This paper gives a class of flow control algorithms for the adaptive allocation of bandwidths to virtual connections (VC) in high-speed, wide-area ATM networks. The feedback rate to the source from the network is parsimonious, with each feedback bit indicating whether the buffer at a distant switch is above or below a threshold. The service discipline at the switch is first-come-first-served. The important goal of adaptability aims to make all of the network bandwidth available to the active VCs, even though the number of such VCs is variable over a given range. Each VC has two parameters, one giving its minimum guaranteed bandwidth and the other is the weight for determining its share of the uncommitted bandwidth. Judicious selection of these parameters defines distinctive services, such as best effort and best effort with minimum bandwidth. We derive design rules for selecting the parameters of the algorithms such that the appropriate guarantees and fairness properties are exhibited in the dynamical behavior. The systematic use of "damping" in right proportion with "gain" is shown to be a powerful device for stabilizing behavior and achieving fairness. Our analyses are based on a simple analytic fluid model composed of a system of first-order delay-differential equations, which reflect the propagation delay across the network. Extensive simulations examine the following: (1) fairness, especially to start-up VCs; (2) oscillations; (3) transient behavior, such as the rate of equalization from different initial conditions; (4) disparate bandwidth allocations; (5) multiple paths with diverse propagation delays; (6) adaptability and robustness with respect to parameters; and (7) interoperability of different algorithms.>

The optimal design of windows for virtual circuits has been studied for high-speed, wide-area data networks in an asymptotic framework in which the delay-bandwidth product is the large parameter. The authors (1990) previously proposed and evaluated a new class of algorithms for dynamically adapting windows in single path, multi-hop networks. Here they develop algorithms for networks having multiple paths with different propagation delays. The source of each virtual circuit (VC) measures the round-trip response time of its packets and uses these measurements to adjust its window with the goal of satisfying certain asymptotic identities that have been proven to hold in stationary asymptotically optimal designs. Also evaluated is the performance of the new adaptive algorithms in realistic, nonstationary conditions by simulations of networks with data rates of 45 Mb/s and propagation delays of up to 47 ms. The simulation results generally confirm that the realizations of the adaptive algorithms give stable, efficient performance and are close to theoretical expectations.>

The performances of two classes of routing algorithms, randomized and deterministic, are evaluated and compared in terms of revenue generated and link failures. The randomized algorithm evaluated is dynamic alternate routing, and for the deterministic algorithm, attempts to carry a call are made in a specific precomputed order. The design of the routing sequences depends upon analytic approximations based on fixed-point equations to evaluate network performance and heuristics for the complicated problem of network revenue maximization. The control mechanism of trunk reservations is shown to play an important role in all cases. The performances of the algorithms were evaluated on a fully connected six-node network, the data for which were extracted from a realistic network. The design tools, time constants of various algorithms, and hybrid algorithms developed using the evaluation results are described.>

Recent results on the asymptotically optimal design of sliding windows for virtual circuits in high speed, geographically dispersed data networks in a stationary environment are exploited here in the synthesis of algorithms for adapting windows in realistic, non-stationary environments. The algorithms proposed here require each virtual circuit's source to measure the round trip response times of its packets and to use these measurements to dynamically adjust its window. Our design philosophy is quasi-stationary: we first obtain, for a complete range of parameterized stationary conditions, the relation, called the “design equation”, that exists between the window and the mean response time in asymptotically optimal designs; the adaptation algorithm is simply an iterative algorithm for tracking the root of the design equation as conditions change in a non-stationary environment. A report is given of extensive simulations of networks with data rates of 45 Mbps and propagation delays of up to 47 msecs. The simulations generally confirm that the realizations of the adaptive algorithms give stable, efficient performance and are close to theoretical expectations when these exist.

An object is moving on a piecewise linear random path with a constant speed. Given the initial location and direction, the probability distribution of the object's location is calculated as a function of time, and the result is presented graphically. Then the probability of detecting such an object is calculated by using circular and line sensors.

A table of weight distributions of198minimal cyclic codes is presented.