A continuous time dynamic model of discrete scheduling problems for a large class of manufacturing systems is considered in the present paper. The realistic manufacturing based on multi-level bills of materials, flexible machines, controllable buffers and deterministic demand profiles is modeled in the canonical form of optimal control. Carrying buffer costs are minimized by controlling production rates of all machines that can be set up instantly. The maximum principle for the model is studied and properties of the optimal production regimes are revealed. The solution method developed rests on the iterative approach generalizing the method of projected gradient, but takes advantage of the analytical properties of the optimal solution to reduce significantly computational efforts. Computational experiments presented demonstrate effectiveness of the approach in comparison with pure iterative method.

In this article we present extension of the recently introduced maximal coupling Rare Perturbation Analysis (RPA), a novel approach for computing gradient estimates in sensitivity analysis, and we extend the result of Bremaud (1992) to the random horizon case. Also we interpret the analysis of Dai and Ho (1992) in terms of maximal coupling (one sided).

Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of a class of “logical” discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications including manufacturing systems and computer networks (Passino et al. 1994, Burgess and Passino 1994). In this paper we extend the conventional notions and analysis of uniform boundedness, uniform ultimate boundedness, practical stability, finite time stability, and Lagrange stability so that they apply to the class of logical DES that can be defined on a metric space. Within this stability-theoretic framework we show that the standard Petri net-theoretic notions of boundedness are special cases of Lagrange stability and uniform boundedness. In addition we show that the Petri ent-theoretic approach to boundedness analysis is actually a Lyapunov approach in that the net-theoretic analysis actually produces an appropriate Lyapunov function. Moreover, via the Lyapunov approach we provide a sufficient condition for the uniform ultimate boundedness of General Petri nets. To illustrate the Petri net results, we study the boundedness properties of a rate synchronization network for manufacturing systems. In addition, we provide a detailed analysis of the Lagrange stability of a single-machine manufacturing system that uses a priority-based part servicing policy.

Recent results on the control of infinite behaviour of finite automata are extended to allow Rabin acceptance conditions as modelling assumptions as well as specifications. The key result is a fixpoint characterization of the automaton'scontrollability subset—the set of states from which it can be controlled to the satisfaction of its associated specification. The fixpoint characterization allows for straightforward computation of the subset and for effective synthesis of controllers. the results have potential applications to supervisory control synthesis, the synthesis of reactive systems, and decision procedures for modal logics.

We consider a discrete event system (DES) modeled by a timed automaton with partial state and event observations. We view the system as an input-output system, where the input is a sequence of event lifetimes, and the output is the resulting sequence of events, states, and transition epochs. We consider the problem of extracting event lifetimes (input) from observations of the output trajectory, which we callinversion. We give necessary and sufficient conditions forinvertibility, and an algorithm that extracts event lifetimes from any given output observation of an invertible system. We describe a distributed timed DES model based on the prioritized synchronous product of subsystems, and study the inversion problem in this framework. We show that invertibility in the subsystems implies invertibility in the global system. To illustrate our results, we provide an example of a tandem network.

In this paper we introduce a new approach to rare event simulation. Because of the extensive simulation required for precise estimation of performance criterion dependent on rare event occurrences, obstacles such as computing budget/time constraints and pseudo-random number generator limitations can become prohibitive, particularly if comparative study of different system designs is involved. Existing methods for rare events simulation have focused on simulation budget reduction while attempting to generate accurate performance estimates. In this paper we propose a new approach for rare events system analysis in which we relax the simulation goal to the isolation of a set of “good enough” designs with high probability. Given this relaxation, referred to as ordinal optimization and advanced by Ho et al. (1992), this paper's approach calls instead for the consideration of an appropriate surrogate design problem This surrogate problem is characterized by its approximate ordinal equivalence to the original problem and its performance criterion's dependence not on rare event occurrences, but on more frequent events. Evaluation of such a surrogate problem under the relaxed goals of ordinal optimization has experimentally resulted in orders of magnitude reduction in simulation burden.

