M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu, "Universal stability results and performance bounds for greedy contention-resolution protocols," Journal of the ACM , vol. 48, no. 1, pp. 39--69, Jan. 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the number of packets which need to cross a channel meets or exceeds a channel s bandwidth, this For convenience, any set used in the scalar sense refers to the size of that set. channel is saturated. This is obviously an upper bound on the performance of any practical network. As discussed in [2], this upper bound is achievable with output queuing in each node router, large queues, a simple scheduling protocol, and a burstiness constraint on the incoming traffic process. Practical systems can typically reach 60 75 of this bound [13] Since the channels in interconnection networks are ....

M. Andrews, B. Awerbuch, A. Fern andez, T. Leighton, Z. Liu, and J. Kleinberg. Universal-stability results and performance bounds for greedy contention-resolution protocols. Journal of the ACM, 48(1):39--69, January 2001.

....need to cross that channel per cycle is less than the bandwidth of the channel. If the number of packets that need to cross a channel meets or exceeds a channel s bandwidth, this channel is saturated. This is obviously an upper bound on the performance of any practical network. As discussed in [5], this upper bound is achievable with output queuing in each node router, large queues, a simple scheduling protocol, and a burstiness constraint on the incoming traffic process. Practical systems can typically reach 60 75 of this bound [6] 2.2 Oblivious Routing as a Flow Problem Oblivious ....

M. Andrews, B. Awerbuch, A. Fern andez, T. Leighton, Z. Liu, and J. Kleinberg, "Universal-stability results and performance bounds for greedy contention-resolution protocols," Journal of the ACM, vol. 48, no. 1, pp. 39--69, January 2001.

....on line scheduling by Adler et al. 2, 1] From the dynamic routing viewpoint, it is worth mentioning the model of adversarial queuing theory [6] where the goal is to keep the bu er size bounded under high packet arrival rate. Many results were recently obtained for this model: see, for example, [4, 3]. It seems that adversarial queuing theory is closely related to the average number of delays, since they both count the number of bu er occupancy slots. Many average case results are known under the assumption that the behavior of the packets is governed by a probability distribution, which is a ....

M. Andrews, B. Awerbuch, A. Fernandez, F. T. Leighton, Z. Liu, and J. M. Kleinberg. Universal-stability results and performance bounds for greedy contention-resolution protocols. J. ACM, 48(1):39-69, 2001.

....arrived by time t and are eventually destined to cross edge e. One then argues by induction on l and by cases, according to whether or not A t Gammaw (e) c Delta w P k i=1 (f i ) ffl For the unidirectional cycle, we modify the definition of the f function in the proof of Theorem 3. 7 of [3]. For our case, we need f(j; T 0 ) Q c(b 1) j Gamma i 0 ) 7 There are some minor differences in notation and in the definitions of a rate 1 Gamma ffl adversary as they appear in [7] and [3] The former paper incorporates the initial queues Q 0 (e) and the latter paper dispenses with the ....

....the unidirectional cycle, we modify the definition of the f function in the proof of Theorem 3. 7 of [3] For our case, we need f(j; T 0 ) Q c(b 1) j Gamma i 0 ) 7 There are some minor differences in notation and in the definitions of a rate 1 Gamma ffl adversary as they appear in [7] and [3]. The former paper incorporates the initial queues Q 0 (e) and the latter paper dispenses with the notion of a window in favor of an additive constant. For simplicity we will just indicate how to modify the proofs as they appear in these papers. f(j; t) Q Gamma c Delta ffl(t Gamma T 0 ) c ....

M. Andrews, B. Awerbuch, A. Fern' andez, J. Kleinberg, F.T. Leighton, Z. Liu. Universal Stability Results and Performance Bounds for Greedy Contention-Resolution Protocols. Journal version of [2]; to appear in JACM.

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M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu, "Universal stability results and performance bounds for greedy contention-resolution protocols," Journal of the ACM , vol. 48, no. 1, pp. 39--69, Jan. 2001.

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M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu, "Universal stability results and performance bounds for greedy contention-resolution protocols," Journal of the ACM , vol. 48, no. 1, pp. 39--69, Jan. 2001.

