This paper presents a control-theoretic approach to reactive flow control in networks that do not reserve bandwidth. We assume a round-robin-like queue service discipline in the output queues of the network’s switches, and propose deterministic and stochastic models for a single conversation in a network of such switches. These models motivate the Packet-Pair rate probing technique, and a provably stable rate-based flow control scheme. A Kalman state estimator is derived from discrete-time state space analysis, but there are difficulties in using the estimator in practice. These difficulties are overcome by a novel estimation scheme based on fuzzy logic. We then present a technique to extract and use additional information horn the system to develop a continuous-time system model. This is used to design a wuisnt of the control law that is also provably stable, and, in addition, takes control action as rapidly as possible. Finally, practical issues such as correcting parameter drift and cmmlination with window flow control are described.

We consider a flow control mechanism that dynamically regulates the rate of data flow into a network based on feedback information about the network state. Such mechanisms have been introduced recently in a variety of networks including the Internet, and have been advocated for future high-speed networks. We first model the flow control mechanism by a discrete-space stochastic process and define appropriate performance measures for transient and steady-state regimes. However, the model does not appear to be analytically tractable and we study it through simulation. We then simplify it to a continuous-space deterministic (or fluid) model for which we can easily derive closed-form solutions. We find the analytical results for the fluid model to agree well with the simulation results obtained using the discrete-space model. Both models explicitly consider delay of the feedback information, thus making them relevant for high-speed networks. 1 Introduction In a computer network, packets g...

Multiple-class multiple-resource (MCMR) systems, where each class of customers requires a particular set of resources, are common. These systems are often analyzed under steady-state conditions. We describe a simple method, referred to as Z-iteration, to estimate both transient and steady-state performances of such systems. The method makes use of results and techniques available from queueing theory, network analysis, dynamic flow theory, and numerical analysis. We show the generality of the Z-iteration by applying it to an ATM network, a parallel disk system, and a distributed batch system. Validations against discreteevent simulations show the accuracy and computational advantages of the Z-iteration. 1 Introduction We consider a general multiple-class multiple-resource (MCMR) system. We have a set R of resources and a set C of customer classes. The nature of a resource depends on the system being modeled; for example, it may be computer memory, floor space, transmission capacity, e...

We present a numerical-analytical method to evaluate multi-service networks with adaptive routing, scheduling and admission controls. We apply our method to connection-oriented networks supporting different types of real-time connections. The network dynamics is described by difference equations which can be solved for both transient and steady-state performances. Results indicate that our method is computationally much cheaper than discrete-event simulation, and yields accurate performance measures. Connection routing algorithms are usually evaluated individually in terms of steady-state performance measures. In this paper, we also use our time-dependent evaluation method to compare several connection routing schemes in terms of instantaneous measures. Our results show that a routing scheme which defines the cost of a path as the sum of measured link utilizations yields more stable behavior and lower connection blocking probability over a wide range of workload parameters and network...

Multiple-class multiple-resource (MCMR) systems, where each class of customers requires a particular set of resources, are common. These systems are often analyzed under steadystate conditions. We describe a simple numerical-analytical method, referred to as Z-iteration, to estimate instantaneous (and steady-state) probability measures of time-dependent systems. The key idea is to approximate the relationship between certain instantaneous measures by the relationship between their steady-state counterparts, and use this approximation to solve dynamic flow equations. We show the generality of the Z-iteration by applying it to an integrated communication network, a parallel database server, and a distributed batch system. Validations against exact numerical solutions and discrete-event simulations show the accuracy and computational advantages of the Z-iteration. Preliminary version appeared in ACM SIGMETRICS/PERFORMANCE '95. This work is supported in part by ARPA and Philips Labs und...

Studies in performance evaluation of automated manufacturing systems, using simulation or analytical models, have always emphasized steady-state or equilibrium performance in preference to transient performance. In this study, we present several situations in manufacturing systems where transient analysis is very important. Manufacturing systems and models in which such situations arise include: systems with failure states and deadlocks, unstable queueing systems, and systems with fluctuating or non-stationary workloads. Even in systems where equilibrium exists, transient analysis is important in studying issues such as accumulated performance rewards over finite intervals, first passage times, sensitivity analysis, settling time computation, and deriving the behavior of queueing models as they approach equilibrium. In certain systems, convergence to steady-state is so slow that only transient analysis can throw light on the system performance. In this paper, we focus on transient analysis of Markovian models of manufacturing systems. After presenting several illustrative manufacturing situations where transient analysis has significance, we discuss two problems for demonstrating the importance of transient analysis. The first problem is concerned with the computation of distribution of time to absorption in Markov models of manufacturing systems with deadlocks or failures, and the second problem shows the relevance of transient analysis to a multiclass manufacturing system with significant setup times. We also briefly discuss computational aspects of transient analysis.

The nonstationary Erlang loss model is a queueing system consisting of a finite number of servers and no waiting room with a nonstationary arrival process or a time-dependent service rate. The Erlang loss model is commonly used to model and evaluate many communication systems. Often, these types of service systems encounter a change in the arrival rate over time while the service rate remains either constant or changes very little over time. In view of this, the focus in this research is the nonstationary Erlang loss queues and network with time-dependent arrival rate and constant service rate. We developed an iterative scheme referred to as the fixed point approximation (FPA) in order to obtain the time-dependent blocking probability and other measures for a single-class nonstationary Erlang loss queue and a nonstationary multi-rate Erlang loss queue. The FPA method was compared against exact numerical results, and two other methods, namely, MOL and PSA, for various nonstationary Erlang loss queues with sinusoidal arrival rates. Although we used sinusoidal functions to model the time-dependent arrival rate, the solution can be obtained for any arrival rate function. Experimental results demonstrate that the FPA

Integrated services networks, such asATM (Asynchronous Transfer Mode) networks, are expected to operate at gigabit per second rates and provide various virtual-circuit and datagram services. For this purpose, new control algorithms (e.g. scheduling, admission, routing) have been proposed. The algorithms are often adaptive, resulting in complex time-dependent interactions. This renders traditional evaluation tools ine ective � analytical approaches are typically too coarse, and simulation approaches are often too expensive. The goal of our research istodevelop accurate analytical models that account for the interaction and time-dependent nature of the control algorithms, while at the same time being inexpensive or easy to solve. This would allow the rapid and tractable evaluation of di erent design alternatives. In this dissertation, we develop both dynamic models and quasi-static models of integrated networks. Dynamic models can be used to evaluate both virtual-circuit and datagram services. We solve dynamic models using a new iterative method, referred to as the Z-iteration. Our method is both accurate and fast. It permits the jointevaluation of various scheduling, admission, and routing schemes used in integrated networks. We showresults comparing dynamic routing schemes on a network with NSFNET-backbone topology. Wealso illustrate the applicability of the Z-iteration to other high-performance systems. Quasi-static models are suitable for evaluating datagram services for which the quasi-static assumption is reasonable. We analyze a quasi-static model of a datagram network o ering di erent classes of service. We apply the Liapunov function method to derive stability conditions for the routes of the di erent tra c classes. We show howwith scheduling support for routing, the routes of the tra c classes can be isolated, thereby improving the overall network performance. Fast Evaluation and Dynamic Control of