N. Lynch, Y. Mansour, and A. Fekete. The data link layer: Two impossibility results. In Proc. of the ACM Symp. on Principles of Distributed Computing, August 1988.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Weiner and Yannakakis [4] showed that certain kinds of data link behavior cannot be achieved with protocols composes of finite state ma chines of particular sizes. The arguments are based on the limitations imposed by small numbers of states. Arguments use case analysis. Lynch, Mansour and Fekete [78] gave impossibility results for implementing desirable data link be havior (reliable message delivery) in terms of typical physical channel behavior (less reliable packet delivery) in either of two cases: 1) if crashes can occur that cause a loss of memory, or (2) if there are only a bounded ....

....This means the network operation must get slower, and s 1 o w e r, and s 1 o w e r . Some interesting open questions remain about the rate at which the num ber of packets required must grow with the number of messages delivered. We found defining the model to be a difficult part of the work in [78]. We used I O automata; in fact, this was our first attempt to use I O automata to prove impossibility results. We found getting the formal definitions right to be exceedingly tricky, espe cially compared to the informal way in which we first discussed the ideas. Much of the difficulty, as usual, ....

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N. Lynch, Y. Mansour, and A. Fekete. The data link layer: two impossibility results. In Proceedings of the 7 Annual ACM Symposium on Principles of Distributed Computing, pages 149-170, Toronto, Canada, August 1988.

....used to show nonexistence of a protocol with certain properties. There has recently been a lot of research in the distributed computing theory research com munity on the problem of constructing a reliable message transmission service using an underlying unreliable packet transmission service (see [9, 1, 18, 13], for example) Most of this work has addressed the case where the physical channel is especially unreliable, in that it can lose packets and also deliver packets out of order. In these cases the natural protocol, due to Stenning ( 15] places each message in a packet with a sequence number as ....

....problem without using some header to distinguish between packets. A key modeling issue is how to define headers in an arbitrary protocol, without assuming a particular structure (such as [sequence number,message] for the packets. The definitions we use are adapted (and simplified) from those in [9, 6]. The rest of the paper is organized as follows. In Section 2, we show how we model physical channels, and also show the existence of a universal physical channel, which exhibits all t]e behaviors that can arise in any physical channel. In Section 3, we give the specification for correct data ....

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Lynch, N. A., Mansour, Y. and Fekete, A., "Data Link Layer: Two Impossibility Results," Proceedings of 7th ACM Symposium on Principles of Distributed Computing, pp. 149-170, August 1988.

....under contracts N00014 83 K 0125 and N00014 89 J 1985. There has recently been a lot of research in the distributed computing theory research commu nity into the possibility of constructing a reliable message transmission service using an underlying unreliable packet transmission service (see [8, 1, 16, 12], for example) Most of tiffs work has addressed the case where the physical channel is especially unreliable, in that it can lose packets and also deliver packets out of order. In these cases the natural protocol, due to Stenning ( 13] places each message into a packet with a sequence number as ....

....some header to distinguish between packets. A key modeling issue is how to measure the existence of a header in an arbitrary protocol, without assuming a particular structure (such as [sequence number,message] for the packets. The definitions we use are adapted (and simplified) from those in [8, 5]. In Sections 2 4, we show how we model the different service specifications and the construction of an arbitrary protocol to provide a data link service using two physical channels. In Section 5 we define the specific physical channels we will use in the main result. In Section 6 we prove a ....

Lynch, N. A., Mansour, Y. and Fekete, A., "Data Link Layer: Two Impossibility Results," Pro- ceedings of 7th A CM Symposium on Principles of Distributed Computing pp. 149-170, August 1988.

....sequence transmission problem was solvable using bounded headers in a non FIFO channel. Indeed, the early evidence indicated that no such protocol existed. Lynch, Mansour, and Fekete showed that any bounded header protocol must use an unbounded number of packets per message in a non FIFO channel [LMF88] Surprisingly, Attiya et al. using a counting protocol, showed that STP was solvable using bounded headers in a non FIFO channel [AFWZ89] This work was later extended by Afek et al. AAF 91] Tempero and Ladner refined the counting protocol technique [Tem90, TL90] Mansour and Schieber ....

.... FIFO channel, for some ff that depends on the loss rate and header size [MS89] Other theoretical work on the sequence transmission problem is concerned with upper and lower bounds on the number of packets required to send the n th message for protocols in an adversarial non FIFO channel [LMF88, MS89, WZ89, TL90, AFWZ89, AAF 91] One basic result of Tempero and Ladner is that there is a counting protocol with the property that no matter how poorly the channel behaves in delivering the first n 0 1 messages, if the channel subsequently behaves well then the n th message can be ....

N. Lynch, Y. Mansour, and A. Fekete. The data link layer: Two impossibility results. In Seventh Annual ACM Symposium on Principles of Distributed Computing, August 1988.

....of system states that satisfy the properties required by the specification. In the remainder of this section a self stabilizing data link protocol is specified. The purpose of a data link protocol is to reliably transmit messages from one end of an error prone communication medium to the other end [BSW69, AUWY82, BS83, LMF88]. By reliably we mean that messages arrive error free, without duplication or loss, and in the order sent. The system consists of two processes, the transmitter T and the receiver R, connected by two directed communication links, T R and R T, oriented in opposing directions. Messages transmitted ....

N. Lynch, Y. Mansour, and A. Fekete. The data link layer: Two impossibility results. In Proceedings of the ACM Symposium on Principles of Distributed Computing, 1988.

....of Stenning s algorithm [Ste76] that uses headers to identify messages and acknowledgements. These headers can grow arbitrarily large. In this paper we refer to the data link layer messages as high level or RL messages and the underlying physical layer messages as low level or UL messages. LMF88] and [AAF ] prove that its not efficient to bound the size of headers. Specifically, protocols that are able to transmit every high level message using only a constant number or O(1) of low level messages once the network starts behaving ideally, must use unbounded headers. Such protocols are ....

