A Switching Fluid Limit of a Stochastic Network Under a State-Space-Collapse Inducing Control with Chattering

Routing mechanisms for stochastic networks are often designed to produce state space collapse (SSC) in a heavy-traffic limit, i.e., to confine the limiting process to a lower-dimensional subset of its full state space. In a fluid limit, a control producing asymptotic SSC corresponds to an ideal sliding mode control that forces the fluid trajectories to a lower-dimensional sliding manifold. Within deterministic dynamical systems theory, it is well known that sliding-mode controls can cause the system to chatter back and forth along the sliding manifold due to delays in activation of the control. For the prelimit stochastic system, chattering implies fluid-scaled fluctuations that are larger than typical stochastic fluctuations. In this paper we show that chattering can occur in the fluid limit of a controlled stochastic network when inappropriate control parameters are used. The model has two large service pools operating under the fixed-queue-ratio with activation and release thresholds (FQR-ART) overload control which we proposed in a recent paper. We now show that, if the control parameters are not chosen properly, then delays in activating and releasing the control can cause chattering with large oscillations in the fluid limit. In turn, these fluid-scaled fluctuations lead to severe congestion, even when the arrival rates are smaller than the potential total service rate in the system, a phenomenon referred to as congestion collapse. We show that the fluid limit can be a bi-stable switching system possessing a unique nontrivial periodic equilibrium, in addition to a unique stationary point

On the Dynamics and Significance of Low Frequency Components of Internet Load

Dynamics of Internet load are investigated using statistics of round-trip delays, packet losses and out-of-order sequence of acknowledgments. Several segments of the Internet are studied. They include a regional network (the Jon von Neumann Center Network), a segment of the NSFNet backbone and a cross-country network consisting of regional and backbone segments. Issues addressed include: (a) dominant time scales in network workload; (b) the relationship between packet loss and different statistics of round-trip delay (average, minimum, maximum and standard-deviation); (c) the relationship between out of sequence acknowledgments and different statistics of delay; (d) the distribution of delay; (e) a comparison of results across different network segments (regional, backbone and cross-country); and (f) a comparison of results across time for a specific network segment. This study attempts to characterize the dynamics of Internet workload from an end-point perspective. A key conclusion from the data is that efficient congestion control is still a very difficult problem in large internetworks. Nevertheless, there are interesting signals of congestion that may be inferred from the data. Examples include (a) presence of slow oscillation components in smoothed network delay, (b) increase in conditional expected loss and conditional out-of-sequence acknowledgments as a function of various statistics of delay, (c) change in delay distribution parameters as a function of load, while the distribution itself remains the same, etc. The results have potential application in heuristic algorithms and analytical approximations for congestion control

Modelling and evaluation of load and performance control mechanisms of B-ISDN/ATM switching systems

Behandelt wird die Problematik der Last- und Leistungsregelung im Kontext der ATM-basierten Breitband-Vermittlungstechnik.Objective of this thesis are load control and performance control concepts for broadband switching systems. Focus is the services integrating network technology B-ISDN using ATM as transfer mode. The studied mechanisms and concepts are principally of generic nature. Specifically they are designed within the envisaged context of B-ISDN, due to its extensive vision with respect to service integration, Quality of Service (QoS) support and ATM bearer capabilities. Area of application is implicitly the network control plane, but interactions between user and control plane have to be considered, too. The prime scope are switching nodes between access and core network domain, i.e., B-ISDN switches which have to provide user-to-network and network-to-network signalling protocol functions. Thus, beside service distinction call type differentiation is also covered due to the considered network positioning