Flow Control Model Research Articles

Mathematical modeling of tundish operation and flow control to reduce transition slabs

Minimization of transition slabs in continuous casting operations is critical for optimum quality and productivity. The number of these slabs is closely related to the tundish geometry and operating practice. Therefore, tundish flow and mixing with various tundish configurations and different tundish operating levels are investigated through computer simulation. Residence time distributions and transitional concentration profiles are predicted. Finally, practical operations for a grade change to reduce transition slabs are assessed.

Bifurcation analysis of nephron pressure and flow regulation.

One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period-doubling cascades. Similar phenomena arise in response to increasing blood pressure. The numerical analyses are supported by existing experimental results on anesthetized rats. (c) 1996 American Institute of Physics.

On the relationship of capacitated production/inventory models to manufacturing flow control models

Characterizing and determining optimal operating policies for production/inventory systems are of paramount importance. Perhaps two of the most important practical factors which make this a difficult problem are the randomness of demand and the finiteness of production capacity. In the traditional inventory literature of operations research and management science, it has been shown that a modified base-stock policy is optimal for a periodic review model; results exist that can be used to estimate the single parameter that characterizes the optimal policy. On the other hand, research found in the control systems community casts the problem in the framework of manufacturing flow control — where inventory is monitored continuously and the production rate is also controlled continuously — and has shown that the optimal policy can also be characterized by a single parameter called the hedging point. Our view is that these two models and approaches solve essentially the same problem, albeit one in discrete time and the other in continuous time. In this paper, we compare the two approaches and discuss various beneficial implications that result from correspondences between the two approaches. For example, both systems have fundamental connections to processes of a single-server queue: one to the discrete-time process of system time, and the other to the continuous-time process of the workload process. Finally we also tackle the problem of stochastic capacity in the context of both approaches.

On the existence of equilibria in noncooperative optimal flow control

The existence of Nash equilibria in noncooperative flow control in a general product-form network shared by K users is investigated. The performance objective of each user is to maximize its average throughput subject to an upper bound on its average time-delay. Previous attempts to study existence of equilibria for this flow control model were not successful, partly because the time-delay constraints couple the strategy spaces of the individual users in a way that does not allow the application of standard equilibrium existence theorems from the game theory literature. To overcome this difficulty, a more general approach to study the existence of Nash equilibria for decentralized control schemes is introduced. This approach is based on directly proving the existence of a fixed point of the best reply correspondence of the underlying game. For the investigated flow control model, the best reply correspondence is shown to be a function, implicitly defined by means of K interdependent linear programs. Employing an appropriate definition for continuity of the set of optimal solutions of parameterized linear programs, it is shown that, under appropriate conditions, the best reply function is continuous. Brouwer's theorem implies, then, that the best reply function has a fixed point.

Turnpikes in flow control models of unreliable manufacturing systems

This paper establishes a link between the concept of hedging point, introduced in a class of models of unreliable manufacturing flow control, and the concept of turnpike, introduced initially in economic growth models and recently extended to a general class of piecewise deterministic control systems. We establish a turnpike property for a control system where the cost does not depend directly on the control. We show that this turnpike corresponds exactly to the hedging points introduced in the manufacturing flow control literature.

On the ordering of optimal hedging points in a class of manufacturing flow control models

The optimal flow control policy of a single-product unreliable manufacturing system that must meet a constant demand rate is known to be a threshold type policy: safety production surplus levels called hedging points (thresholds) are associated with each discrete stochastic capacity state of the system and serve to protect the production process from uncertainty in future capacity availability. This correspondence extends and generalizes previous results on the ordering of optimal hedging points. The authors' method is based on examining special properties of the Bellman optimality conditions of the underlying stochastic control problem. >

Solving a class of network models for dynamic flow control

In modeling flows and controls in transportation, distribution, communication, manufacturing systems, etc., it is often convenient to represent the system as a store-and-forward network. In such networks it is common for time, space, attention, or other resources, to be shared between sets of neighbouring nodes. For example, neighbouring nodes may share storage space, machine time, operating time, etc. The allocation of this shared resource among nodes determines a set of ‘controls’ on the network arc flows. We develop a multi-period network model which describes such storage and forwarding, and the sharing of resources (controls) between subsets of nodes. To solve the model we develop algorithms which take advantage of the embedded network structure of the problem. Each of the algorithms is based on iterating between (a) solving a least-cost capacitated network flow problem with fixed capacities (controls) and (b) solving a set of simple small scale problems to update these controls. In a series of computational experiments we found that an (‘unoptimized’) implementation of the algorithms performed between 13 and 42 times faster than a good linear programming code, which is the natural alternative. Also, by decomposing the problem, the algorithms make solving larger scale problems tractable, and are suitable for implementation on parallel processors.

