BORODIN, A., KLEINBERG, J., RAGHAVAN, P., SUDAN, M., AND WILLIAMSON, D. P. 2001. Adversarial queueing theory. J. ACM 48, 1 (Jan.), 13--38.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....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 ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. Journal of the ACM, 48(1):13--38, Jan. 2001.

....for sensor networks, c should be as small as possible. In the following, B will always mean the buffer size of an optimal routing algorithm. 1. 2 Previous results The study of adversarial models in communication networks was initiated, in the context of queueing disciplines, by Borodin et al. [12]. Other work on adversarial queueing includes [6, 13, 14, 15, 23, 26] In these papers it is assumed that the adversary has to provide a path for every injected packet and reveals these paths to the system. The paths have to be selected in a way that they do not overload the system. Hence, it ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 376--385, 1996.

....overfull buffers may tremendously decrease the number of successfully delivered packets. However, we will show that the seemingly impossible task is possible, both for anycasting and multicasting. The study of adversarial models was initiated, in the context of switching alone, by Borodin et al. 16] Other work on switching includes [6, 22, 23, 24, 42, 45] In these papers it is assumed that the adversary has to provide a path for every injected packet and reveals these paths to the system. The paths have to be selected in a way that they do not overload the system. Hence, it only remains ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 376--385, 1996.

....interconnection network applications. The cost functions used in this work address this problem by optimizing performance over all traffic patterns. Another set of network problems closely related to throughputcentric routing algorithm design are those considered in adversarial queuing theory [25]. Notably, Andrews et al. 26] show an on line routing algorithm that finds feasible paths for packets through a network subject to capacity constraints if any feasible solution exists. Although similar to the worst case throughput problem considered in this paper, these results also incorporate ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson, "Adversarial queueing theory," Journal of the ACM, vol. 48, no. 1, pp. 13--38, Jan. 2001.

.... Queueing: What is the next packet to be transmitted on an edge In particular, which destination should be preferred Admission control: What is the packet to be dropped if a bu#er is full The study of adversarial models was initiated, in the context of queueing alone, by Borodin et al. [12]. Other work on queueing includes [6, 13 15, 17, 18] In these papers it is assumed that the adversary has to provide a path for every injected packet and reveals these paths to the system. The paths have to be selected so that they do not overload the system. Hence, it remains to find the right ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In STOC '96, pages 376--385, 1996.

.... FIFO queues [17] as well as networks of GPSqueues [13] where GPS rates are exactly matched to packet flow rates, are stable (according to Definitions 5 and 7) As an alternative to the two cited stochastic techniques, a new analytical framework, called Adversarial Queueing Theory (AQT) 14] [18], was developed. Applying AQT, several interesting results were obtained. Common service disciplines, such as FIFO, LIFO, and Nearest To Go (NTG) where priority is given to packets nearest to their destination) were proved not to be universally stable in all networks of queues. Instead, other ....

....(CRST) constraint. The CRST constraint implies that, for any pair of flows f i and f j whose paths are not disjoint, the ratios between GPS weights and packet actual rates are in the same order relation at every shared node. B. Adversarial Queueing Theory Adversarial queueing theory [14] [18] follows a deterministic approach to define stability criteria for queueing networks, in the sense that packet generation at the network inputs, packet service times, and packet routing, are supposed to be deterministic. In AQT, a queueing network is represented by a directed graph, where edges ....

A.Borodin, J.Kleimberg, P.Raghavan, M.Sudan, D.P.Williamson, "Adversarial Queueing Theory", Journal of the ACM, Vol. 48, n. 1, January 2001.

....some sort of ow control to make sure that the network does not become overloaded. Overloaded networks perform poorly) Typical ow control methods include: Nodes must negotiate network bandwidth before they are allowed to inject packets. Nodes must wait for a long deterministic adversarial [22, 6] or random [19, 16, 21, 25] duration between injections. Nodes must await acknowledgments of previous packets before injecting new packets. Current real world ow control mechanisms use the rst and third approach. An overview of the current state of the art can be found in the books of Gouda ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, pages 376-385, Philadelphia, Pennsylvania, 22-24 May 1996.

