An algorithm for clock synchronization with the gradient property in sensor networks

We introduce a distributed algorithm for clock synchronization in sensor networks. Our algorithm assumes that nodes in the network only know their immediate neighborhoods and an upper bound on the network's diameter. Clock-synchronization messages are only sent as part of the communication, assumed reasonably frequent, that already takes place among nodes. The algorithm has the gradient property of [2], achieving an O(1) worst-case skew between the logical clocks of neighbors. As in the case of [3,8], the algorithm's actions are such that no constant lower bound exists on the rate at which logical clocks progress in time, and for this reason the lower bound of [2,5] that forbids constant skew between neighbors does not apply

On Time Synchronization Issues in Time-Sensitive Networks with Regulators and Nonideal Clocks

Flow reshaping is used in time-sensitive networks (as in the context of IEEE TSN and IETF Detnet) in order to reduce burstiness inside the network and to support the computation of guaranteed latency bounds. This is performed using per-flow regulators (such as the Token Bucket Filter) or interleaved regulators (as with IEEE TSN Asynchronous Traffic Shaping). Both types of regulators are beneficial as they cancel the increase of burstiness due to multiplexing inside the network. It was demonstrated, by using network calculus, that they do not increase the worst-case latency. However, the properties of regulators were established assuming that time is perfect in all network nodes. In reality, nodes use local, imperfect clocks. Time-sensitive networks exist in two flavours: (1) in non-synchronized networks, local clocks run independently at every node and their deviations are not controlled and (2) in synchronized networks, the deviations of local clocks are kept within very small bounds using for example a synchronization protocol (such as PTP) or a satellite based geo-positioning system (such as GPS). We revisit the properties of regulators in both cases. In non-synchronized networks, we show that ignoring the timing inaccuracies can lead to network instability due to unbounded delay in per-flow or interleaved regulators. We propose and analyze two methods (rate and burst cascade, and asynchronous dual arrival-curve method) for avoiding this problem. In synchronized networks, we show that there is no instability with per-flow regulators but, surprisingly, interleaved regulators can lead to instability. To establish these results, we develop a new framework that captures industrial requirements on clocks in both non-synchronized and synchronized networks, and we develop a toolbox that extends network calculus to account for clock imperfections.Comment: ACM SIGMETRICS 2020 Boston, Massachusetts, USA June 8-12, 202

Bounded Determinization of Timed Automata with Silent Transitions

Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable. This is unfortunate since deterministic automata play a major role in model-based testing, observability and implementability. However, by bounding the length of the traces in the automaton, effective determinization becomes possible. We propose a novel procedure for bounded determinization of timed automata. The procedure unfolds the automata to bounded trees, removes all silent transitions and determinizes via disjunction of guards. The proposed algorithms are optimized to the bounded setting and thus are more efficient and can handle a larger class of timed automata than the general algorithms. The approach is implemented in a prototype tool and evaluated on several examples. To our best knowledge, this is the first implementation of this type of procedure for timed automata.Comment: 25 page

Verifying Real-Time Systems using Explicit-time Description Methods

Timed model checking has been extensively researched in recent years. Many new formalisms with time extensions and tools based on them have been presented. On the other hand, Explicit-Time Description Methods aim to verify real-time systems with general untimed model checkers. Lamport presented an explicit-time description method using a clock-ticking process (Tick) to simulate the passage of time together with a group of global variables for time requirements. This paper proposes a new explicit-time description method with no reliance on global variables. Instead, it uses rendezvous synchronization steps between the Tick process and each system process to simulate time. This new method achieves better modularity and facilitates usage of more complex timing constraints. The two explicit-time description methods are implemented in DIVINE, a well-known distributed-memory model checker. Preliminary experiment results show that our new method, with better modularity, is comparable to Lamport's method with respect to time and memory efficiency

Lower bounds in distributed computing

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 167-170).Distributed computing is the study of achieving cooperative behavior between independent computing processes with possibly conflicting goals. Distributed computing is ubiquitous in the Internet, wireless networks, multi-core and multi-processor computers, teams of mobile robots, etc. In this thesis, we study two fundamental distributed computing problems, clock synchronization and mutual exclusion. Our contributions are as follows. 1. We introduce the gradient clock synchronization (GCS) problem. As in traditional clock synchronization, a group of nodes in a bounded delay communication network try to synchronize their logical clocks, by reading their hardware clocks and exchanging messages. We say the distance between two nodes is the uncertainty in message delay between the nodes, and we say the clock skew between the nodes is their difference in logical clock values. GCS studies clock skew as a function of distance. We show that surprisingly, every clock synchronization algorithm exhibits some execution in which two nodes at distance one apart have Q( lo~gD clock skew, where D is the maximum distance between any pair of nodes. 2. We present an energy efficient and fault tolerant clock synchronization algorithm suitable for wireless networks. The algorithm synchronizes nodes to each other, as well as to real time. It satisfies a relaxed gradient property. That is, it guarantees that, using certain reasonable operating parameters, nearby nodes are well synchronized most of the time. 3. We study the mutual exclusion (mutex) problem, in which a set of processes in a shared memory system compete for exclusive access to a shared resource. We prove a tight Q(n log n) lower bound on the time for n processes to each access the resource once. .(cont.) Our novel proof technique is based on separately lower bounding the amount of information needed for solving mutex, and upper bounding the amount of information any mutex algorithm can acquire in each step. We hope that our results offer fresh ways of looking at classical problems, and point to interesting new open problemsby Rui Fan.Ph.D