L. Lamport and P. Melliar-Smith, "Synchronizing clocks in the presence of faults," J. ACM, vol. 32, no. 1, pp. 52--78, 1985.  Home/Search   Document Not in Database   Summary   ACM   TOC   Related Articles   Check

....xx requires synchronized clocks with precision . are commonly used in modern textbooks on very different subjects, like communication protocols and data base systems. The clock synchronization algorithms of Halpern Simons Strong Dolev [3] Lundelius Lynch [5] Lamport Melliar Smith [4], Mahaney Schneider [6] Cristian Aghili Strong [1] Srikant Toueg [7] and the many variants derived from them) but also related theoretical work form a well established basis for applications that require synchronized clocks. So why wasting time and money by publishing a 1997 special issue ....

L. Lamport, P.M. Melliar-Smith. Synchronizing Clocks in the Presence of Faults, Journal of the ACM, 32(1), January 1985, p. 52--78.

....of the synchronized clocks are proven to be optimal. 1 Introduction Most distributed systems encountered in practice are asynchronous, in that they do not guarantee a bound on message communication delays. Traditional deterministic, fault tolerant clock synchronization algorithms such as those of [2, 3] assume bounded communication delays. Thus, they cannot be directly used to synchronize clocks in asynchronous systems. Moreover, these protocols typically require the transmission of at least messages each time clocks are synchronized and all messages are exchanged in a bursty manner within a ....

....can be used to synchronize clocks despite unbounded communication delays. Since probabilistic reading achieves higher precisions than deterministic reading, the protocols achieve synchronization precisions better than those achievable by previously known deterministic algorithms, such as those of [2, 3, 7, 8]. Our algorithms use several new midpoint convergence functions, derived from the original fault tolerant midpoint convergence function of [3] These new convergence functions achieve optimal accuracy: the drift rate of the synchronized clocks is bounded by the maximum drift rate of correct ....

L. Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, Jan 1985.

....of California San Diego, La Jolla, CA 92093 0114. This research was partially supported by a grant from the Air Force Office of Scientific Research. quired to meet their deadlines, provided no more than a bounded number of failures occur [9] Examples are internal clock synchronization [18] and synchronous atomic broadcast [7] and membership services [8] The implementation of such services depends critically on the existence of an upper bound for message transmission and process scheduling delays. Synchronous fault tolerant services cannot be implemented in asynchronous systems ....

....fail aware distributed service. An example of the usage of an indicator in distributed services are the membership services of [8, 11] each of which has a joined indicator telling the service clients whether they are joined to a group or not. Most internal clock synchronization protocols, e.g. [18, 19], mask arbitrary failures, in the sense that correct clocks are synchronized when less than a third of the clocks suffer failures. Our proposed fail aware clock synchronization service handles performance, omission, and crash failures but does not tolerate arbitrary failures. An extension to mask ....

[Article contains additional citation context not shown here]

L. Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, Jan 1985.

....is ambiguity as to which clock a process should use when an external application requests the time. Moreover, setting the clock forward at each resynchronization introduces a discontinuity in the logical time (when a process switches to a new logical clock) As Lamport and Melliar Smith noted in [9], an algorithm for discontinuously resynchronizing clocks can be easily transformed into one where logical clocks are continuous. This can be achieved by spreading out each resynchronization adjustment over the next resynchronization period. In this section we provide details on how to modify our ....

....averaging, and for the nonauthenticated case, given Dmx, the maximum permitted deviation between correct clocks, our algorithm needs about half as many resynchronizations as in the best previous result [ 10] The minimum value olDmax that our algorithm can achieve depends only on 9 and tdel. In [9], the minimum Dmax possible is proportional to the number of processes in the system. In the preceding sections, we have assumed a completely connected network. This assumption can be relaxed using well known techniques. For an authenticated system, node connectivity off 1 is sufficient. This ....

LAMPORT, L., AND MELLIAR-SMITH, P.M. Synchronizing clocks in the presence of faults. J. ACM 32, I (Jan. 1985), 52-78.