We examine two schemes for parametric parallel simulation on SIMD supercomputers. In SIMD machines, the parallel processors execute a common instruction stream using local data-under the control of a front-end processor. In contrast to most parallel simulation approaches-which simulate a single system using multiple processors-we simulate distinct parametric variants at each processor. We extract some of the common computation embedded in these simulations and perform it on the front-end, leaving the rest to the parallel processors.

In this paper we apply the ideas of ordinal optimization and the technique of Standard Clock (SC) simulation to the voice-call admission-control problem in integrated voice/data multihop radio networks. This is an important problem in networking that is not amenable to exact analysis by means of the usual network modeling techniques. We first describe the use of the SC approach on sequential machines, and quantify the speedup in simulation time that is achieved by its use in a number of queueing examples. We then develop an efficient simulation model for wireless integrated networks based on the use of the SC approach, which permits the parallel simulation of a large number of admission-control policies, thereby reducing computation time significantly. This model is an extension of the basic SC approach in that it incorporates fixed-length data packets, whereas SC simulation is normally limited to systems with exponentially distributed interevent times. Using this model, we demonstrate the effectiveness of ordinal-optimization techniques, which provide a remarkably good ranking of admission-control policies after relatively short simulation runs, thereby facilitating the rapid determination of good policies. Moreover, we demonstrate that the use of crude, inaccurate analytical and simulation models can provide highly accurate policy rankings that can be used in conjunction with ordinal-optimization methods, provided that they incorporate the key aspects of system operation.

We review two approaches, the Standard Clock (SC) technique and Augmented System Analysis (ASA), that have been proposed for generating sample paths of Discrete Event Systems (DES) in parallel. These are placed in the unifying framework of the fundamentalsample path constructability problem: for a finite discrete parameter set Θ = {θ1, ..., θm}given a sample path under θ1 the problem is to simultaneously construct sample paths under all remaining parameter values. Using the ASA approach we then consider the problem of smoothing arbitrary, generally bursty, and possibly nonstationary traffic processes which are encountered in many applications, especially in the area of flow control for integrated-service, high-speed networks. We derive some basic structural properties of a smoothing scheme known as the Leaky Bucket (LB) mechanism through which it is seen that the variability of a traffic process can be monotonically decreased by decreasing an integer-valued parameter of this scheme. Finally, we show that a sample path under any value of this parameter is constructable with respect to an observed sample path under any other value. Therefore, by controlling this parameter on line, we show how simple iterative optimization schemes can be used to achieve typical design objectives such as keeping both the mean packet delay due to smoothing and the variability of the traffic process low.

The simulation of high-speed telecommunication systems such as ATM (Asynchronous Transfer Mode) networks has generally required excessively long run times. This paper reviews alternative approaches using parallelism to speed up simulations of discrete event systems, and telecommunication networks in particular. Subsequently, a new simulation method is introduced for the fast parallel simulation of a common network element, namely, a work-conserving finite capacity statistical multiplexer of bursty ON/OFF sources arriving on input links of equal peak rate. The primary performance measure of interest is the cell loss ratio, due to buffer overflows. The proposed method is based on two principal techniques: (1) the derivation of low-level (cell level) statistics from a higher level (burst level) simulation and (2) parallel execution of the burst level simulation program. For the latter, atime-division parallel simulation method is used where simulations operating at different intervals of simulated time are executed concurrently on different processors. Both techniques contribute to the overall speedup. Furthermore, these techniques support simulations that are driven by traces of actual network traffic (trace-driven simulation), in addition to standard models for source traffic. An analysis of this technique is described, indicating that it offers excellent potential for delivering good performance. Measurements of an implementation running on a 32 processor KSR-2 multiprocessor demonstrate that, for certain model parameter settings, the simulator is able to simulate up to 10 billion cell arrivals per second of wallclock time.