and mean waiting time are studied by this approximation procedure. The general approach is to approximately characterize the arrival processes by two parameters, and then to analyze the individual nodes separately. The two parameters, mean and variance, will be obtained by using linear (or quadratic) approximations. This method is a QNA version for handling queueing networks with blocking. The numerical examples show that the approximations compare favorably with simulation results.

An ME-based approximation for multi-server queues with preemptive priority

Entropy maximisation is applied to characterise the distributional form of the steady-state probabilities of a G/G/ c/PR queue with c (≥ 2) parallel servers and R (≥ 2) priority classes under preemptive resume (PR) rule. For R = 2, closed-form expressions are derived as explicit functions of appropriate but unknown constraints which are approximately determined using analytical results for GE-type queues. The applicability of the maximum entropy (ME) solutions for R = 2 is also extended to the case of R > 2 via the method of class aggregation. Typical numerical results are presented to illustrate the credibility of ME approximations against simulations. Comments on the role of the GE/GE/ c/PR queue as a building block for the approximate analysis of arbitrary queueing networks are included.

Improvement on the computational efficiency of inverse queueing network analysis

This paper describes the improvement on computational Efficiency of “inverse queueing network analysis (IQNA)”, which is an optimization method coupling a queueing network model and any local search algorithm. The advantages and disadvantage of simulated annealing and tabu search as the local search method are discussed in the case of applying IQNA to input control for a job-shop type production system. A hybrid algorithm using simulated annealing and tabu search is proposed and the effectiveness of the proposed algorithm is shown based on a series of computational results on input controlling problems.

Performance sensitivity analysis of open Markovian queueing networks

In this paper, we study the sensitivity of a class of performance measures in open networks with exponentially distributed service requirements and state-dependent service rates. We derive a set of analytical formulae for the sensitivities of performance with respect to the service rates or the arrival rates. We also develop algorithms for estimating these performance sensitivities; the algorithms are based on a single sample path of the network. The approach is based on perturbation analysis (PA). The main concept of PA, the realization factor of a perturbation, is extended to open networks. A set of linear equations specifying the realization factors is derived. We show that, under a mild condition called the quasi-Lipschitz condition, the normalized sensitivity of the steady-state performance with respect to a service rate (or an arrival rate) equals the negative expected value of the realization factor, and that the estimate given by the single-sample-path-based algorithm converges with probability one to the normalized sensitivity of the steady-state performance. As an example, the sensitivities of the response time in an M/M/1 queue are studied. The results provide a new analytical method of calculating performance sensitivity and justify the application of PA to open networks.

Towards better multi-class parametric-decomposition approximations for open queueing networks

Methods are developed for approximately characterizing the departure process of each customer class from a multi-class single-server queue with unlimited waiting space and the first-in-first-out service discipline. The model is σ(GTi/GIi)/1 with a non-Poisson renewal arrival process and a non-exponential service-time distribution for each class. The methods provide a basis for improving parametric-decomposition approximations for analyzing non-Markov open queueing networks with multiple classes. For example, parametric-decomposition approximations are used in the Queueing Network Analyzer (QNA). The specific approximations here extend ones developed by Bitran and Tirupati [5]. For example, the effect of class-dependent service times is considered here. With all procedures proposed here, the approximate variability parameter of the departure process of each class is a linear function of the variability parameters of the arrival processes of all the classes served at that queue, thus ensuring that the final arrival variability parameters in a general open network can be calculated by solving a system of linear equations.

Modeling and queueing analysis of variable-bit-rate coded video sources in ATM networks

Traffic models and queueing performance of variable-bit-rate (VBR) video sources in an asynchronous transfer mode (ATM) network are studied. A discrete-time discrete-state Markov chain is used to model the aggregate video traffic with each VBR-coded source being modeled by a renewal process, which has been successfully applied in the analysis of packet voice traffic. Three different methods including the stationary-interval (SI) method, the asymptotic method (ASM), and the hybrid method for queueing network analyzer (QNA) are used to approximate the average queue size. Results for different traffic conditions and different number of VBR sources are compared with the simulation results. It can be observed that as the number of sources increases the aggregate traffic becomes more predictable and the congestion at the common queue becomes smaller. This result verifies the fact that multiplexing a large number of identical video sources on a single high speed link statistically yields significant bandwidth saving. It is also interesting to note that the SI method provides an upper bound and the ASM method yields a lower bound for the average queue size for the type of traffic used in the study. When the number of VBR sources increases, the result deviates from the SI method and approaches the ASM method. In general, the QNA method provides a close match to the simulation result.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Approximate mean value performance analysis of cyclic queueing networks with production blocking

A simple approximation method is developed for performance analysis of exponential cyclic queues with production blocking. With a modified Arrival Instant Theorem to cater for finite queue capacity, a set of equations involving the mean values of performance measures are established and an efficient algorithm is proposed. Numerical experiments show that the approximation method is very efficient in providing results with good accuracy.

Approximate analysis of discrete-time tandem queueing networks with bursty and correlated input traffic and customer loss

We first describe an approximation method for fitting a two-state MMBP to the departure process of a two-state MMBP/Geo/1/ K queue. The fittin model is then used in a simple decomposition algorithm to analyze a tandem configuration of finite capacity queues with customer loss.

Performance analysis method for system bus architectures in multimedia communication terminals

AbstractThis paper proposes a new method for analyzing the performance of system bus architectures, e.g., first‐come/first‐served (FCFS) bus, priority bus transfer control, separate bus, and multiple bus, in a multimedia communication terminal. Performance is analyzed using a queueing network model (QNM). The QNM of each system bus architecture is converted into an equivalent QNM by using virtual server expressions and then analyzed by a queueing network analyzer (QNA). Numerical results show that this method is sufficiently accurate by comparison with simulation results and that the effectiveness of a system bus architecture depends on the relationship between processing speed and bus speed.

Optimal input control for job-shop type production systems using inverse queueing network analysis

This paper describes an input controlling problem of the job-shop type production systems where multiple model of products are produced repeatedly. We present an efficient method to obtain the desirable level of work-in-process (WIP) which achieves the required throughputs and approximately minimizes the shop residence time of each product. The method uses a closed queueing network model and a simulated annealing algorithm alternately to achieve the objectives of the problem. The computational results of a sample problem on the hypothetical semiconductor manufacturing line are shown and the significance of the method presented is discussed.