Queueing models for the analysis of communication systems

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discrete-time models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays.     

Rejoinder on: Queueing models for the analysis of communication systems

In this rejoinder, we respond to the comments and questions of three discussants of our paper on queueing models for the analysis of communication systems. Our responses are structured around two main topics: discrete-time modeling and further extensions of the presented queueing analysis.     

Comments on: Queueing models for the analysis of communication systems

The paper under discussion is a well-written exposition on the performance modeling of communication systems by discrete-time queueing systems, and their analysis. It basically consists of two parts: a review of the literature, focusing on the modelling of information streams and on scheduling disciplines (Sects. 2, 3), and a demonstration of some key methods for the analysis of discrete-time queueing systems, focusing on a particular two-class discrete-time queue with correlated arrivals and two priority classes (Sects. 4–6). In Sect. 1 of the present note, we make some introductory comments. In Sect. 2, realizing that the literature review in Bruneel et al. (TOP, 2014) is authoritative and extensive, we focus on a few adjacent topics which fall outside the scope of Bruneel et al. (TOP, 2014) but which in our view may also be of some interest. Finally, in Sect. 3, we discuss the analysis in Sects. 4–6 of Bruneel et al. (TOP, 2014).     

Integrated cellular manufacturing systems design with production planning and dynamic system reconfiguration

This paper presents and analyzes a comprehensive model for the design of cellular manufacturing systems (CMS). A recurring theme in research is a piecemeal approach when formulating CMS models. In this paper, the proposed model, to the best of the authors’ knowledge, is the most comprehensive one to date with a more integrated approach to CMS design, where production planning and system reconfiguration decisions are incorporated. Such a CMS model has not been proposed before and it features the presence of alternate process routings, operation sequence, duplicate machines, machine capacity and lot splitting. The developed model is a mixed integer non-linear program. Linearization procedures are proposed to convert it into a linearized mixed integer programming formulation. Computational results are presented by solving some numerical examples, extracted from the existing literature, with the linearized formulation.     

Stability analysis of models of cell production systems

We investigate the qualitative behaviour of the models of cell production systems, in the form of systems of nonlinear delay differential equations. Considered are three general models of a system involving the subpopulations of stem cells, precursor cells and mature cells, with different configurations of regulation feedbacks. The models correspond basically to the blood cell production process; however, other applications are possible. First, the simplified version (describable by ordinary differential equations) is considered. Fairly complete characterization of the trajectories is possible in this case, using the Lyapunov functions and phase plane techniques. Next, for the general models, the stability of equations linearized around the equilibria is investigated. Certain results can be obtained here, using both exact methods and numerical procedures based on an original lemma on the zeros of exponential polynomials. Then global properties (boundedness, attractivity, etc.) are examined for the nonlinear, delay case using a range of methods: Lyapunov functionals, Razumikhin functions and direct estimates on solutions. Certain special cases of our models reduce to previous literature models of blood production. Results of our analysis enable to exclude these configurations of regulation feedbacks which yield model behaviour not compatible with biological and medical observations. Techniques developed in this paper are applicable to a wide range of possible models of cell production systems.     

A visual programming system for defining behavior in simulation models of manufacturing systems

A visual programming system is described that allows the modeler full flexibility in defining the behavior of a manufacturing system simulation model. Decision-making behavior of objects in the simulation can be viewed by watching an animation of the system layout, viewing function block diagrams of rules that govern behavior, or noting the progress of an object in carrying out sequences of activities that are pictured as operation networks. Rules, elemental operations and operation networks are structured and associated with particular objects, groups of objects, and locations on the manufacturing system layout. The objective of this system is to reduce the time and expense required to construct and modify models, given that manufacturing system data have been collected.     