....total number of processes. The closeness of synchronization achi.eved depends only on the initial closeness of synchronization, the message delivery time and its uncertainty, and the drift rate. Since the closeness of synchronization depends on the initial closeness, this is, in the terminology of [LM], an interactive convergence algorithm. We give explicit bounds on how the difference between the clock values and real time grows. The algorithm can be easily adapted to become a reintegration procedure for repaired processes. Lamport and Melttar Smith [LM] Halpern, Simons and Strong [HSS] and ....

....this is, in the terminology of [LM] an interactive convergence algorithm. We give explicit bounds on how the difference between the clock values and real time grows. The algorithm can be easily adapted to become a reintegration procedure for repaired processes. Lamport and Melttar Smith [LM], Halpern, Simons and Strong [HSS] and Marzullo [M] also have clock synchronization algorithms that run in rounds. The three algorithms in [LM] as do ours, require a reliable, completely connected communication network and handle arbitrary faults. However, the closeness of synchronization ....

[Article contains additional citation context not shown here]

L. Lamport and P.M. Melliar-Smith, Synchronizing clocks in the presence of faults, SRI International Report (March 1982).

....at slightly different rates) The restart problem is to reestablish synchronization after transient faults have afflicted one or more (or all) controllers. The synchronization problem is well understood and many algorithms to solve it have been developed, analyzed, and formally verified [LMS85, Min93, Sha92, WL88] The algorithm employed in TTA belongs to the general class of averaging synchronization algorithms [Sch87] each controller i estimates its skew relative to each controller p by comparing the reading of its local clock at the instant when the message in slot p arrives ....

L. Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, January 1985. 23

....in the full version of the paper. 5. FUTURE DIRECTIONS Our results require that at most a third of the processors are faulty during each period. Previous clock synchronization protocols assuming authenticated channels (as we do) were able to require only a majority of non faulty processors [19, 27]. It is interesting to close this gap. In [10] there is another weaker requirement: only that subnetwork containing non faulty processors remain connected (but [10] also assumes signatures) It may be possible to prove a variant of this for our protocol, in particular it would be interesting to ....

L. Lamport and P.M. Melliar-Smith, Synchronizing clocks in the presence of faults, JACM Vol. 32, No. 1, Jan. 1985, pp. 52--78.

....O(t 1) rounds of message exchange. Since our implementation of a k fail stop processor need tolerate at most k failures and involves at least 2k 1 processors for running s processes, IC1 and IC2 can be achieved. Protocols to achieve clock synchronization, as required by IC3, are described in [LM82] These protocols require at least 2t 1 processors in order to tolerate at most t faulty ones, if the origin of messages can be authenticated. For a single k fail stop pro cessor, IC3 requires the k 1 processors running p processes to have synchronized clocks. However, it is impossible to use ....

Lamport, L., P.M. Melliar-Smith. Synchronizing Clocks in the Presence of Faults. Op. $0, Com- puter Science Laboratory, SRI International, Menlo Park, California, March I982.

....on FCA. This provides the background necessary for understanding the modifications required to CCA so that it can be used for clock synchronization. We next sketch that. A detailed analysis of the performance of our clock synchronization protocols is not given here, since it differs from that in [LM85] only in the use of a different value for precision. 4.1. Using FCA to Synchronize Clocks Each processor p is assumed to have a real time clock which we model as a function c p from real time to clock time. Correct real time clocks satisfy Rate Restriction: dc p (t ) 1 for some ....

Lamport, L. and P.M. Melliar-Smith. Synchronizing clocks in the presence of faults. JACM 32, 1 (Jan. 1985), 52-78.

....CF Avg (x p , x 1, x N ) is the average of arguments x 1 through x N after the k highest and k lowest values have been discarded. The degree k of fault tolerance for CF Avg is characterized by 3k 1 = N . Precision p is N 2k f d a(d) d. CF EA was first proposed and analyized in [Lamport Milliar Smith 85] in connection with a clock synchronization algorithm. CF FCA is discussed in [Mahaney Schneider 85] who were the first to view convergence functions (there, called inexact agreement protocols) in terms of accuracy and precision. CF Mid and CF Avg are given in [Dolev et al. 83] CF Avg is the ....

