B. S. Tsybakov and V. A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback," Problemy Peredachi Informatsii, vol. 14, no. 4, pp. 32--59, Oct.-Dec. 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....packets forms a stationary and independent Poisson process. In this paper we investigate the effect of capture on colli sion resolution algorithms. We focus here on the basic static binary tree CRA (having maximal throughput of 0. 346) due to Capetanakis [1] and Tsybakov and Mikhailov [2], which is known to be very flexible and insensitive to channel errors [3] the ideas and modifications presented in this paper can be implemented in other tree CRA s as well) In the present algorithm, the conventional three channel states (idle, success, collision) are enhanced by a fourth ....

....between success and capture. Two models are described: the general model for which the extended tree algorithms are described, and the simplified model (which is a special case of the general model) which is used in the analysis part. In Sections III and 1V we show how the basic tree CRA [1] [2] can be applied to the situations where the receiver can distinguish between success slots and capture slots and to the one where it cannot, respectively. In each case; explicit recursive equations for the simplified model are given from wlfich the average collision resolution interval (CRI) ....

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B. S. Tsybakov and V. A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback," Probl. Peredachi Inform., vol. 14, pp. 32-59, Oct.-Dec. 1978.

....scheme that allows each node to randomly choose to transmit in one of several allowable levels of power. Design issues such as number of levels, selection schemes, etc. are discussed. I. INTRODUCTION HE collision resolution algorithm (CRA) proposed by Capetanal is [1] and Tsybakov and Mikhailov [8] has been devised to enable the nodes in a slotted ALOHA type network to exploit the channel history for resolving collisions among competing nodes. Originally, in devising the algorithm, it has been assumed that each slot can be either a) idle slot; no packet is transmitted or b) success slot; ....

....may detect a collision instead of an idle or a success slot. The latter is referred to as noise error. Multiple access algorithms that handle noise errors were presented in [5] 9] and in [6] In [5] 9] the proposed algorithm is based on the tree collision resolution algorithm (CRA) Ill, [8], while that in [6] is based on Gallager s 0.487 algorithm [4] 10] Erasures have been handled in [3] A deterministic capture model in which the nodes of the network are divided into priority groups has been studied in [2] 7] In this paper, we propose and analyze (in Section HI) the ....

B. S. Tsybakov and V. A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback," Problemy Peredachi Informatsii, vol. 14, no. 4, pp. 32-59, Oct.-Dec. 1978.

....used in these studies is that the total arrival process of new packets into the system forms a stationary Poisson process. Under this assumption, conflict resolution algorithms that yield a stable system for arrival rates under 0.462 and 0. 487 packets per 1ot were suggested in [4] and [1] [2], 5] respectively. In this paper we take another point of view which does not assume knowledge of the statistical characteristics of Manuscript received August 25, 1986; revised March 15, 1987. This work was supported in part by the Bat Sheva de Rothshild fund. This paper was presented in part ....

....is optimal in this algorithm that yields efficiency as high as 0.346. CIDON AND SIDI: BATCH RESOLUTION ALGORITHMS 103 2 : 5 I0 . I I (a) b) c) Fig. 1. Binary tree algorithms. a) Basic. b) Modified. c) Clipped. B. Modified Binary Tree Algorithm Massey [4] and Tsybakov and Mikhailov [2] found a simple way to improve the basic algorithm by avoiding sure collisions. The modified algorithm is identical to the basic algorithm except that whenever nodes can infer at some slot that a conflict must occur in the next slot, they skip that slot by tossing the coin before the conflict ....

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B. S. Tsybakov and V. A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback," Probl. Peredach. Inform., vol. 14, .no. 4, pp. 32-59, Oct.-Dec. 1978.

....chosen time. However, the performance of the ALOHA scheme becomes very poor when the channel occupancy increases beyond a certain level. Basically, there are two approaches to improve the performance of MAC protocols: carrier sense multiple access [9] and collision resolution algorithms [4] [14]. A given access network contains a finite number of users or customers, where this number typically ranges from ten to a few thousand. All users share the same up and downstream channel. From the users point of view, the HE can be seen as their common connection with the outer world. ....