Estimation of the production frequencies for manufacturing systems

Email: dimitri.lefebvre{at}utbm.fr This work deals with the production frequencies estimation formanufacturing systems by measurement of the buffers content.The considered systems are modelled by continuous Petri nets.The estimation problem has exact and approximated solutionsthat are described. In the case of approximated solutions, theestimation error is also valued. At last, when the set of solutionscontains several elements, the Petri net evolution equationis completed to give one unique solution.     

A review of open queueing network models of manufacturing systems

In this paper we review open queueing network models of manufacturing systems. The paper consists of two parts. In the first part we discuss design and planning problems arising in manufacturing. In doing so we focus on those problems that are best addressed by queueing network models. In the second part of the paper we describe developments in queueing network methodology. We are primarily concerned with features such as general service times, deterministic product routings, and machine failures — features that are prevalent in manufacturing settings. Since these features have eluded exact analysis, approximation procedures have been proposed. In the second part of this paper we review the developments in approximation procedures and highlight the assumptions that underlie these approaches.     

A technique for on-line sensitivity analysis of flexible manufacturing systems

The recent perturbation analysis approach to discrete event systems is applied to flexible manufacturing systems (FMS). While analytic (queueing) models are useful in preliminary design of such systems, they are not accurate enough at the detailed design/operation stage. Thus, experimentation on detailed simulations or on the actual system has been the way to optimize system performance. Perturbation analysis allows us to derive the sensitivity of system performance, with respect to several design/operating parameters, by observing a single experiment (and without having to actually alter the parameters — often a costly operation). Thus, observation of one experiment can give accurate directions for the improvement of several parameter values. Here we give a simulation example illustrating how perturbation analysis could be used on-line on an FMS to improve its performance, including reducing its operating cost. Experimental results are also presented validating the estimates obtained from this technique.Work supported by U.S. Office of Naval Research Contracts N00014-75-C-0648 and N00014-79-C-0776, and NSF Grant ENG78-15231, at Harvard University.A preliminary version of this paper appeared in the Proc. 1st ORSA/TIMS Conf. on Flexible Manufacturing Systems, August 1984. This version includes two appendices, which relate to implementation of the technique described in the main body of the paper.     

Taxonomy of batch queueing models in manufacturing systems

Batching plays an important role in performance evaluation of manufacturing systems. Three types of batching are commonly seen: transfer batches, parallel batches and serial batches. To model the batching behavior correctly, a comprehensive classification of batching is proposed. Eight types of batching behavior are classified and corresponding queueing models are given. The newly proposed models are validated by simulation.     

Real-time production planning and control system for job-shop manufacturing: A system dynamics analysis

Much attention has been paid to production planning and control (PPC) in job-shop manufacturing systems. However, there is a remaining gap between theory and practice, in the ability of PPC systems to capture the dynamic disturbances in manufacturing process. Since most job-shop manufacturing systems operate in a stochastic environment, the need for sound PPC systems has emerged, to identify the discrepancy between planned and actual activities in real-time and also to provide corrective measures. By integrating production ordering and batch sizing control mechanisms into a dynamic model, we propose a comprehensive real-time PPC system for arbitrary capacitated job-shop manufacturing. We adopt a system dynamics (SD) approach which is proved to be appropriate for studying the dynamic behavior of complex manufacturing systems. We study the system’s response, under different arrival patterns for customer orders and the existence of various types real-time events related to customer orders and machine failures. We determine the near-optimal values of control variables, which improve the shop performance in terms of average backlogged orders, work in process inventories and tardy jobs. The results of extensive numerical investigation are statistically examined by using analysis of variance (ANOVA). The examination reveals an insensitivity of near-optimal values to real-time events and to arrival pattern and variability of customer orders. In addition, it reveals a positive impact of the proposed real-time PPC system on the shop performance. The efficiency of PPC system is further examined by implementing data from a real-world manufacturer.     