....Message delivery times are typically non trivial and unpredictable. Thus, it is impossible for a single processor in a distributed system to compute CF (c p (t T ) c p (t T ) as required by the resynchronization protocol outlined in section 2. 6 A technique originally proposed in [Lamport Milliar Smith 85] allows one processor to compute an approximation for a virtual clock at another. Each processor p maintains a collection of tables t p [1 . N ] containing values that transform c p (t ) into an approximation for c q (t ) Processor p approximates c q (t ) by c p (t ) t p [q ] To ....

[Article contains additional citation context not shown here]

Lamport, L. and P.M. Milliar-Smith. Synchronizing clocks in the presence of faults. J. ACM 32, 1 (Jan. 1985), 52-78.

....servers. We assume that the clients can send any request at any time. If we impose restrictions on the behavior of the clients, then we can derive protocols that violate the lower bounds in this paper. SOur protocols can be extended to the case where clocks are only approximately synchronized [14]. 6Another approach would be assume that servers are interconnected with redundant broadcast busses [2, 8] We have not pursued this approach. Define to be the potential causality relation [12] on server events el and e2. Thus is the transitive closure of the following relation : el e2 ....

Leslie Lampoft and P.M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52-78, January 1985.

....any key of the one way key chain commits to all following keys, so we call such a key a one way key chain commitment, or simply key chain commitment. 2. 2 Time Synchronization TESLA does not need the strong time synchronization properties that sophisticated time synchronization protocols provide [22, 24, 37], but only requires loose time synchronization, and that the receiver knows an upper bound on the sender s local time. We now outline a simple and secure time synchronization protocol that achieves this requirement. For simplicity, we assume the clock drift of both sender and receiver is ....

....3.3 Bootstrapping Receivers Before a receiver can authenticate messages with TESLA, it needs to be loosely time synchronized with the sender, know the disclosure schedule of keys, and receive an authenticated key of the one way key chain. Various approaches exist for time synchronization [24, 37, 22]. TESLA, however, only requires loose time synchronization between the sender and the receivers, so a simple algorithm is sufficient. The time synchronization property that TESLA requires is that each receiver can place an upper bound of the sender s local time, as we discuss in Section 2.2. The ....

L. Lamport and P. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, 1985. 10

....are almost synchronized with real time. This structure is depicted in Figure 10.1. We model the clock subsystem as a live timed I O automaton that issues ticks to the sender and the receiver. Exactly how to implement a clock subsystem in a distributed system falls outside the scope of this work [LMS85] C is a timed protocol. Besides having the clock subsystem, we shall assume that channel delays and the maximum time difference between certain process steps are bounded. Thus, each component of C is specified as a live timed I O automaton, and consequently C itself is a live timed I O ....

L. Lamport and P.M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, January 1985.

....However, verification of the basic algorithm provides a foundation for the TTA case. Formal verification of clock synchronization algorithms has quite a long history, beginning with Rushby and von Henke s verification [60] of the interactive convergence algorithm of Lamport and Melliar Smith [32]; this is similar to the Welch Lynch algorithm, except that the egocentric mean is used as the fault tolerant average. Shankar [70] formally verified Schneider s abstract algorithm and its instantiation for interactive convergence. This formalization was subsequently improved by Miner (reducing ....

L. Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, January 1985. 4

....the system. Other algorithms exist that send clock update messages periodically on the system. One proposed method is that all of the nodes of the system periodically request the time from a central server [18] Another method has nodes broadcast their times to all other nodes at a specified rate [19]. The local nodes update their clocks based on the average of the times received. In both cases, updating the clocks during program execution is intrusive, and the accuracy of the clocks is limited by the message transmission delay time. 3.3. The Loki Clock Synchronization Algorithm For Loki, ....