....seem, though, that making the pdf a function of time would affect the impossibility result. Other cases that need to be studied are when the different UL message on the link don t have independent delays and links can behave in a faulty and byzantine manner and the processor can also crash. LMF88] shows that no constant bounded Data Link protocol can work in the presence of processor crashes. GHM89] shows an O(n) bounded algorithm that has a small probabilistic error. BS88] gives an algorithm that is resilient to processor crashes if a single bit of non volatile memory is made available ....

Nancy Lynch, Yishay Monsour, and Alan Fekete. Data link layer: Two impossibility results. In PODC, pages 149--170, 1988.

....of the model in the context of asynchronous concurrent systems. The model has been used extensively to model concurrency control and recovery in transaction systems, resource allocation, concurrent data structures, network communication, and other problems (e.g. LT89, LM88, LMWF88, Blo87, WLL88, LMF88, Her88] It has been used to specify these problems, to describe and analyze algorithmic solutions, and to prove lower bounds and impossibility results. The model has many natural properties (such as compositionality) and this work was motivated by our desire to find an equally intuitive ....

Nancy A. Lynch, Yishay Mansour, and Alan Fekete. Data link layer: Two impossibility results. In Proceedings of the 7th Annual ACM Symposium on Principles of Distributed Computing, pages 149--170. ACM, August 1988. Also available as MIT Technical Report MIT/LCS/TM-355.

....there is an upper bound on message delivery time, then the modified Stenning protocol [Ste76] gives a finite state solution. In fact, in [AFWZ88] it is shown that if we allow messages to be reordered and duplicated, then there is no solution using a finite message alphabet, and both [AFWZ88] and [LMF88] show that under most natural requirements, if we allow messages to be reordered and deleted, then there is no solution using a finite message alphabet. If we allow undetectable corruption of messages (so that any message can be converted to any other) then there is no solution at all, either ....

N. A. Lynch, Y. Mansour, and A. Fekete. Data link layer: two impossibility results. In Proc. 7th ACM Symp. on Principles of Distributed Computing, pages 149--170, 1988.

....are necessary in order to manage incarnations, under various requirements and assumptions. LeLann and LeGoff [18] show that a connection cannot be established by protocols of a particular form. Other theoretical studies of communication protocols have mostly concentrated on the data link layer [1, 3, 13, 16, 20, 22, 26, 29]. Most of this work concerns implementing protocols using bounded size packets, an issue we do not address. Our protocols for message transfer on bounded capacity FIFO networks use an idea from self stabilizing protocols for cleaning the system with a new label. This idea was first employed in ....

N. Lynch, Y. Mansour and A. Fekete, "The Data Link Layer: Two Impossibility Results," Proceedings of the 7th ACM Symposium on Principles of Distributed Computing, pp. 149--170, August 1988.

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N. Lynch, Y. Mansour, and A. Fekete. The data link layer: Two impossibility results. In Proc. of the ACM Symp. on Principles of Distributed Computing, August 1988.

....bit that is the same as the one it is currently transmitting, it knows that its current message has been received and switches to the next message, using the opposite header bit. This protocol does not work if the physical channels can reorder mes48 sages. In fact, Lynch, Mansour, and Fekete [LMF88] showed that no protocol with bounded headers can work over non FIFO physical channels, if the best case number of packets required to deliver each message must be bounded. Attiya et al. AFWZ89] complete the picture by showing that this latter assumption is necessary that there is a (not very ....

....without bound. Baratz and Siegel [BS88] developed link protocols that tolerate crashes of the participating nodes, with loss of information in the nodes states. Their algorithm requires the node at each end of the link to have one bit of stable memory that survives crashes. It is shown in [LMF88] that this bit of stable memory is necessary. Aho et al. AUWY82] have studied the basic capabilities of finite state link protocols. 4.4 Concurrency Control in Databases A database consists of a collection of items that are individually read and written by the operations of programs called ....

Nancy A. Lynch, Yishay Mansour, and Alan Fekete. The data link layer: two impossibility results. In In Proceedings of the 7th ACM Symposium on Principles of Distributed Computation, pages 149--170, ACM SIGACT and ACM SIGOPS, Toronto, Canada, August 1988. Also, MIT Technical Memo, MIT/LCS/TM-355, May 1988.

....infinite number of messages does not require either the sender or the receiver to have infinite space. A single buffer at the sender (receiver) suffices in order to store the next data item to be transmitted. The precise formulation of this interactive statement of the problem can be found in [LMF88] 5 3 Informal Description In this section, we informally describe the slide protocol, and then describe three end to end communication protocols that use it as a building block. The formal presentation of these protocols, their proof of correctness and their analysis follow in the next ....

N. Lynch, Y. Mansour, and A. Fekete. The data link layer: Two impossibility results. In Proc. of the ACM Symp. on Principles of Distributed Computing, August 1988.

....4. Results related to ours appear in several other papers. A collection of general definitions and composition results about layered protocols in a model related to ours is given in [LS90] A preliminary version of Theorem 5.10 appears in [AFWZ89] A preliminary version of Theorem 6. 4 appears in [LMF88]. Subsequent papers consider other versions of RMTP and other definitions of efficiency. For example, MS92] contains an impossibility result for efficient RMTP using a related but incomparable notion of efficiency, and it extends the result to channels where message loss is probabilistic rather ....

N. Lynch, Y. Mansour, and A. Fekete. Data link layer: Two impossibility results. In Proc. 7th ACM Symp. on Principles of Distributed Computing, pages 149--170, August 1988.

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