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M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu, "Universal stability results and performance bounds for greedy contention-resolution protocols," Journal of the ACM, vol. 48, no. 1, pp. 39--69, Jan. 2001.

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M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu. Universal stability results and performance bounds for greedy contention-resolution protocols. Journal of the ACM, 48(1):39--69, Jan. 2001.

No context found.

M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu, "Universal stability results and performance bounds for greedy contention-resolution protocols," Journal of the ACM, vol. 48, no. 1, pp. 39--69, Jan. 2001.

No context found.

M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu, "Universal stability results and performance bounds for greedy contention-resolution protocols," Journal of the ACM, vol. 48, no. 1, pp. 39--69, Jan. 2001.

No context found.

M.Andrews,B.Awerbuch,A.Fern andez, J. Kleinberg, T. Leighton, and Z. Liu, "Universal stability results and performance bounds for greedy contention-resolution protocols," Journal of the ACM, vol. 48, no. 1, pp. 39--69, Jan. 2001.

....whether or not user i is served at time t and satisfies the following conditions. x i (t) 1 8t; a i (t) 1 Gamma ) r i (t)x i (t) 8i; 8[T ; T w) We observe that if r i (t) 1 for all i; t then we have the standard admissibility condition for the Adversarial Queueing Model [8, 3], i.e. the total amount of data that arrives for the server in a window of size w is at most (1 Gamma )w. Note that at the end of each window [T ; T w) a (computationally unbounded) online algorithm could examine the data that arrived during the window and could deduce the adversary s ....

M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu. Universal stability results and performance bounds for greedy contention-resolution protocols. Journal of the ACM, 48(1):39--69, Jan. 2001.

....scheduling problem typically assumes that the paths of the packets are given as part of the input. The goal is then to schedule the packets along their paths in such a way that they all reach their destinations in a short time. Much recent work has focused on the Adversarial Queueing Model, e.g. [7, 2, 8]. We follow their convention and assume that all packets are unit size and each link processes one packet per time step. In this Adversarial Queueing Model, the adversary chooses the injection time, source, destination, and route for each packet injected. A sequence of injections is called (w; ....

....(w; r) admissible. Previous work has examined the performance of a number of simple scheduling protocols in this model. A packet scheduling protocol is said to be universally stable if it guarantees bounded buffer sizes and packet transmission delays for any (w; r) admissible injections. In [2] it was proved that several natural protocols (Longest In System, Shortest In System, Furthest To Go) are universally stable, whereas several others (First InFirst Out, Last In First Out, Nearest To Go) are not. In this paper we study both routing and scheduling. The adversary no longer ....

[Article contains additional citation context not shown here]

M. Andrews, B. Awerbuch, A. Fern' andez, J. Kleinberg, T. Leighton, and Z. Liu, Universal stability results and performance bounds for greedy contentionresolution protocols, Journal of the ACM, 48 (2001), pp. 39--69. -- 20 --

....scheduling problem typically assumes that the paths of the packets are given as part of the input. The goal is then to schedule the packets along their paths in such a way that they all reach their destinations in a short time. Much recent work has focused on the Adversarial Queueing Model, e.g. [7, 2, 8]. We follow their convention and assume that all packets are unit size and each link processes one packet per time step. In this Adversarial Queueing Model, the adversary chooses the injection time, source, destination, and route for each packet injected. A sequence of injections is called (w; ....

....called (w; r) admissible. Previous work has examined the performance of a number of simple scheduling protocols in this model. A packet scheduling protocol is said to be universally stable if it guarantees bounded buffer sizes and packet transmission delays for any (w; r) admissible injections. In [2] it was proved that several natural protocols (Longest In System, Shortest In System, Furthest ToGo) are universally stable, whereas several others (First InFirst Out, Last In First Out, Nearest To Go) are not. In this paper we study both routing and scheduling. The adversary no longer specifies ....

[Article contains additional citation context not shown here]

M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu. Universal stability results and performance bounds for greedy contention-resolution protocols. Journal of the ACM, 48(1):39--69, Jan. 2001.