L. Lamport and P. M. Melliar-Smith, "Synchronizing clocks in the presence of faults," Journal of the ACM, vol. 32, pp. 52-78, January 1985.

....sound, light, air pressure) is sensed by di erent smart things. These examples indicate that temporal ordering and other real time issues play an important role in such environments. As we will see later, neither logical time [12, 14] nor classical physical clock synchronization algorithms [3, 13, 16, 17] can be used to solve this problem in general. We will suggest an algorithm that solves the temporal ordering problem and other real time issues in environments sketched above. 2. AD HOC NETWORKS Ad hoc networks [2] are networks of mobile wireless computing devices. Due to the limited ....

....at the ends. It remains an open task to determine good probability distributions. Furthermore it has to be investigated for which cases knowing a probability instead of MAYBE is advantageous for applications. 8. RELATED WORK There has been much work on physical clock synchronization in the past [3, 13, 16, 17]. However, most of the proposed synchronization algorithms, including the well known Network Time Protocol [15] rely on a network that is not partitioned and where it is always possible to produce good estimations for the message delay. As pointed out in section 3, this is not the case for sparse ....

L. Lamport and P. M. Melliar-Smith. Synchronizing Clocks in the Presence of Faults. Journal of the ACM, 32(1), January 1985.

....of UTC for the University Time Service. Allowing clients to connect directory to Stratum 1 Time Servers is not only a waste of bandwidth, it could also tax the Stratum 1 servers. This may cause unwanted latency and other inaccuracies. Distributed time systems has also been extensively studied[4][5][6] That is why this next major group, the Stratum 2 Time servers, are necessary. In the particular case of the Ateneo de Manila University. The campus network is configured in such a way that each major group of network users would have their tra#c access certain network gateways. These gateways ....

Lamport, L., and P.M. Melliar-Smith. Synchronizing clocks in the presence of faults. JACM 32, 1 (January 1985), 52-78.

....schedule. This would present an unacceptable interface to the hosts, so it is clear that the clocks need to be synchronized. Two clocks do not suffice for fault tolerant clock synchronization (we cannot tell which is wrong) at least four are required for the most demanding fault models [LMS85] although three may be enough in certain circumstances [Rus94] Rather than synchronize multiple buses, each with a single clock, it is better to replicate clocks within a single bus. Now, the hosts are full computers equipped with clocks so it might seem that they could undertake the clock ....

L. Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, January 1985.

....1 (the indefinite time point) as the end. In distributed environments time and events acquire another dimension due to the lack of a global view of the system. Thus, events in distributed contexts are associated to global time that should be computed using methods such as those proposed in [Sch96, LMS85] For global time we also adopt a discrete representation. Table 1 describes dimensions associated to event definition. Events characterization and semantics depend largely on their source (dimension 1) Events may come from internal sources, in this case they represent operations inherent to ....

Lamport L. and P.M Melliar-Smith, Synchronizing Clocks in the Presence of Faults, Journal of the ACM 32 (1985), no. 1, 52--78.

....is to employ a correction algorithm to adjust the local clock, which would be the application s function. We demonstrate the use of VDL to express two convergence algorithms: Interactive Convergence and Fast Convergence. Figure 6 gives an example of the Interactive Convergence Algorithm (CNVA) [21] implemented in VDL. The synchronizing node first collects clock values from all other nodes, and then replaces the values that are too far away from ##### #####, where too far away means not within a given distance # from ##### #####. If all the values are excluded (replaced) an exception is ....

L. Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. J. Assoc. Comput. Mach., 21(1):52-- 78, January 1985.

....is to define a reference moment and a unit (i.e. second, minute, hour, etc. In distributed environments time and events acquire another dimension due to the lack of a global view of the system. Thus, events are associated to global time that should be computed using methods as those proposed in [21, 17]. For global time we adopt a discrete representation 2 . An expression can describe primitive or composite events. In an FDBMS, primitive event types represent database operations (e.g. update, method call, transaction com 2 This means that we consider the Gregorian calendar and a discrete ....

