Vikram R. Saksena

Singular perturbations and time-scale methods in control theory: Survey 1976-1983

Recent progress in the use of singular perturbation and two-time-scale methods of modeling and design for control systems is reviewed. Over 350 references are organized into major problem areas. Representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application. The survey is aimed at engineers and applied mathematicians interested in model-order reduction, separation of time scales and allied simplified methods of control system analysis and design. The exposition does not assume prior knowledge of singular perturbation methods.

Dependence in packet queues

The burstiness of the total arrival process has been previously characterized in packet network performance models by the dependence among successive interarrival times. It is shown that associated dependence among successive service times and between service times and interarrival times also can be important for packet queues involving variable packet lengths. These dependence effects are demonstrated analytically by considering a multiclass single-server queue with batch-Poisson arrival processes. For this model and more realistic models of packet queues, insight is gained from heavy-traffic limit theorems. This study indicates that all three kinds of dependence should be considered in the analysis and measurement of packet queues involving variables packet lengths. Specific measurements are proposed for real systems and simulations. This study also indicates how to predict expected packet delays under heavy loads. Finally, this study is important for understanding the limitations of procedures such as the queuing network analyzer (QNA) for approximately describing the performance of queuing networks using the techniques of aggregation and decomposition. >

Topological analysis of packet networks

The author describes a unified approach for the topological analysis of nonhierarchical and hierarchical packet networks. The approach differs from previous approaches in adopting an end-to-end mean delay objective and including a variety of practical routing constraints. These include limits on the number of paths allowed in a route, limits on the number of hops allowed in a path, and constraints due to prevalent virtual circuit implementations. For a broad range of networks, quantitative analysis based on this approach provides new insights into the complex relationships between network topology and routing and delay constraints. It is shown that the sole use of a network average delay criterion often leads to network designs that exhibit poor end-to-end mean delays for some node pairs, and that it is possible to configure networks that meet an end-to-end mean delay objective for every node pair at little or no additional cost. >

Investigating dependence in packet queues with the index of dispersion for work

The authors continue an investigation of the way diverse traffic from different data applications affects the performance of packet queues. This traffic often exhibits significant dependence among successive interarrival times, among successive service times, and between interarrival times and service times, which can cause a significant degradation of performance under heavy loads (and often even under moderate loads). This dependence and its effects on performance (specifically, the mean steady-state workload) are partially characterized here by the cumulative correlations in the total input process of work, which is referred to as the index of dispersion for work (IDW). The authors evaluate approximations for the mean steady-state workload based on the IDW by making comparisons with computer simulations. >

Analysis and design of a highly reliable transport architecture for ISDN frame-relay networks

The authors explore control strategies in the design of a high-performance transport architecture for integrated services digital network (ISDN) frame-relay networks. For real-time congestion control, buffer management, priority queueing, adaptive windowing, and selective frame, discard policies are described that can effectively maximize network efficiency while preventing unfair usage of shared network resources. Virtual-circuit routing strategies are proposed that ensure an efficient distribution of traffic loads across the network despite variations in traffic patterns and topology changes. It is shown that source routing provides significant performance benefits over link-by-link routing, particularly in large networks that are not so densely connected. Routing table update and call acceptance mechanisms are described that provide for efficient bandwidth management in the network. Fault-tolerant strategies are described that include fast failure detection and local reroute. These strategies are capable of restoring affected virtual circuits in less than 10 s, which is adequate for session maintenance under most application scenarios. >

Error performance of IEEE 802.6 metropolitan area networks

Error performance issues concerning IEEE Standard 802.6 metropolitan area networks (MANs) which will be based on fiber transmission systems are investigated. The error protection requirements for MAN cell headers are studied, and a simple cyclic redundancy check (CRC)-based scheme to provide single-bit correction and multiple-bit detection is proposed. The functions of the adaptation layer for data end points are discussed. A critical function of the data adaptation layer is to prevent corruption of information carried in 802.6 cells. Alternative ways of providing error protection are discussed and analyzed. It is shown that the alternative based on a CRC check per segment provides robust error protection and is amenable to very-high-speed implementation.<<ETX>>

An approach to decentralized control of large scale systems using aggregation methods

A two-level decentralized control structure is formulated for large scale interconnected subsystems controlled by N decision makers. Chained aggregation is used to decompose the overall team problem with a decentralized information structure into ( N + 1 ) subproblems: one low order team problem with a centralized information structure and N decentralized optimal control problems. Accordingly, the control of each decision maker is decomposed into three components: a decoupling control which induces aggregation, a local control which controls the subsystem dynamics, and an aggregate control which controls the dynamics of the interconnection variables. The robustness of this composite control with respect to perturbations in the system dynamics and the cost functional is established.

Analysis and engineering of a voice/data packet multiplexer

This paper investigates performance and engineering issues concerning a multiplexer scheme that has been implemented in AT&Ts Integrated Access Terminal (IAT) to transport packetized voice and data traffic on shared facilities. The multiplexer serves voice and data traffic according to a dynamic bandwidth allocation scheme in order to simultaneously meet their performance requirements. A bit-dropping procedure is employed for voice packets to provide a graceful degradation of voice quality under overload conditions. An analytical model is developed for the multiplexer service scheme that estimates performance parameters given the voice and data offered loads. The model is used to demonstrate the capacity advantages of dynamic bandwidth allocation, and to generate load-service curves that illustrate the tradeoffs of carrying different combinations of voice and data traffic on the multiplexer. Sensitivity of voice and data performance to the multiplexer time-slice parameters is also investigated. The model is readily embedded in a design approach that determines the bandwidth required to carry the voice and data traffic demands while satisfying all desired performance objectives. >

Performance of alternative MAN architectures for high-speed data applications

The authors analyze the performance of alternative metropolitan area network architectures for traditional data networking and for emerging distributed client/server computing applications. A simple traffic model contains the essential features of distributed computing applications. Delay performance on the MAN is examined for two architectures: networking based on variable-size datagrams, and networking based on asynchronous transfer mode protocols that use short, fixed-length cells. It is shown that the traffic characteristic of client/server computing-bimodal message-length distributions and bursty, clustered arrivals-can have significant effects on the delay performance of MANs. In particular, the presence of large and variable-size datagrams leads to large delays and variabilities in delay in connectionless networks as the length of network connections increases. Networks that use small cells in the style of ATM provide superior end-to-end delay performance and therefore provide a superior architecture for MANs designed to carry a diverse traffic mix.<<ETX>>

Performance analysis of a LAN/WAN bridging architecture

A performance analysis of a virtual-circuit-based wide-area network (WAN) that performs local-area-network (LAN) bridging is presented. This type of WAN is suitable for LAN bridging because the conversion of functions between the LAN protocol and the WAN protocol can be simplified by assigning a virtual circuit to each bridge-to-bridge (edge-to-edge) connection. With this architecture, routing is performed efficiently and network resources are used on demand. Analytical approximations of bridge throughput packet delay and packet-loss rates are provided as a function of network and protocol parameters.<<ETX>>