On the perturbation analysis of discrete-event dynamic systems

The paper describes a new approach to the analysis and optimization of discrete-event dynamic systems, such as queueing networks.Dedicated to G. LeitmannThe work reported in this paper was supported in part by ONR Contracts Nos. N00014-75-C-0648 and N00014-79-C-0776 and in part by NSF Grant No. NSF-ECS-82-13680.     

Convergence properties of ordinal comparison in the simulation of discrete event dynamic systems

Recent research has demonstrated that ordinal comparison has fast convergence despite the possible presence of large estimation noise in the design of discrete event dynamic systems. In this paper, we address the fundamental problem of characterizing the convergence of ordinal comparison. To achieve this goal, an indicator process is formulated and its properties are examined. For several performance measures frequently used in simulation, the rate of convergence for the indicator process is proven to be exponential for regenerative simulations. Therefore, the fast convergence of ordinal comparison is supported and explained in a rigorous framework. Many performance measures of averaging type have asymptotic normal distributions. The results of this paper show that ordinal comparison converges monotonically in the case of averaging normal random variables. Such monotonicity is useful in simulation planning.The author would like to thank C. G. Cassandras, X. Chao, S. G. Strickland, X. Xie, and the reviewers for their helpful suggestions.     

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.     

Estimating the sojourn time sensitivity in queueing networks using perturbation analysis

The sample path perturbation analysis technique developed earlier for the analysis of throughput sensitivities (Refs. 1–3) is extended to the performance measures involving mean sojourn times of customers. The major features of the sojourn time sensitivity problem are twofold. Firstly, it is a performance associated with servers, and not with customers. Secondly, the average sojourn time in any finite observation period can be a discontinuous function of mean service times when blocking is involved in a system. This discontinuity causes errors which must be accounted for in the estimation of sensitivities. Numerical experiments and analysis validate this method of computation of the sensitivities.This work was supported by the US Office of Naval Research, Contracts N00014-84-K-0465 and N00014-79-C-0776, and by the National Science Foundation, Grant No. ENG-78-15231.     

A discrete event simulation model in the case of managing a software project

The design and development of large-scale software projects is a complex endeavor, often facing problems like cost and schedule overruns as well as low quality. Over the last years the management of software development projects has been recognized as the cornerstone point of seeking improvement and solutions. Simulation modeling of the software project process is gaining interest among academics and practitioners, as a method to tackle the complex questions with which relevant enterprises are confronted. It offers support on several issues, such as defining software product development strategies, decision-making regarding process improvement and training, in a time span ranging from a short portion of the life cycle to long term product evolution, with organization-wide implications. The aim of this work is to implement a model simulating a core part of a software project process, enabling the estimation of several project development details such as delivery times and quality metrics. The purpose of the model is to assist project managers in control and monitoring, but also in identifying the best planning alternatives. The model scope covers a portion of the life cycle of an incremental software development venture.     

Infinitesimal perturbation analysis for queueing networks with general service time distributions

We study infinitesimal perturbation analysis (IPA) for queueing networks with general service time distributions. By general we mean that the distributions may have discrete components. We show that in the presence of service time distributions with discrete components commuting condition (CC) is no longer sufficient for unbiasedness of IPA. To overcome this difficulty, we introduce the notion of separability of realvalued random variables, and show that separability of service times together with (CC) establishes unbiasedness of IPA for queueing systems with general service time distributions. It turns out that the piecewise analyticity of service times is a sufficient condition for separability.     

Maximal coupling and rare perturbation sensitivity analysis

In this article, we introduce a new method for obtaining the ersatz sample derivatives useful in sensitivity analysis: the maximal coupling RPA method.     

Robust decentralized diagnosability of networked discrete event systems against DoS and deception attacks

Denial-of-Service (DoS) are attacks conducted by malicious agents that consists in disrupting, temporally or indefinitely, the services provided by a communication network. When a malicious agent gets access to some network node, it may also perform deception attacks by inserting valid packets with fake information into vulnerable channels. We address, in this paper, DoS and deception attacks (DoS-D attack) that flood some communication channels with fake packets causing delays, loss of observations and insertion of fake observations, and their implications in decentralized fault diagnosability of networked discrete event systems (NDES). To this end, we propose an automaton model for NDES subject to DoS-D attacks that represents the adverse effects of DoS-D attacks on the observations of local diagnosers. We introduce a new codiagnosability definition called DoS-D-robust codiagnosability, and present a necessary and sufficient condition for a language to be DoS-D-robustly codiagnosable. We also propose a verification algorithm for regular languages to check DoS-D-robust codiagnosability.     

Stochastic quasigradient methods for optimization of discrete event systems

In this paper, stochastic programming techniques are adapted and further developed for applications to discrete event systems. We consider cases where the sample path of the system depends discontinuously on control parameters (e.g. modeling of failures, several competing processes), which could make the computation of estimates of the gradient difficult. Methods which use only samples of the performance criterion are developed, in particular finite differences with reduced variance and concurrent approximation and optimization algorithms. Optimization of the stationary behavior is also considered. Results of numerical experiments and convergence results are reported.     