....previous request. This procedure of processing successful and retransmitting unsuccessful requests continues until all requests are processed. Such a tree will be called a contention tree. This is shown in Figure 3. For details the readers are referred to [2] 3] 4] 6] 7] 10] 12] 13] [14]. Fig. 3. Example of a ternary contention tree. The basic idea of a ternary contention tree can be used in several ways to obtain slightly different contention resolution procedures. We now describe three different such contention resolution mechanisms. Two of the mechanisms are in fact ....

B. S. Tsybakov and V. A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback", Probl. Info. Trans., vol. 14, pp. 259-- 280, 1978.

....access in this environment from the energy efficiency perspective. We consider a single communication channel shared by all uplink users and look at the basic form of random access that was proven to have the best stable throughput properties, namely the one based on conflict resolution [1] 2] [3], 4] We focus on random, rather than scheduled, access because at some level (perhaps at the reservation sub channel level) some form of random access will be unavoidable in any wireless network. Prepared through collaborative participation in the Communications and Networks Consortium ....

B. S. Tsybakov and V. A. Mikhailov, "Free Synchronous Packet Access in a Broadcast Channel with Feedback," Probl. Pered. Inform., vol.14, No. 4, pp. 32-59, 1978

....= maxf1; A(t) 1 1 e g otherwise A(t 1) A(t) 1 e 2 1 e . Tsitsiklis [108] proved that this protocol is stable for the arrival rate e 1 0:368. Another paradigm of full sensing algorithms was proposed independently by Capetanakis [17] Hayes [59] and Tsybakov and Mikhailov [112]. The algorithms they developed are usually called tree algorithms. They operate as follows. Let A be a positive integer interpreted as the arity of a tree. The algorithm run by a station is either in a waiting phase or a con ict resolution phase, switching between them accordingly. A con ict ....

....1, then stage A need not be performed, Randomized Communication in Radio Networks 23 it will certainly result in a collision, hence the stations might branch out immediately. Tree algorithms are stable for suciently small arrival rates, namely their variants were shown to be stable for 3=8 in [112] and for 0:430 in [17] Notice that tree algorithms are not FCFS. A modi cation of the tree algorithm paradigm, called splitting algorithm, was proposed independently by Gallager and by Tsybakov and Mikhailov (see [42] This algorithm is FCFS. The idea is to abandon the underlying tree ....

B.S. Tsybakov, and V.A. Mikhailov, Free synchronous packet access in a broadcast channel with feedback, Probl. Information Transmission 14 (1978) 259-280.

....manner the feedback information that is available to the nodes in order to control the retransmission process so that collisions are resolved more efficiently. The most basic collision resolution scheme is called the binary tree CRS (or binarytree scheme) and was proposed in [6] 24] and [51]. According to this scheme when a collision occurs, in slot k say, all nodes that are not involved in the collision wait until the collision is resolved. The nodes involved in the collision split randomly into two subsets, by (for instance) each flipping a coin. The nodes in the first subset, ....

.... and captures have been studied in [9] 10] 12] 42] 54] Collision resolution protocols yielding high throughputs for general arrival processes (even if their statistics are unknown) were developed in [11] 21] The expected packet delay of the binary tree protocol has been derived in [15] [51]. Bounds on the expected packet delay of the algorithm with the epoch mechanism have been obtained in [20] 52] ....

B.S. Tsybakov and V.A. Mikhailov, Free Synchronous Packet Access in a Broadcast Channel with Feedback, Probl. Inf. Trans., 14 (4), 259-280, October-December 1978.

....the area of multiple access communications was the development of random access protocols that resolve conflicts algorithmically. The invention of Conflict Resolution Algorithms (CRAs) is usually attributed to Capetanakis [Capet78, Capet79, Capet79b] and, independently, to Tsybakov and Mikhailov [Tsyba78]. The same idea, but in a slightly different context, was also presented, earlier, by Hayes [Hayes78] Later, it was recognized [Berge84, Wolf85] that the underlying idea had been known for a long time in the context of Group Testing [Dorfm43, Sobel59, Ungar60] Group Testing was developed during ....

