Abstract. Part II continues the development of policy synthesis techniques for multiclass queueing networks based upon a linear fluid model. The following are shown: (i) A relaxation of the fluid model based on workload leads to an optimization problem of lower dimension. An analogous workload-relaxation is introduced for the stochastic model. These relaxed control problems admit pointwise optimal solutions in many instances. (ii) A translation to the original fluid model is almost optimal, with vanishing relative error as the networkload ρ approaches one. It is pointwise optimal after a short transient period, provided a pointwise optimal solution exists for the relaxed control problem. (iii) A translation of the optimal policy for the fluid model provides a policy for the stochastic networkmodel that is almost optimal in heavy traffic, over all solutions to the relaxed stochastic model, again with vanishing relative error. The regret is of order | log(1 − ρ)|.

. Motivated by dynamic scheduling control for queueing networks, Chen and Yao [8] developed a systematic method to generate dynamic scheduling control policies for a fluid network, a simple and highly aggregated model that approximates the queueing network. This study addresses the question of how good these fluid policies are as heuristic scheduling policies for queueing networks. Using simulation on some examples these heuristic policies are compared to traditional simple scheduling rules. The results show that the heuristic policies perform at least comparable to classical priority rules, regardless of the assumptions made about the traffic intensities and the arrival and service time distributions. However they are certainly not always the best and, even when they are, the improvement is seldom dramatic. The comparative advantage of these policies may lie in their application to nonstationary situations such as might occur with unreliable machines or nonstationary demand patterns. ...

This paper concerns control of stochastic networks using state-dependent safetystocks. Three examples are considered: a pair of tandem queues; a simple routing model; and the Dai-Wang re-entrant line. In each case, a single policy is proposed that is independent of network load # .

It is shown that stability of the celebrated MaxWeight or back pressure policies is a consequence of the following interpretation: either policy is myopic with respect to a surrogate value function of a very special form, in which the “marginal disutility ” at a buffer vanishes for vanishingly small buffer population. This observation motivates the h-MaxWeight policy, defined for a wide class of functions h. These policies that share many of the attractive properties of the MaxWeight policy: (i) The policy does not require arrival rate data. (ii) The h-myopic policy is stabilizing when h is a perturbation of a monotone linear function, or a monotone Lyapunov function for the fluid model. (iii) A perturbation of the relative value function for a workload relaxation gives rise to a myopic policy that is approximately average-cost optimal in heavy traffic, with logarithmic regret. The first results are obtained for a completely general stochastic network model. Asymptotic optimality is established for the general scheduling model with a single bottleneck.

Current strategic and technological trends in discrete-part manufacturing require extensive and #exible automation of the underlying production systems. However, even though a great deal of work has been done to facilitate manufacturing automation at the hardware component level, currently there is no adequately developed control methodology for these environments.

This paper presents a new distributed real-time control architecture for flexibly automated production systems. The modelling assumptions underlying the design are driven by, and abstract, the structure and operations of the emerging 300 mm semiconductor manufacturing fab, one of the most extensively automated environments in contemporary manufacturing. The key element of the controller design itself, which differentiates it from past efforts, is the distribution of the control function to the constituent components of the system shop-floor architecture, while maintaining both the logical correctness and the efficiency of the system behaviour. The architecture was designed to be easily implementable in the actual system shop-floor, and therefore is aligned with, and augments, current practices in these environments. From a theoretical perspective, the proposed design has employed, integrated and extended a series of theoretical results from the field of Discrete Event Dynamical Systems. It is our expectation that the proposed architecture will also provide a formal framework for further analytical studies on the performance evaluation and performance-oriented control/scheduling of the considered class of manufacturing systems.

Traditionally, the semiconductor manufacturing industry has been driven by continuous technological advancement of the underlying production processes. Yet, as the industry matures, mere technology development is no longer sufficient. The effective deployment and exploitation of the system production capacity and operational capability become critical for competitive success. Hence, currently, there is an increasing interest towards the development of a control paradigm / framework that will allow the effective and efficient deployment and operation of contemporary fabs, including the upcoming 300mm fab. The research program presented in this paper seeks to define a detailed modeling and control framework for the real-time 300mm fab operations, by exploiting and integrating emerging results in Discrete Event Systems theory. The proposed approach is demonstrated through a small-scale example, modeling the operation of a 300mm fab bay. Furthermore, in addition to the development of the formal specification, the presented program will also implement the proposed fab modeling and control framework in a Web-based simulation platform, that will function as a fab (re-)configuration and control synthesis tool for the fab control engineer, and as an educational tool for manufacturing system modeling and control.

In this paper we present a novel formulation for the optimal control of discrete event dynamic processes which represent production systems with unreliable machines and buffers of finite capacity. We derive an optimum control strategy that is critically based on the fact that the discrete event dynamic behavior of the system is approximatively represented with a hybrid model. We introduce a deterministic fluid network model where the average flow rates through the machines are the control variables and with an original approach we show that the dynamics of the system easily translate into a discrete–time, time–varying state variable model, where the optimum machine production rates can be easily obtained by solving a sequence of linear programming problems.

Traditionally, the semiconductor manufacturing industry has been driven by continuous technological advancement of the underlying production processes. Yet, as the industry matures, mere technology development is no longer sufficient. The effective deployment and exploitation of the system production capacity and operational capability become critical for competitive success. Hence, currently, there is an increasing interest towards the development of a control paradigm / framework that will allow the effective and efficient (re-)deployment and operation of contemporary fabs. The research program presented in this paper seeks to define a detailed modeling and control framework for the real-time fab operations, by exploiting and integrating emerging results in Discrete Event Systems theory. Furthermore, in addition to the development of the formal specification, the presented program will also implement the proposed fab modeling and control framework in a Web-based simulation platform, ...

We propose a novel approach for controlling queueing networks that minimizes weighted holding costs over a finite time horizon. Our approach approximates the discrete problem by a fluid system for which an optimization problem is formulated. This problem is a separated continuous linear program, it is solved optimally using a simplex based algorithm of Weiss. The solution consists of piecewise constant allocations of the activities, with a finite number of breakpoints over the time horizon. Once solved, we associate a multi-class queueing network with infinite virtual queues with each interval of the fluid solution, and this measures the deviations of the original system from the fluid solution. We then track the fluid solution by using an adaptation of Dai and Lin’s maximum pressure policy that keeps these deviations rate stable. This procedure is asymptotically optimal as we scale up the number of jobs and the processing speed. We illustrate the details of the approach on a simple example composed of two servers and three queues. Simulation results confirm that the system performance is near optimal when the network is scaled up.