B. Tsybakov and V. Mikhailov, "Ergodicity of slotted Aloha system," Problemy Peredachi Informatsii, vol. 15, pp. 73--87, Oct.-Dec. 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... stability i.e. the rate pairs (in terms of packets slot) for which queues are stable for slotted ALOHA with the collision channel and with perfectly orthogonal channels (no interference) For orthogonal channels we have a unit square, whereas for the collision channel we have a complex form [1]. Our motivation was to look at the behavior of the stability region when the diversity we have lies in between these two extreme cases. We find that the stability region makes a smooth phase transition from concavity to convexity as we move from one extreme to another. In other words, as we allow ....

....transmissions in that slot. Thus, this model can capture the event of simultaneous packet successes although it is not sufficient to capture asymmetry among users since all users are treated equal by the model, which need not be true for a multiple antenna wireless system. Tsybakov and Mikhailov [1] initiated the study of the slotted ALOHA system in terms of the stability of queues at each of the terminals in the system. They found separate necessary and sufficient conditions for stability of the queues in the system using the principle of stochastic dominance. They also found the stability ....

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B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems, " Probl. Inform. Transmission, vol.15, no. 4, pp. 73-87, 1979.

....transmissions in that slot. Thus, this model can capture the event of simultaneous packet successes although it is not sufficient to capture asymmetry among users since all users are treated equal by the model, which need not be true for a multiple antenna wireless system. Tsybakov and Mikhailov [1] initiated the study of the slotted ALOHA system in terms of the stability of queues at each of the terminals in the system. By stability we mean that all queues are finite with probability one. In such a bu#ered system, stability is not easy to establish because of the stochastic interdependence ....

....= ## ] 9) If either Q1 or Q2 equals zero, then we assume 0 = our result still holds. Proof: We use Lemma 1. Since we know the stability region for a fixed retransmission probability vector p, we need to find the union of all the stability regions as the parameter p varies over [0, 1] . One way of doing this is to setup a corresponding constrained optimization problem i.e. for a fixed #1 , maximize #2 as p varies over [0, 1] where #1 and #2 are related by (4) and (5) This is the method which we used in our proof [9] PSfrag replacements 2 (q 1 Q2 1 q # 2 = ....

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B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems, " Probl. Inform. Transmission, vol. 15, no. 4, pp. 7387, 1979.

....transmit probability of each user is a function of the channel state in that particular slot. This function is called scheduler. We also assumed that the channel state varies independently and identically from slot to slot and from user to user. We then derived the maximum stable throughput (see [18]) of a finite user symmetric system as a function of the reception model and the scheduler employed. Optimal schedulers were obtained for some simple reception models [13] It turns out that obtaining optimal scheduler for complicated reception models is in general a hard problem. In this paper, ....

....slot . The packet arrival process for different for is assumed to be independent and identically distributed as well. The arrival process has a finite mean # and finite variance. The above model for the arrival process is the same as that in [18] for a symmetric system. The channel between the th user and the base station during slot is parametrized by . It is assumed that the quantities for ( are independent and identically distributed with probability distribution, 0 . ....

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B.S. Tsybakov and V.A. Mikhailov. Ergodicity of Slotted Aloha System. Problemy Peredachi Informatsii, 15(4):73--87, Oct-Dec 1979.

....transmissions in that slot. Thus, this model can capture the event of simultaneous packet successes although it is not sufficient to capture asymmetry among users since all users are treated equal by the model, which need not be true for a multiple antenna wireless system. Tsybakov and Mikhailov [1] initiated the study of the slotted ALOHA system in terms of the stability of queues at each of the terminals in the system. By stability we mean that all queues are finite with probability one. In such a buffered system, stability is not easy to establish because of the stochastic interdependance ....

....A f(A2, 10) If either Q or Q2 equals zero, then we assume = x: and our result still holds. 12) Proof: We use Lemma 1. Since we know the stability region for a fixed retransmission probability vector p, we need to find the union of all the stability regions as the parameter p varies over [0, 1] 2. One way of doing this is to setup a corresponding constrained optimization problem i.e. for a fixed A, maximize A2 as p varies over [0, 1] 2, where A and A2 are related by (7) and (8) This is the method which we used in our proof [22] q2( qiJ ) Q1)2 (1 (1) ql q2 q )Q2 Q2 ....

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B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems," Probl. Inform. Transmission, vol.15, no. 4, pp. 73-87, 1979.

....ALOHA protocol where the knowledge of channel state is utilized to vary the transmission probability is used as the random access protocol. The function that maps the channel state information to the probability of transmission is termed the transmission control scheme. Maximum stable throughput [22] is used as a figure of merit to compare different trans mission control schemes. We assume a network with finite number of users and infinite buffers and derive the expression of maximum stable throughput of the network as a function of the reception model, CSI distribution and the transmission ....