....CRA protocol is separable if no packet given to the CRA by the CAA is ever returned undelivered for rescheduling. 1.2.1. The Standard Tree Algorithm The first CRA we present is usually referred to as the standard, or basic, or the Capetanakis, or the Capetanakis Tsybakov Mikhailov tree algorithm [Capet78, Tsyba78, Capet79, Capet79b]. It is not identical to the one initially proposed by Capetanakis, it seems, however, more natural than Capetanakis since it is based on a preorder traversal of the tree [Knuth68] Therefore, it has been adopted in most subsequent works. We refer to it as the Standard Tree Algorithm (STA) and ....

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B. S. Tsybakov and V. A. Mikhailov, "Free Synchronous Packet Access in a Broadcast Channel with Feedback," Problemy Peredachi Informatsii 14(4), pp. 32-59 (259-280) (Oct.-Dec. 1978).

....A(t) Gamma 1 1 e g otherwise A(t 1) A(t) 1 e Gamma2 1 e . Tsitsiklis [99] proved that this protocol is stable for the arrival rate e Gamma1 0:368. Another paradigm of full sensing algorithms was proposed independently by Capetanakis [16] Hayes [53] and Tsybakov and Mikhailov [103]. The algorithms they developed are usually called tree algorithms. They operate as follows. Let A be a positive integer interpreted as the arity of a tree. The algorithm run by a station is either in the waiting phase or the conflict resolution phase, switching between them accordingly. A ....

....1, then stage A need not be performed, it will certainly result in a collision, hence the stations might branch out immediately. Tree algorithms are stable for sufficiently small arrival rates, namely their variants were shown to be Randomized Communication in Radio Networks 25 stable for 3=8 in [103] and for 0:430 in [16] Notice that tree algorithms are not FCFS. A modification of the tree algorithm paradigm, called splitting algorithm, was proposed independently by Gallager and by Tsybakov and Mikhailov (see [37] This algorithm is FCFS. The idea is to abandon the underlying tree ....

B.S. Tsybakov, and V.A. Mikhailov, Free synchronous packet access in a broadcast channel with feedback, Probl. Information Transmission 14 (1978) 259--280.

....algorithm without the restriction (that of Vvedenskaya and Pinsker) does not beat this upper bound. The algorithm of Humblet and Mosely satis es the rst come rst served restriction. 4 Mosely and Humblet s protocol is a tree protocol in the sense of Capetanakis [3] and Tsybakov and Mikhailov [24]. For a simple analysis of the protocol, see [25] Vvedenskaya and Pinsker have shown how to modify Mosely and Humblet s protocol to achieve an improvement in the capacity (in the seventh decimal place) 26] 3 1.2 Improvements We choose = 0:42 in order to make the proof of Lemma 10 (see the ....

B.S. Tsybakov and V. A. Mikhailov, Free synchronous packet access in a broadcast channel with feedback, Probl. Information Transmission, 14(4) (1978) 259-280. 17

....Once a subset is completely resolved, waiting subsets are resolved in a first in last out order. Algorithms of this type can be viewed as a tree search. Each split moves the algorithm one level deeper in the tree. In Capetanakis original splitting algorithm a binary tree was used (i.e. B = 2) [1, 2, 6]. An example is shown in Figure 1 for the case where m = 4. Nodes in the tree are labeled according to their activities: W = Wait, C = Collision, S = Single Reply and Z = Zero Reply. The algorithm starts at the root node. Solid branches show the portion of the tree spawned by the splitting ....

B.S. Tsybakov and V.A. Mikhailov. Free synchronous packet access in a broadcast channel with feedback. Problemy Peredachi Inform., (USSR), 14(4):32--59, 1978.