Lamport L. and P.M Melliar-Smith. Synchronizing Clocks in the Presence of Faults. Journal of the ACM, 32(1):52--78, 1985.

....1 (the indefinite time point) as the end. In distributed environments time and events acquire another dimension due to the lack of a global view of the system. Thus, events in distributed contexts are associated to global time that should be computed using methods such as those proposed in [Sch96,LMS85] For global time we also adopt a discrete representation. Table 1 describes dimensions associated to event definition. Events characterization and semantics depend largely on their source (dimension 1) Events may come from internal sources, in this case they represent operations inherent to ....

Lamport L. and P.M Melliar-Smith. Synchronizing Clocks in the Presence of Faults. Journal of the ACM, 32(1):52--78, 1985.

....Interactive Convergence Algorithm (ICA) for Byzantine fault tolerant clock synchronization. At the time, this was one of the hardest mechanized veri cations that had been attempted and we began by simply trying to reproduce the arguments in the journal paper that introduced the algorithm [25]. Eventually, we succeeded, but discovered in the process that the proofs or statements of all but one of the lemmas, and also the proof of the main theorem, were awed in the journal presentation. In developing our mechanically checked veri cation we eliminated the approximations used by ....

....productive pencil and paper mathematics is done. In the case of the examples considered here, it was relatively straightforward to describe the necessary concepts directly within higher order logic in a manner that reproduced the presentation in standard journal treatments of the topics concerned [25], 32] fairly closely, or that followed a style that had proved comfortable in earlier pencil and paper development (e.g. compare the pencil and paper development of a fault masking model [48] with a fully formal version [49] However, allowing these formal 5 These systems are developed under ....

L. Lamport and P. M. Melliar-Smith, \Synchronizing clocks in the presence of faults", Journal of the ACM, vol. 32, no. 1, pp. 52-78, Jan. 1985.

....the other components, etc. As a result, faultfree components must agree on how to use consistently the information obtained and, therefore, protect against possibly inconsistent failures (e.g. Byzantine agreement [Pease et al. 1980] atomic broadcast [Cristian et al. 1985] clock synchronisation [Lamport MelliarSmith 1985, Kopetz Ochsenreiter 1987] or membership protocols [Cristian 1988] It should be noted, however, that the unavoidable presence of structural redundancies in any fault tolerant system requires a resource distribution at one level or another, leading to the persistence of the consensus problem. ....

L. Lamport and P. M. Melliar-Smith, "Synchronizing Clocks in the Presence of Faults", Journal of the ACM, 32 (1), pp.52-78, 1985.

....time base is available in the system [8, 9] Maintaining a consistent global notion of time in a distributed computing environment involves synchronization of all the local clocks. Clock synchronization problem has been studied extensively in the past and several solutions have been proposed [10, 11, 12, 13, 14, 15]. However, most of these solutions depend either on special purpose hardware or complicated protocols. This will add extra processing overhead and complexity to the system, thereby increasing the clock skews in a distributed system. The proposed time management unit can be used to achieve very ....

....896 Futurebus systems [23] The differences are mainly of hardware implementation details. Baek et al. proposed a hardware based clock synchronization technique for synchronizing the clock signals [15] Their technique implements a modified version of the interactive convergence algorithm CNV [13] and they assume that the actual clock signals are available for skew measurements. However, their scheme is not suitable for large distributed systems because of the problems (such as clock skews and signal to noise ratio) associated with distributing the high frequency clock signal over large ....

L. Lamport and P. Meilliar-Smith, "Synchronizing Clocks in the presence of Faults," Journal of the ACM, vol. 32, pp. 52--78, January 1985.

....base is available in the system [12] Maintaining a consistent global notion of time in a distributed computing environment involves synchronizing all the local clocks. Clock synchronization problem has been studied extensively in the past and several solutions have been proposed [9] 16] 5] [13], 14] 1] But, most of these solutions either depend on special purpose hardware or complicated protocols. This will add extra processing overhead and complexity to the system, there by increasing the clock skews in a An Accurate Time management Unit for Real time Processors 3 distributed ....