....packet arrival process for different X ) for m = 1, n and t 1N is assumed to be independent and identically distributed as well. The arrival process has a finite mean (so that the cumulative input rate is ) and finite variance. The above model for the arrival process is the same as that in [22] for a symmetric system. The channel between the mth user and the base station during slot t is parametrized by ff) It is assumed that the quantities ff) for m = 1, and t IN are independent and identically distributed with probability distribution F(ff) Further, we assume that the user m has ....

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B. Tsybakov and V. Mikhailov, "Ergodicity of Slotted Aloha System," Problemy Peredachi Informatsii, vol. 15, pp. 73-87, Oct-Dec 1979.

....ALOHA protocol where the knowledge of channel state is utilized to vary the transmission probability is used as the random access protocol. The function that maps the channel state information to the probability of transmission is termed the transmission control scheme. Maximum stable throughput [22] is used as a figure of merit to compare different transmission control schemes. We assume a network with finite number of users and infinite buffers and derive the expression of maximum stable throughput of the network as a function of the reception model, CSI distribution and the transmission ....

....arrival process for different X(m t) for m 1, n and t lt is assumed to be independent and identically distributed as well. The arrival process has a finite mean (so that the cumulative input rate is A) and finite variance. The above model for the arrival process is the same as that in [22] for a symmetric system. The channel between the mth user and the base station during slot t is parametrized by ) It is 7 assumed that the quantities ) for m 1, n and t lt are independent and identically distributed with probability distribution F( Further, we assume that the user ....

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B. Tsybakov and V. Mikhailov, "Ergodicity of Slotted Aloha System," Problemy Peredachi Informatsii, vol. 15, pp. 73- 87, Oct-Dec 1979.

....and there are potential benefits of adaptive connectivity depending on the topology and channel usage. 1. 3 Related Work In the literature, the wireless network stability problems have been studied extensively both for networks with centralized scheduling [5] 12] and the ALOHA protocol [13] [18]. Our problem formulation is closest to the model used by Tassiulas and Ephremides in [5] where they studied the network stability with a specific probabilistic model and characterized the network stability region. They also gave an elegant throughput optimal policy that stabilizes the network at ....

.... (5) is called substability by Loynes [44] and tightness by Billingsley [45] In the wireless networking context, as a network stability criterion, substability is first used by Tsybakov and Bakirov [13] Depending on the network model, other stability notions are also used in the literature [14] [18], 5] 12] In network stability considerations we classify the packets according to their destinations, that is, Arrival rate # = # ij : i, j ) is called stabilizable if there exists a policy that makes the network stable. The stability region of a network is the closure of the set ....

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B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems," Probl. Inform. Transmission, vol. 15, no. 4, p. 301312, Oct.Dec. 1979.

....random variables. The packet arrival process for different X ) for m 1, M is assumed to be independent and identically distributed as well. It is assumed that the arrival process has a finite mean A and finite variance er 2. The above model for the arrival process is the same as that in [1] for a symmetric system. The uplink channel between the m tn user and the base station during slot t is parametrized by the SNR 7 ) It is assumed that the quantities 7 ) for m 1, M and t 0, 1, are independent and identically distributed with probability density f(7) Further, we ....

....in a network employing time division duplex access or in a network where in the base station continuously transmits a pilot signal in a control channel. We define a very general reception model that is given by a set of M functions g( for k 1, M where, g( 0, cx) x 0,1 [0,1]. 1) Let 0 be a binary k tuple that describes the outcome of a slot. Let .A(0) be the set of indexes at which 0 is equal to one. That is, if 0 = bz, b) we have ,A(0) 1 n k: bn = 1 . 2) Given that 1 k M users are transmitting, and that their ordered k tuple of SNRs given by ....

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B.S.Tsybakov and V.A.Mikhailov. "Ergodicity of a Slotted ALOHA System". Problemy Peredachi Informatsii, 15(4):73-87, October 1979.

....be interesting if it turns out that these ideas have wider applicability in models of en gincaring interest. SETUP We consider tile discrete time slotted ALOHA protocol operating witIx M buffered terminals over the collision channel. Thus, transmission attempts are made at discrete times CH2642 7 89 0000 057951.00 1989 IEEE 579 at each time n each terlninal i attempts transmission with probability p, if there is a packet in buffer at time n. If two or more packets attempt transmission at the same time, all attempting terminals are unsuccessful. Transmission attempts by a terminal ....

B. S. Tsybakov and V. A. Mikhailov, "Ergodicity of Slot- ted ALOHA System", Problems of Information Transmis- sion, Vol. 15, pp. 73-87, Mar. 1979.

....are diversi ed among the stations, then we need the probability of performing a broadcast in Aloha also diversi ed, that is, station i performs a broadcast in a step with some probability f i , provided its queue is nonempty, independently of the other steps and stations. Tsybakov and Mikhailov [111] considered arbitrary arrival processes, not necessary Bernoulli, and showed that Aloha was stable for certain con gurations of parameters. For more on the topic see [97, 105, 106] These results are in contrast with the situation for the in nitely many users model where Aloha is not even weakly ....