Approximate solutions for large-scale piecewise deterministic control systems arising in manufacturing flow control models

We propose a numerical technique for approximately solving large-scale piecewise deterministic control systems that are typically related to manufacturing flow control problems in unreliable production systems. The method consists of reformulating the stochastic control problem under study into a Markov decision process. Then we exploit the associated dynamic programming conditions and we propose an "approximate" policy iteration algorithm. This will be based on an approximation of the Bellman functions by a combination of a set of base functions, using a specific decomposition technique. The numerical method is applicable whenever a turnpike property holds for some associated infinite horizon deterministic control problem. To illustrate the approach, we solve an example and compare this new approximation method with a more classical approximation-by-decomposition technique.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A dual-window model for flow and congestion control

This paper examines the window mechanism that has been widely used for flow and congestion control. The analysis shows that the mono-window model, which combines flow control and congestion control in a single window, can cause pipe breakdown after packet losses. A dual-window model is then presented, in which flow control and congestion control are decoupled. The dual-window model allows the traffic flow to be sustained while retransmission is being carried out. The dual-window model is particularly suitable for high-speed and long-delay networks where the pipelining of the packets is more crucial. The estimation of the window sizes, advance of the window edges, acknowledgement and retransmission are discussed in detail. Finally the performance of the dual-window model is examined with illustrated examples and by simulation.

Convergence of stochastic approximation coupled with perturbation analysis in a class of manufacturing flow control models

This paper deals with a class of piecewise determinstic control systems for which the optimal control can be approximated through the use of an optimization-by-simulation approach. The feedback control law is restricted to belong to an a priori fixed class of feedback control laws depending on a (small) finite set of parameters. Under some general conditions developed in this paper, infinitesimal perturbation analysis (IPA) can be used to estimate the gradient of the objective function with respect to these parameters for finite horizon simulation and the consistency of the IPA estimators, as the simulation length goes to infinity, is assured. Also, the parameters can be optimized through a stochastic approximation (SA) algorithm combined with IPA. We prove that in this context, under appropriate conditions, such an approach converges towards the optimum.

Work flow control in the flexible flow line

This research involves the development and evaluation of a part flow control model for a type of flexible manufacturing system (FMS) called a dedicated flexible flow line (FFL). In the FFL, all part types flow along the same path between successive machine groups. The specific objective of the part flow control model for the FFL is to minimize makespan for a given set of parts produced in a FFL near-term schedule, given fixed available buffer constraints. The control model developed in this research involved the repeated, real-time execution of a mathematical programming algorithm. The algorithm attempts to release the right mix of parts at the tight time to keep the FFL operating smoothly. The focus of the approach is directed toward managing WIP buffers for each machine group queue. The algorithm specifically incorporates stochastic disturbance factors such as machine failures. Through a limited number of simulation experiments, performance of the control model is shown to be superior to other parts releasing and control methods reported in the literature.

Turnpike properties for a class of piecewise deterministic systems arising in manufacturing flow control

This paper deals with a general class of piecewise deterministic control systems that encompasses FMS flow control models. One uses the Markov renewal decision process formalism to characterize optimal policies via a discrete event dynamic programming approach. A family of control problems with a random stopping time is associated with these optimality conditions. These problems can be reformulated as infinite horizon deterministic control problems. It is then shown how the so-calledturnpike property should hold for these deterministic control problems under classical convexity assumptions. These turnpikes have the same generic properties as the attractors obtained via a problem specific approach in FMS flow control models and production planning and are calledhedging points in this literature.

ISDN frame relay and its congestion control

Frame relay is a new ISDN (integrated services digital network) packet mode bearer service which is expected to provide an efficient means of information transport using high-speed transmission media. Several new applications requiring high bandwidth, such as file transfer, video and packetized voice, are suitable candidates to use this streamlined protocol. However, as there are no control frames present within the network for traffic flow management, congestion may arise during periods of peak offered loads. Efficient congestion control mechanisms are needed to make the frame relay effective. In this paper, after a brief discussion of the frame relay protocol, we consider the congestion problem in networks using this protocol and evaluate the performance. Specifically, we consider static and dynamic window flow control methods and develop models to determine the throughput under various load conditions. The throughput of the static window flow control model is determined by computing the frame loss probability and the virtual retransmission time, which is the time between arrivals of retransmitted frames at the destination. The frame loss probability is calculated by modelling the bottleneck resource as a finite state Markov chain. The results are validated by simulation. Furthermore, to analyse the dynamic interactions between the virtual circuits and their effect on the throughput and delay characteristics, we develop a simulation model which incorporates a dynamic window congestion control mechanism. It is shown that when the offered load is high, the performance of dynamic window flow control is superior to that of static window flow control.

A turnpike improvement algorithm for piecewise deterministic control

This paper proposes a numerical technique, called turnpike improvement, for the approximation of the solution of a class of piecewise deterministic control problems typically associated with manufacturing flow control models. This algorithm exploits the structure of Markov decision processes with continuous state and action spaces that can be associated with piecewise deterministic control systems. The numerical method is applicable whenever a turnpike property holds for some associated infinite horizon deterministic control problem. To illustrate the approach, we use a simple model fully studied from an analytic point of view in the literature. We compare the turnpike improvement technique with a direct approximation of the solution of the continuous-time Hamilton-Jacobi dynamic programming equations inspired by Kushner's work. The two approaches agree remarkably on this simple problem. We conclude with a discussion of the relative advantages of the two approaches.