Decision architectures for production planning in multi-stage multi-product manufacturing systems

Recent trends in automated manufacturing call for hierarchical decision architectures for production planning, suitable for integration with part flow controls. Different design approaches are currently adopted for implementing production planning architectures, depending either on the objective of defining a centralized production plan for the whole manufacturing system (as in the case of MRP and OPT), or on the desire of coordinating local plans for the component work cells (as for JIT). The paper analyzes such approaches by use of a unifying mathematical formulation of the production plan optimization problem, to recognize the main features of the existing planning approaches, and compare their usefulness in different manufacturing processes.     

Models for cellular manufacturing systems design: matching processing requirements and operator capabilities

Cellular manufacturing systems comprise categorizing machines used in the firm's production system into cells dedicated to part families that have similar requirements in terms of tooling, setups and operations sequences. Although worker assignment to cells has a significant impact on cell effectiveness, scant attention has been paid to this issue in previous research. We present two models—sequential and concurrent—for cell formation. The sequential model uses a machine–part incidence matrix (MPIM)-based similarity coefficient while the concurrent model uses a similarity coefficient based on both MPIM and machine–operator incidence matrix (MOIM). Our results show that for 50 problem sets widely reported in literature, the concurrent model outperformed the sequential model in most cases. A measure quantifying the difference in MPIM and MOIM was developed and the relative out-performance of the concurrent model was shown to depend on the value of this measure.     

Queueing systems with leadtime constraints: A fluid-model approach for admission and sequencing control

We study how multi-product queueing systems should be controlled so that sojourn times (or end-to-end delays) do not exceed specified leadtimes. The network dynamically decides when to admit new arrivals and how to sequence the jobs in the system. To analyze this difficult problem, we propose an approach based on fluid-model analysis that translates the leadtime specifications into deterministic constraints on the queue length vector. The main benefit of this approach is that it is possible (and relatively easy) to construct scheduling and multi-product admission policies for leadtime control. Additional results are: (a) While this approach is simpler than a heavy-traffic approach, the admission policies that emerge from it are also more specific than, but consistent with, those from heavy-traffic analysis. (b) A simulation study gives a first indication that the policies also perform well in stochastic systems. (c) Our approach specifies a “tailored” admission region for any given sequencing policy. Such joint admission and sequencing control is “robust” in the following sense: system performance is relatively insensitive to the particular choice of sequencing rule when used in conjunction with tailored admission control. As an example, we discuss the tailored admission regions for two well-known sequencing policies: Generalized Processor Sharing and Generalized Longest Queue. (d) While we first focus on the multi-product single server system, we do extend to networks and identify some subtleties.     

Multi-product economic lot scheduling problem with separate production lines for manufacturing and remanufacturing

We study the economic lot scheduling problem with two production sources, manufacturing and remanufacturing, for which operations are performed on separate, dedicated lines. We develop an exact algorithm for finding the optimal common-cycle-time policy. The algorithm combines a search for the optimal cycle time with a mixed integer programming (MIP) formulation of the problem given a fixed cycle time. Using case study data from an auto part producer, we perform a sensitivity study on the effects of key problem parameters such as demand rates and return fractions. Furthermore, by comparing to results in Tang and Teunter [Tang, O., Teunter, R.H., 2006. Economic lot scheduling problem with returns. Production and Operations Management] for the situation where all operations are performed on the same line, we analyze the cost benefits of using dedicated lines.     

Application of operational research models and techniques in flexible manufacturing systems

In this paper, classification of Flexible Manufacturing Systems (FMSs) and flexibilities is presented. It would be difficult to efficiently implement an FMS without solving its design problems. These problems, as well as a number of operations problems, are discussed. A planning and scheduling framework is developed. Based on this framework, the relevant FMS literature is discussed. Most of the tools and techniques applicable for solving FMS problems are listed. Recommendations for future researh are also presented.     

A review of major paradigms and models for the design of civil engineering systems

In this paper, the author presents the five classical paradigms of the process of design in civil engineering and identifies a new emerging paradigm: the interactive multi-attribute learning paradigm. This paradigm is studied in terms of actors, structures and OR instruments which can help to fulfil its application to modern design of civil engineering systems.