Boaz Patt-Shamir

Self-stabilization by local checking and correction

The first self-stabilizing end-to-end communication protocol and the most efficient known self-stabilizing network reset protocol are introduced. A simple method of local checking and correction, by which distributed protocols can be made self-stabilizing without the use of unbounded counters, is used. The self-stabilization model distinguishes between catastrophic faults that abstract arbitrary corruption of global state, and other restricted kinds of anticipated faults. It is assumed that after the execution starts there are no further catastrophic faults, but the anticipated faults may continue to occur.<<ETX>>

Buffer Overflow Management in QoS Switches

We consider two types of buffering policies that are used in network switches supporting Quality of Service (QoS). In the FIFO type, packets must be transmitted in the order in which they arrive; the constraint in this case is the limited buffer space. In the bounded-delay type, each packet has a maximum delay time by which it must be transmitted, or otherwise it is lost. We study the case of overloads resulting in packet loss. In our model, each packet has an intrinsic value, and the goal is to maximize the total value of transmitted packets. Our main contribution is a thorough investigation of some natural greedy algorithms in various models. For the FIFO model we prove tight bounds on the competitive ratio of the greedy algorithm that discards packets with the lowest value when an overflow occurs. We also prove that the greedy algorithm that drops the earliest packets among all low-value packets is the best greedy algorithm. This algorithm can be as much as 1.5 times better than the tail-drop greedy policy, which drops the latest lowest-value packets. In the bounded-delay model we show that the competitive ratio of any on-line algorithm for a uniform bounded-delay buffer is bounded away from 1, independent of the delay size. We analyze the greedy algorithm in the general case and in three special cases: delay bound 2, link bandwidth 1, and only two possible packet values. Finally, we consider the off-line scenario. We give efficient optimal algorithms and study the relation between the bounded-delay and FIFO models in this case.

Time optimal self-stabilizing synchronization

In the network synchronization model, each node maintains a local pulse counter such that the advance of the pulse numbers simulates the advance of a clock in a synchronous network. In this paper we present a tame optimai sel&stabilizing scheme for network synchronization. Our construction has two parts. First, we give a simple rule by which each node can compute its pulse number as a function of its neighbors’ pulse numbers. This rule stabilizes in time bounded by t?te diameter of the network, it does not revoke global operations, and does not require any additional memory space. However, this rule works correctly only if the pulse numbers may grow unfoundedly. The second part of the construction (whzch is of independent interest in its own right) takes care of this problem. Specifically, we present the jirst self-stabilizing reset procedure that stabilizes in tzme proportional to the diameter of the network. This procedure can be combined with unbounded-register protocols to yield bounded-register algorithms. “Lab. for Computer Science, MIT. Supported by Air Force Contract TNDGAFOSR-86-0078, ARO contract DAAL03-86K-01 71, NSF contract CCR861 1442, DARPA contract NOOO1489-J-1988, and a special grant from IBM. t IBM T.J. Watson Research Center.

Buffer overflow management in QoS switches

Tel-Aviv University and IBM T.J. Watson Research Center.

Jitter control in QoS networks

Lab. for Computer Science, MIT. Research partly done while visiting IBM T.J. Watson Research Center. Supported in part by DARPA contracts NOOO1 4-92J-4o33 and NOOO1492-J-1799, ONR contract NOOO14-91-J-1O46, and NSF contract 8915206-CCR. !IDEG, 55o King Street, Llttleton, MA 01460. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice ia given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. 25th ACM STOC ‘93-51931CA,USA @ J993 AG~ Q-89~9J-59 J-7/93 /QQQ51Q652,..