....896 Futurebus systems [20] The differences are mainly of hardware implementation details. Another hardware based clock synchronization technique for synchronizing the clock signals can be found in [1] This technique implements a modified version of the interactive convergence algorithm CNV [13] and assumes that the actual clock signals are available for skew measurements. However, this scheme is not suitable for large distributed system because of the problems associated with distributing the clock signal over large distances. The hardware assisted software clock synchronization scheme ....

L. Lamport and P.M. Meilliar-Smith. Synchronizing Clocks in the presence of Faults. Journal of the ACM, 32(1):52--78, January 1985.

....internet system. Current network clock synchronization techniques have evolved from both linear systems and Byzantine agreement methodologies. Linear methods for digital telephone network synchronization are summarized in [16] while Byzantine methods for clock synchronization are summarized in [15]. While reliable clock synchronization has been studied using agreement algorithms [15] 33] in practice it is not possible to distinguish the truechimer clocks, which maintain timekeeping accuracy to a previously published (and trusted) standard, from the falseticker clocks, which do not, on ....

....both linear systems and Byzantine agreement methodologies. Linear methods for digital telephone network synchronization are summarized in [16] while Byzantine methods for clock synchronization are summarized in [15] While reliable clock synchronization has been studied using agreement algorithms [15], 33] in practice it is not possible to distinguish the truechimer clocks, which maintain timekeeping accuracy to a previously published (and trusted) standard, from the falseticker clocks, which do not, on other than a statistical basis. In addition, the algorithms discussed in the literature ....

[Article contains additional citation context not shown here]

Lamport, L., and P.M. Melliar-Smith. Synchronizing clocks in the presence of faults. JACM 32, 1 (January 1985), 52-78.

....pulse generators for each processors. It is easy to see that the less centralized the clock implementation is the more resilient to faults it is. 2. The Model 2 In the past clock synchronization solutions that can tolerate faults have been proposed for the case of arbitrary, or Byzantine, faults [19, 18, 20, 8, 21, 23]. In those model characteristics they proved that no algorithm can work unless more than one third of the processors are nonfaulty [8] In the case of authenticated Byzantine faults the things are not so bad; there exist algorithms that can tolerate any number of faulty processors [12] The ....

L. Lamport and P.M. Melliar-Smith. Synchronizing Clocks in the Presence of Faults. Journal of the ACM 32, 1, 1985, pp. 1--36.

....control require a precision better than that normally achieved with software based algorithms. In fact, a major limitation of all known software clock synchronization algorithms designed for arbitrary networks, is that precision is limited either by the variance of the message delivery delay [14], or by its upper bound [23] This problem may be attenuated in special architectures, either by implementing clock synchronization exclusively by hardware [8,13] or by using hybrid schemes [18,11] which attempt at reducing that variance. Probabilistic or statistical solutions to damp the effect ....

....technique [7,23,1] are attractive. Since what is disseminated is the event that a node believes it is now a pre agreed time rather than a response to a read clock request, they are inherently resilient to failures, requiring less messages and synchronization cycles than averaging algorithms[14,16,3]. Before proceeding, we present our assumptions about the system: ffl clocks may have arbitrary failures (e.g. provide erroneous or conflicting values when read) ffl clock server processes (the ones running the protocol over the network) may have failures from crash to uncontrolled omission or ....

[Article contains additional citation context not shown here]

L. Lamport and P. Melliar-Smith. Synchronizing Clocks in the Presence of Faults. Journal of the ACM, 32(1):52--78, January 1985.

....(with deterministic algorithms) and proposes an algorithm achieving that precision. In [Cr 89] a probabilistic algorithm is introduced that achieves a higher precision (at the price of being non deterministic) Examples of fault tolerant algorithms for clock synchronization can be found in [LMS 85, KoO 87, LuL 88, Ver 92] These protocols have in common that they spend a relatively high overhead for communication in order to achieve a sufficient level of precision and fault tolerance. Implicitly, they are designed for wired communication links that offer a sufficiently high bandwidth (e.g. ....