....certain arrival rates. Consider the Markov chain M o which has the sequences of sizes of the bu ers hq 1 ; q n i as its states. This chain is not state homogeneous, in the sense that the probability of moving from state a to b by vector c = b a does not depend only on c. The approach in [111] was by way of considering another state homogeneous Markov chain, which was suggested by the observation that Aloha has its worst time when all the bu ers are nonempty. First let us present intuitions of this approach, inspired by [111] For the simplicity of calculations, let us consider the ....

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B.S. Tsybakov, and V.A. Mikhailov, Ergodicity of a slotted Aloha system, Probl. Information Transmission 16 (1980) 301-312.

....among the stations, we need the probability of performing a broadcast in Aloha also diversified among the stations, that is, station i performs a broadcast at a step with some probability f i , provided its queue is nonempty, independently of the other steps and stations. Tsybakov and Mikhailov [102] considered arbitrary arrival processes, not necessary Bernoulli, and showed that Aloha was stable for certain configurations of parameters. For more on the topic see [89, 96, 97] These results are in contrast with the situation for the infinitely many users model where Aloha is not even weakly ....

....arrival rates. The associated Markov chain M o has the sequences of sizes of the buffers hq 1 ; q n i as its states. This chain is not state homogeneous, in the sense that the probability of moving from state a to b by vector c = b Gamma a does not depend only on c. The approach in [102] was by way of considering another state homogeneous Markov chain, which was suggested by the observation that Aloha has its worst time when all the buffers are nonempty. First let us present intuitions of this approach, inspired by [102] For the simplicity of calculations, let us consider the ....

[Article contains additional citation context not shown here]

B.S. Tsybakov, and V.A. Mikhailov, Ergodicity of a slotted Aloha system, Probl. Information Transmission 16 (1980) 301--312.

.... C o A is the set of all 2 R N such that for some p (depending on ) i p i Q j:j 6=i (1 Gamma p j ) Equivalently, C o A is CA with all points on the upper boundary deleted, and for the case of N = 2 users: C o A = f( 1 ; 2 ) p 1 p 2 1g: 12) Tsybakov and Mikhailov [84] first published this result, and moreover they showed for the case N = 2 that the region C o A is the complete stability region for the ALOHA network, rather than a proper subset of it. Specifically, with N = 2 and independent, identically distributed arrivals at each of the two users with ....

B.S. Tsybakov and V.A. Mikhailov, "Ergodicity of a slotted ALOHA system," Problemy Peredachi Informatsii, vol. 15, no. 4, pp. 73-87, October-December 1979. English translation in Problems in Information Transmission, pp. 301-312, vol. 15, no. 4, pp. 301-312, October-December 1979.

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B. Tsybakov and V. Mikhailov, "Ergodicity of slotted Aloha system," Problemy Peredachi Informatsii, vol. 15, pp. 73--87, Oct.-Dec. 1979.

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B. Tsybakov and V. Mikhailov, "Ergodicity of slotted Aloha system," Problemy Peredachi Informatsii, vol. 15, pp. 73--87, Oct-Dec 1979.

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B. S. Tsybakov and V. A. Mikhailov, "Ergodicity of a slotted ALOHA system," Probl. Pered. Inform., vol. 15, no. 4, pp. 73--87, Oct./Dec. 1979.

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B. S. Tsybakov and V. A. Mikhailov. Ergodicity of a Slotted ALOHA System. Problemy Peredachi Informatsii, 15(4):301--312, 1979.

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B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems," Probl. Inform. Transmission, vol. 15, no. 4, p. 301312, Oct.Dec. 1979.

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B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems," Probl. Inform. Transmission, vol. 15, p. 301312, Oct.Dec. 1979.

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B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems," Probl. Inform. Transmission, vol. 15, no. 4, pp. 73--87, 1979.

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B. S. Tsybakov and V. A. Mikhailov, "Ergodicity of a Slotted ALOHA System," Problemy Peredachi Informatsii, vol. 15, no. 4, pp. 301--312, 1979.

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B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems," Probl. Inform. Transmission, vol. 15, p. 301?12, Oct.Dec. 1979.

No context found.

B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems," Probl. Inform. Transmission, vol. 15, p. 301?12, Oct.Dec. 1979.

No context found.

B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems," Probl. Inform. Transmission, vol. 15, no. 4, pp. 301--312, Oct.-Dec. 1979.

No context found.

B. S. Tsybakov and V. A. Mikhailov. Ergodicity of a Slotted ALOHA System. Problemy Peredachi Informatsii, 15(4):301--312, 1979.

No context found.

B. Tsybakov and W. Mikhailov, "Ergodicity of slotted ALOHA systems," Probl. Inform. Transmission, vol. 15, p. 301?12, Oct.Dec. 1979.

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Tsybakov, B. and Mikhailov, W. (1979), Ergodicity of slotted ALOHA system, Probl. Peredachii Infor., 15, 73--87.

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