Time-adaptive self stabilization

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Traversals of object structures: Specification and Efficient Implementation

We consider two types of buffering policies that are used in network switches supporting QoS (Quality of Service). In the FIFO type, packets must be released in the order they arrive; the difficulty in this case is the limited buffer space. In the bounded-delay type, each packet has a maximum delay time by which it must be released, or otherwise it is lost. We study the cases where the incoming streams overload the buffers, resulting in packet loss. In our model, each packet has an intrinsic value; the goal is to maximize the total value of packets transmitted Our main contribution is a thorough investigation of the natural greedy algorithms in various models. For the FIFO model we prove tight bounds on the competitive ratio of the greedy algorithm that discards the packets with the lowest value. We also prove that the greedy algorithm that drops the earliest packets among all low-value packets is the best greedy algorithm. This algorithm can be as much as 1.5 times better than the standard tail-drop policy, that drops the latest packets. In the bounded delay model we show that the competitive ratio of any online algorithm for a uniform bounded delay buffer is bounded away from 1, independent of the delay size. We analyze the greedy algorithm in the general case and in three special cases: delay bound 2; link bandwidth 1; and only two possible packet values. Finally, we consider the off-line scenario. We give efficient optimal algorithms and study the relation between the bounded-delay and FIFO models in this case.

Self-stabilization by local checking and global reset

We study jitter control in networks with guaranteed quality of service (QoS) from the competitive analysis point of view: we propose on-line algorithms that control jitter and compare their performance to the best possible (by an off-line algorithm) for any given arrival sequence. For delay jitter, where the goal is to minimize the difference between delay times of different packets, we show that a simple on-line algorithm using a buffer of B slots guarantees the same delay jitter as the best off-line algorithm using buffer space B/2. We prove that the guarantees made by our on-line algorithm hold, even for simple distributed implementations, where the total buffer space is distributed along the path of the connection, provided that the input stream satisfies a certain simple property. For rate jitter, where the goal is to minimize the difference between inter-arrival times, we develop an on-line algorithm using a buffer of size 2B + h for any h ≥ 1, and compare its jitter to the jitter of an optimal off-line algorithm using buffer size B. We prove that our algorithm guarantees that the difference is bounded by a term proportional to B/h.

Rent, Lease, or Buy: Randomized Algorithms for Multislope Ski Rental

Time-Adaptive Self Stabilization Shay Kutten Boaz Patt-Shamir* Dept. of Industrial Engineering College of Computer Science The Technion Northeastern University and boez~ccs. neu. edu IBM T.J, Watson Research Center kutten@ie. technion. ac. il We study the scenario where a transient fault hit ~ of the n nodes of a dktributed system by corrupting their state. We consider the basic problem of persistent bit, where the system is required to maintain a value in the face of transient failures by means of replication. We give an algorithm to recover the value quickly: the value of the bit is recovered at all nodes in 0(~) time units for any unknown value of j < n/2. Moreover, complete state quiescence occurs in O(dhun) time units, where diam denotes the diameter of the network. This means that the value persists indefinitely so long as any ~ < n/2 faults are followed by fl(diam) fault-free time units. We prove lower bounds which show that both time bounds are asymptotically optimal. Using the algorithm for persistent bit, we present a general transformer which takes a distributed nonreactive, non-stabilizing protocol P, and produces a self-stabilizing protocol P’ which solves the problem P solves, with the additional property that if the number of faults that hit the system after stabilization is j, for any unknown ~ < n/2, then the output of P’ regains stability in O(f) time units, and the state stabilizes in O(dlam) time units. ● Research supported by DARPA and Rome Laboratory under agreement F30602-96-0239. Permission to make digitalllmrd copies of fill or part of [his nmleriol for personal or clo.wroum use is granted wiU1outfee pmvi(ied UmtUw copies are not made or dislrihutcd for profit or commercin I w{vnnl~tgc.UWcopyrigbl notice. the tine oftlw publication and iL

A theory of clock synchronization (extended abstract)

date oppew’, *MInotice is given Uralcopyright is hy permission oftbe AChl, IIW To copy oUwn\,ise, to republish, to post on servers or to redisirilw! c to IISIS,requires specific Pemlissiotl oncVorfee 1997 F’(]D~ 97 Simla Bdmm (‘A lJ,V1 Copyright 1997 ACM 0-89791 -952 -1/97/8..