....if output j decides to transmit E packets from input i then input i makes sure that the E packets with the highest urgency are at the front of the queue. Such an assumption is reasonable since the enqueue operation is local to the input and does not involve communication among different ports. In [2] it was shown that the Longest in System (LIS) Farthest to Go (FTG) and Shortest inSystem (SIS) protocols are stable for the case in which E = 1. In this paper we first show that 2 Such a switch is called an output queued switch since we can think of the packets as being logically queued at the ....

....by Kar, Lakshman, Stiliadis and Tassiulas [8] They showed how some traditional scheduling algorithms can be adapted to work with large envelopes. A large body of literature studies the case in which E = 1. For example, 3 [5, 10, 9, 1] present scheduling algorithms for input queued switches and [4, 2] analyze stability in networks of output queued switches. 2 Output queued Switches with Envelopes Achieving stability for a single output queued switch with large envelopes is easy. For example, if each output schedules an envelope from the queue with the most number of packets then the switch ....

[Article contains additional citation context not shown here]

Matthew Andrews, Baruch Awerbuch, Antonio Fern'andez, Jon Kleinberg, Tom Leighton, and Zhiyong Liu. Universal stability results and performance bounds for greedy contentionresolution protocols. Journal of the ACM, 48(1):39--69, January 2001.

....scheduling problem typically assumes that the paths of the packets are given as part of the input. The goal is then to schedule the packets along their paths in such a way that they all reach their destinations in a short time. Much recent work has focused on the Adversarial Queueing Model, e.g. [7, 2, 8]. We follow their convention and assume that all packets are unit size and each link processes one packet per time step. In this Adversarial Queueing Model, the adversary chooses the injection time, source, destination, and route for each packet injected. A sequence of injections is called (w; ....

....called (w; r) admissible. Previous work has examined the performance of a number of simple scheduling protocols in this model. A packet scheduling protocol is said to be universally stable if it guarantees bounded buffer sizes and packet transmission delays for any (w; r) admissible injections. In [2] it was proved that several natural protocols (Longest In System, Shortest In System, Furthest ToGo) are universally stable, whereas several others (First InFirst Out, Last In First Out, Nearest To Go) are not. In this paper we study both routing and scheduling. The adversary no longer specifies ....

[Article contains additional citation context not shown here]

M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu. Universal stability results and performancebounds for greedy contention-resolution protocols. Journal of the ACM, 48(1):39--69, Jan. 2001.

No context found.

Andrews, M., Awerbuch, B., Fernandez, A., Leighton, T., and Liu, Z., Universal-Stability Results and Performance Bounds for Greedy Contention-Resolution Protocols, Journal of the ACM, Vol. 48, No 1, January 2001, pp. 39-69 11

No context found.

Andrews, M., Awerbuch, B., Fernandez, A., Leighton, T., and Liu, Z., UniversalStability Results and Performance Bounds for Greedy Contention-Resolution Protocols, Journal of the ACM, Vol. 48, No 1, January 2001, pp. 39-69

No context found.

Andrews, M., Awerbuch, B., Fernandez, A., Leighton, T., and Liu, Z., UniversalStability Results and Performance Bounds for Greedy Contention-Resolution Protocols, Journal of the ACM, Vol. 48, No 1, January 2001, pp. 39-69

No context found.

M. Andrews, B. Awerbuch, A. Fern' andez, J. Kleinberg, F.T. Leighton, Z. Liu. Universal Stability Results and Performance Bounds for Greedy Contention-Resolution Protocols. Journal version of [2]; to appear in JACM.

No context found.

M. Andrews, B. Awerbuch, A. Fern andez, T. Leighton, Z. Liu, and J. Kleinberg, "Universal-stability results and performance bounds for greedy contention-resolution protocols," Journal of the ACM, vol. 48, no. 1, pp. 39--69, January 2001.

No context found.

M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu, "Universal-stability results and performance bounds for greedy contention-resolution protocols," J. Assoc. Comput. Mach., pp. 39--69, Jan. 2001.

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