Robustness of perturbation analysis estimators for queueing systems with unknown distributions

Sample-path-based stochastic gradient estimators for performance measures of queueing systems rely on the assumption that a probability distribution of the random vector of interest (e.g., a service or interarrival time sequence) is given. In this paper, we address the issue of dealing with unknown probability distributions and investigate the robustness of such estimators with respect to possibly erroneous distribution choices. We show that infinitesimal perturbation analysis (IPA) can be robust in this sense and, in some cases, provides distribution-independent estimates. Comparisons with other gradient estimators are provided, including experimental results. We also show that finite perturbation analysis (FPA), though only providing gradient approximations, possesses some attractive robustness properties with respect to unknown distribution parameters. An application of FPA estimation is included for a queueing system performance optimization problem involving customers with real-time constraints.This work was supported in part by the National Science Foundation Grant ECS-88-01912 and by the Office of Naval Research Contract N00014-87-K-0304.The authors wish to thank Dr. Jack Holtzman for several useful comments and suggestions.     

Smoothed perturbation analysis algorithms for estimating the derivatives of occupancy-related functions in serial queueing networks

We present unbiased Smoothed Perturbation Analysis (SPA) estimators for the derivatives of occupancy-related performance functions in serial networks ofG/G/1 queues with respect to parameters of the distributions of service times at the queues. The sample functions for these performance measures are piecewise constant, and established Infinitesimal Perturbation Analysis (IPA) methods typically fail to provide unbiased estimators in this case. The performance measures considered in this paper are: the average network occupancy as seen by an arrival, the average occupancy of a specific queue as seen by an arrival to it, the probability that a customer is blocked at a specific queue, and the probability that a customer leaves a queue idle. The SPA estimators derived are quite simple and flexible, and they lend themselves to straightforward analysis. Unlike most of the established SPA algorithms, ours are not based on the comparison of hazard rates, and the proofs of their unbiasedness do not require the boundedness of such hazard rates.Supported in part by the National Science Foundation under Grant ECS-8801912, by the Office of Naval Research under Contract N00014-87-K-0304, and by NASA under Contract NAG 2-595.     

Statistical analysis of queueing systems

This paper provides an overview of the literature on statistical analysis of queueing systems. Topics discussed include: model identification, estimation, hypothesis testing and other related aspects. Not all of these statistical problems are covered in books on queueing theory or stochastic processes. The bibliography is not exhaustive, but comprehensive enough to provide sources from the literature.     

Sequence of decisions on discrete event systems modeled by Petri nets with structural alternative configurations

The management of certain systems, such as manufacturing facilities, supply chains, or communication networks implies assessing the consequences of decisions, aimed for the most efficient operation. This kind of systems usually shows complex behaviors where subsystems present parallel evolutions and synchronizations. Furthermore, the existence of global objectives for the operation of the systems and the changes that experience the systems or their environment during their evolution imply a more or less strong dependence between decisions made at different time points of the life cycle. This paper addresses a complex problem that is scarcely present in the scientific literature: the sequences of decisions aimed for achieving several objectives simultaneously and with strong influence from one decision to the rest of them. In this case, the formal statement of the decision problem should take into account the whole decision sequence, making impractical the solving paradigm of “divide and conquer”. Only an integrated methodology may afford a realistic solution of such a type of decision problem. In this paper, an approach based on the formalism of the Petri nets is described, several considerations related to this problem are presented, a solving methodology based on the previous work of the authors, as well as a case-study to illustrate the main concepts.     

A new development for the Tikhonov Theorem in nonlinear singular perturbation systems

This paper deals with the exponential stability of nonlinear perturbation systems under a new condition. A novel criterion of exponential stability of nonlinear systems is firstly given in a general form. In this criterion, a new kind of characteristic value is introduced, which makes the exponential stability measurable. Based on this criterion, a new development for the Tikhonov Theorem in nonlinear singular perturbation systems is presented.     

Invariance of deficiency indices under perturbation for discrete Hamiltonian systems

This paper deals with discrete Hamiltonian systems with one singular endpoint. Using Hermitian linear relation generalized by linear Hamiltonian system, the invariance of the minimal and maximal deficiency indices under bounded perturbation for discrete Hamiltonian systems is built. This parallels the well-known results for linear Hamiltonian differential systems obtained by F.V. Atkinson.     

Rare events in queueing systems—A survey

Several practical approaches have been used to estimate the probabilities of rare events occurring in queueing processes. Rare events of practical interest can be considered as large deviations for a fixed queueing process (such as level crossing by the waiting time, or the queue length) or as those for a limiting triangular scheme. This paper is a survey of the literature devoted to the regenerative analysis of rare events. Because of the importance of busy period parameters, rare events within a busy period are discussed. A number of small parameter theorems useful in rare events analysis are outlined, including singular states aggregation theorems. Simulation methods for rare events analysis and other numerical methods are also presented.     

A perturbation theory for the discrete harmonic oscillator equation

This work deals with the existence, uniqueness and stability of solutions for the semilinear discrete harmonic oscillator equation on Banach spaces by using recent characterization of maximal regularity for a best difference approximation of the discrete harmonic oscillator equation.     

Stochastic petri net analysis of finite-population vacation queueing systems

We consider queueing systems in which the server occasionally takes a vacation of random duration. The vacation can be used to do additional work; it can also be a rest period. Several models of this problem have been analyzed in the past assuming that the population of the system is infinite. Similarly, it is generally assumed that the capacity of the system is infinite. In this paper we show how the finite-population system can be modeled by the stochastic Petri net. We also extend the model to the finite-capacity system. This research was sponsored by the SDIO Innovative Science and Technology Office and was managed by the Office of Naval Research under grant N3014-88-K-0623.