L. Lamport, and P. Melliar-Smith. Synchronizing Clocks in the Presence of Faults. Journal of the ACM , 32(1):pp. 52-78, January 1985.

....initial state q 0;i and a distinguished fail state. A configuration is a vector C = q 1 ; q n ) where q i is the local state of p i ; denote state i (C) q i . The initial configuration is the vector (q 0;1 ; q 0;n ) Processes communicate by sending messages 4 See [13, 22, 25, 27, 37, 39], for example. 5 These definitions could be expressed in terms of the general timed automaton model described in [1] and [29] however, we choose here to present the definitions directly, in order to avoid the intervening layer of definitions. 5 (taken from some alphabet M) to each other. A ....

Lamport, L., and Melliar-Smith, P. Synchronizing clocks in the presence of faults. J. ACM 32, 1 (January 1985), 52--78. 31

....time, leading to a faulty local interval measurement, and an instantaneous backward correction additionally causes negative interval measurements. Continuous synchronization avoids these drawbacks by spreading the correction over the next synchronization period and applying it continuously. In [4,10], a general approach for achieving continuous correction in any round based clock synchronization protocol is shown. However, message losses in the wireless environment can lead for some systems to miss some rounds, thus making this basic approach not applicable. In [12] the authors show how a ....

L. Lamport, and P. Melliar-Smith, "Synchronizing Clocks in the Presence of Faults", Journal of the ACM 32(1), January 1985, pp. 52-78.

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L. Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, 1985.

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L. Lamport and P. Melliar-Smith, "Synchronizing clocks in the presence of faults," J. ACM, vol. 32, no. 1, pp. 52--78, 1985.

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L. Lamport, P. Melliar-Smith, Synchronizing clocks in the presence of faults, J. ACM 32 (1) (1985) 52--78.

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Lamport, L., and P.M. Melliar-Smith. Synchronizing clocks in the presence of faults. JACM 32, 1 (January 1985), 52-78.

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L. Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, Jan. 1985.

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Lamport, L., and P.M. Melliar-Smith. Synchronizing clocks in the presence of faults. JACM 32, 1 (January 1985), 52-78.

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Leslie Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, January 1985.

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L. Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1):52--78, January 1985.

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Lamport, L., and P. Melliar-Smith "Synchronizing Clocks in the Presence of Faults", JACM 32, No. 1, pgs. 52-78, January 1985.

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L.Lamport and P.M. Mellair-Smith, "Synchronizing Clocks in the Presence of Faults", In Journal of the ACM, Vol. 32, No. 1, pp. 1-36, 1985

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L. Lamport and P. Melliar-Smith. Synchronizing clocks in the presence of faults. J. ACM, 32(1):52--78, 1985.

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L. Lamport and P. M. Melliar-Smith. Synchronizing clocks in the presence of faults. Journal of the ACM, 32(1), pages 52--78, 1985.

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L. Lamport and M. Melliar-Smith, `Synchronizing clocks in the presence of faults', Journal of the ACM, 32, (l), 52--78 (1985).

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L. Lamport and P. J. Melliar-Smith, "Synchronizing clocks in the presence of faults," Journal of the ACM, vol. 32, no. 1, pp. 52--78, 1985.

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Lamport, L. and P.M. Melliar-Smith. Synchronizing clocks in the presence of faults. J. ACM 32, 1 (lan. 1985), 52-78.

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L. Lamport and Melliar-Smith P. M. Synchronizing clocks in the presence of faults. Journal of the Association for Computer Machinery, 32(1):52--78, January 1985.

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Lamport, L. and Melliar-Smith, P. M. "Synchronizing Clocks in the Presence of Faults", J. ACM, Vol. 32, No. 1, pp. 52-78, January 1985

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Lamport L. and Melliar-Smith P.M. 1985. "Synchronizing clocks in the presence of faults". Journal of the ACM, Vol 32, No. 1, Jan 1985.

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