A theoretical analysis of feedback flow control

Congestion is a longstanding problem in datagram networks. One congestion avoidance technique is feedback flow control, in which sources adjust their transmission rate in response to congestion signals sent (implicitly or explicitly) by network gateways. The goal is to design flow control algorithms which provide time-scale invariant, fair, stable, and robust performance. In this paper we introduce a simple model of feedback flow control, in which sources make synchronous rate adjustments based on the congestion signals and other local information, and apply it to a network of Poisson sources and exponential servers. We investigate two different styles of feedback, aggregate and individual, and two different gateway service disciplines, FIFO and Fair Share. The purpose of this paper is to identify, in the context of our simple model, which flow control design choices allow us to achieve our performance goals . Aggregate feedback flow control, in which congestion signals reflect only the aggregate congestion at the gateways, can provide time-scale invariant and stable performance, but not fair or robust performance. The properties of individual feedback flow control, in which the congestion signals reflect the congestion caused by the individual source, depend on the service discipline used in the gateways. Individual feedback with FIFO gateways can provide time-scale invariant, fair, and stable performance, but not robust performance. Individual feedback with Fair Share gateways can achieve all four performance goals. Furthermore, its stability properties are superior to those of the other two design choices. By making robust and more stable performance possible, gateway service disciplines play a crucial role in realizing effective flow control .

Optimal queueing systems controls with finite buffers and with multiple component cost functions

An analytical and tractable framework of an optimal feedback control policy is developed for queueing networks with limited storage buffers and with sequence-dependent service times. The general response measure used incorporates delay, shortage, and the setup costs. This formulation provides a perspective to dynamic flow-control models that are based on a rational function of the queue lengths of various downstream queues rather than on time. This formulation also enables the derivation of various performance measures for each node. Presented measures include throughput rate, utilization, queue length, starvation intervals, and setups. Detailed numerical examples provide some insights into the structure and performance of the optimal policy. It is explained that the buffer capacity vector has a minimal effect on the routing decisions in the interior of the state space and that the relative value of the buffer spaces declines with the increase in the delay costs. The impact of major resource-allocation decisions and of changes in the performance cost measures is also explained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A nuclear data acquisition system flow control model

A general Petri-Net representation of a nuclear data-acquisition model is presented. This model provides for the unique requirements of a nuclear data-acquisition system, including the capabilities of concurrently acquiring synchronous and asynchronous data, of providing multiple priority levels of flow-control arbitration, and of permitting multiple input sources to reside at the same priority without the problem of channel lockout caused by a high-rate data source. Finally, a previously implemented gamma-camera/physiological-signal data-acquisition system is described using the models presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Combined routing and flow control in computer communication networks: A two-level adaptive scheme

The problem of designing combined routing and flow control strategies for packet-switched computer communication networks is considered in this paper and a new two-level adaptive scheme is presented. State dependent models for routing and input buffer limit flow control are introduced to facilitate formulating the problem, for which a solution in the framework of system stabilization is developed. The overall decision-making consists of a distributed computation of the routing parameters and the flow control parameters at the lower level of network nodes and a computation on a slower time-scale of a set of combined parameters by a supervisor (network control center) at a higher hierarchical level. The parameters are adaptively updated at both levels to improve the network performance with respect to a set of objectives concerning delay, throughput, and buffer utilization. Some implementational aspects of the algorithm are discussed and simulation results that illustrate the performance are presented. Major strong points of the present scheme are i) adaptivity to changes in load and/or network topology, ii) capability of handling different objectives individually at different hierarchical levels, and iii) consideration of capacity constrained nodal buffers in addition to capacity limited links, unlike in the earlier developed schemes, for a more realistic representation of network environment.

A model of transport level flow control

A Markov Decision Process model is developed to analyze buffer assignment at the transport level of the ARPAnet protocol. The result of the analysis is a method for obtaining an assignment policy which is optimal with respect to a delay/throughput/overhead reward function. The nature of the optimal policy is investigated by varying parameters of the reward.

A control system model of renal blood flow regulation

A model of renal blood flow control is developed from a dynamic model of electrolyte and water flows in the renal medulla. The model of the medulla includes juxtaglomerular and cortical nephrons and the vasa recta to give an accurate mass balance of fluid flows. This model is extended to include algebraic representations of the glomeruli, proximal tubules, and the viscous resistance to fluid flows for both classes of nephron. Renal blood flow is controlled by a feedback loop in the cortical nephron which is completed by the juxtaglomerular apparatus (JGA). The JGA reacts to electrolyte levels in the nephron near the glomerulus, mediates blood flow through the glomerulus, and consequently controls renal blood flow. The transient behavior of this model is shown to conform to experimental data. The results indicate that there are stringent limits on the time within which the biochemical sensor of electrolyte levels at the JGA must respond to its stimulus; limits which appear not to have previously been considered.