....that, as a segment of the community pursued the development of practical protocols that depended on ALOHA to variable extents, information theorists relentlessly continued to pursue the basic collision channel model. The major thrust began when Capetanakis [67] and Tsybakov and Mikhailov [68] adopted a radically different approach to the problem of retransmission, that was also suggested by Hayes [69] in a somewhat different context. Capetanakis and Tsybakov and Mikhailov explored the simple idea that every collision should be resolved before additional transmissions could be ....

B.S. Tsybakov and V.A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback," Prb. Peredachi Infor. (USSR). vol. 14, no. 4, pp 32-59, 1978.

....epoch in which the last of its packets is resolved, must be finite with probability one. Because of the probabilistic (Poisson) model for the message arrivals, this is the best one can do. To this end, it suffices that the number of active users in subsequent epochs form a stable Markov chain [6]. The supremum of the set of intensities for which a certain protocol still gives raise to a stable Markov chain of active users is called its throughput. It is the relative fraction of time slots with successful transmission. A throughput of 1 means full channel utilization; the difference ....

....channels, also called random access channels, started with Abramson s ALOHA system [5] which is non slotted and uses only binary feedback (collision no collision) An unstable throughput of (2e) Gamma1 0:18394 was achieved. Later work for the slotted channel gave better throughputs (0. 375 [6], 0.429 [7] 0.48775 [11] The best upper bound to the capacity is currently 0.587 [12] but see also [9] Also the collision channel without feedback [13, 15] and the collision channel with bounded multiplicity feedback [10] were studied. The collision channel with multiplicity feedback was ....

B.S. Tsybakov & V.A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback", Problemy Peredachi Informatsii vol. 14 no. 4, pp. 32--59, 1978.

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B. S. Tsybakov and V. A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback," Problemy Peredachi Informatsii, vol. 14, no. 4, pp. 32--59, Oct.-Dec. 1978.

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B. S. Tsybakov and V. A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback," Problemy Peredachi Informatsii, vol. 14, no. 4, pp. 32--59, Oct.-Dec. 1978.

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B. S. Tsybakov and V. A. Mikhailov, "Free Synchronous Packet Access in a Broadcast Channel with Feedback," Problemy Peredachi Informatsii 14(4), pp. 32-59 (259-280) (Oct.-Dec. 1978).

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B. S. Tsybakov and V. A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback," Probl. Pered. Inform., vol. 14, no. 4, pp. 32--59, 1978.

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B. S. Tsybakov and V. A. Mikhailov, "Free Synchronous Packet Access in a Broadcast Channel with Feedback," Prob. Information Transmission, vol. 14, no. 4, pp. 256-280, October-December 1978.

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B.S. Tsybakov and V.A. Mikhailov. Free synchronous packet access in a broadcast channel with feedback. Probl. Inform. Trans. 14 (1978), 259--280.

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B. S. Tsybakov and V. A. Mikhailov, Free Synchronous Packet Access in a Broadcast Channel with Feedback. Problemy Peredachi Informatsii, vol. 14, pp. 32--59, 1978.

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B. S. Tsybakov and V. A. Mikhailov, Free Synchronous Packet Access in a Broadcast Channel with Feedback. Problemy Peredachi Informatsii, vol. 14, pp. 32--59, 1978.

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B.S. Tsybakov and V.A. Mikhailov, Free synchronous packet access in a broadcast channel with feedback, Probl. Information Transmission, 14, 1978, 259-280.

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B. S. Tsybakov and V. A. Mikhailov, "Free synchronous packet access in a broadcast channel with feedback," Probl. Pered. Inform., vol. 14, no. 4, pp. 32--59, Oct.--Dec.

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B.S. Tsybakov and V.A. Mikhailov, "Free Synchronous Packet Access in a Broadcast Channel with Feedback," Prob. Inform. Trans., Vol. 14, pp. 259--280, Oct.-Dec. 1978.

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Tsybakov, B. and Mikhailov, W. (1978), Free Synchronous Packet Access in a Broadcast Channel with Feedback, Probl. Peredachii Infor., 14, 259-280.

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