The impact of timing on linearizability in counting networks

{\em Counting networks} form a new class of distributed, low-contention data structures, made up of {\em balancers} and {\em wires,} which are suitable for solving a variety of multiprocessor synchronization problems that can be expressed as counting problems. A {\em linearizable} counting network guarantees that the order of the values it returns respects the real-time order they were requested. Linearizability significantly raises the capabilities of the network, but at a possible price in network size or synchronization support. In this work, we further pursue the systematic study of the impact of {\em timing} assumptions on linearizability for counting networks, along the line of research recently initiated by Lynch~{\em et~al.} in [18]. We consider two basic {\em timing} models, the {instantaneous balancer} model, in which the transition of a token from an input to an output port of a balancer is modeled as an instantaneous event, and the {\em periodic balancer} model, where balancers send out tokens at a fixed rate. In both models, we assume lower and upper bounds on the delays incurred by wires connecting the balancers. We present necessary and sufficient conditions for linearizability in these models, in the form of precise inequalities that involve not only parameters of the timing models, but also certain structural parameters of the counting network, which may be of more general interest. Our results extend and strengthen previous impossibility and possibility results on linearizability in counting networks

Sequentially consistent versus linearizable counting networks

We compare the impact of timing conditions on implementing sequentially consistent and linearizable counters using (uniform) counting networks in distributed systems. For counting problems in application domains which do not require linearizability but will run correctly if only sequential consistency is provided, the results of our investigation, and their potential payoffs, are threefold: • First, we show that sequential consistency and linearizability cannot be distinguished by the timing conditions previously considered in the context of counting networks; thus, in contexts where these constraints apply, it is possible to rely on the stronger semantics of linearizability, which simplifies proofs and enhances compositionality. • Second, we identify local timing conditions that support sequential consistency but not linearizability; thus, we suggest weaker, easily implementable timing conditions that are likely to be sufficient in many applications. • Third, we show that any kind of synchronization that is too weak to support even sequential consistency may violate it significantly for some counting networks; hence

Small-depth counting networks and related topics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.Includes bibliographical references (p. 89-92).by Michael Richard Klugerman.Ph.D