....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; ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson, Adversarial queueing theory, Journal of the ACM, 48 (2001), pp. 13--38.

....routing. In the static routing problem, all packets are present in the network initially. Since our main result employs many techniques from [10] we give a detailed summary of [10] in Section 4.1. A contrasting model, the connectionless adversarial queueing model, is also much studied, e.g. [4, 1]. Here the paths on which packets are injected can change over time giving the adversary more power. In the adversarial queueing model the best delay bound known is polynomial in the maximum path length [1] 1.5 Our Results We first provide a randomized, distributed scheduler that achieves a ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. Williamson. Adversarial queueing theory. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pages 376 -- 385, Philadelphia, PA, May 1996.

....routing. In the static routing problem, all packets are present in the network initially. Since our main result employs many techniques from [10] we give a detailed summary of [10] in Section 4.1. A contrasting model, the connectionless adver sar ial queueing model, is also much studied, e.g. [4, 1]. Here the paths on which packets are injected can change over time giving the ad versary more power. In the adversarial queueing model the best delay bound known is polynomial in the maximum path length [1] 1.5 Our Results We first provide a randomized, distributed scheduler that achieves a ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. Williamson. Adversarial queueing theory. In Proceedings of the 23th Annual A CM Symposium on Theory of Computing, pages 376 385, Philadelphia, PA, May 1996.

....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; ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. Journal of the ACM, 48(1):13--38, Jan. 2001.

....Alternatively, in the temporary session model sessions come and go over time. A temporary session only injects packets during its active period. The unused link bandwidth during its inactive period can be claimed by other sessions. This model is identical to the adversarial queueing model of [1, 4] in terms of the permitted injection patterns. However, these two papers have no notion of session rate. We choose to perform our analysis in terms of temporary sessions, thereby allowing us to study popular protocols that are rate based. Our aim is to discover how the performance of networks ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pages 376 -- 385, Philadelphia, PA, May 1996.

....environment If so, is there a distributed protocol that can guarantee end to end delays within a constant factor of the requirements We have concentrated on a connection oriented model, in which packets follow a fixed set of session routes. In a contrasting connectionless adversarial model [5, 1], no fixed rate is associated with any route and the adversary is given the power to choose the route upon each packet injection. In this model, it only makes sense to associate a delay requirement with each packet. Similar questions arise such as identifying and meeting schedulable sets of delay ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, Philadelphia, PA, May 1996.

....Partially supported by the IST Programme of the EU under contracts number IST1999 14186 (ALCOM FT) and IST 2001 33116 (FLAGS) and by the Spanish CICYT projects TIC 1999 0754 C03 (Mallba) and TIC 2000 1970 CE. The second author was also supported by pre doctoral grant 2001FI 00659 Borodin et al. [3], was developed as a robust model of queueing theory in network trac, and replaces stochastic by worst case inputs. Adversarial Queueing Theory considers the time evolution of a packet routing network as a game between an adversary and a protocol. The adversary, at each time step, may inject a set ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. Williamson. Adversarial queueing theory. Journal of the ACM, 48(1):13-38, January 2001.

....and IST 2001 33116 (FLAGS) and by the Spanish CICYT projects TIC 1999 0754 C03 (Mallba) and TIC 2000 1970 CE. The second author was also supported by pre doctoral grant 2001FI 00659 1 Introduction Adversarial Queueing Theory The model of Adversarial Queueing Theory proposed by Borodin et al. [3] considers the time evolution of a packet routing network as a game between an adversary and a protocol. At each time step the adversary may inject a set of packets to some of the nodes. For each packet the adversary speci es a sequence of edges that it must trasverse, after which the packet will ....

....edge. The reason for studying the behavior of packet communication networks, is to determine the conditions of stability, the fact that the number of packets in the system remains bounded, as the system dynamically evolves in time. Andrews et al. 2] solved several open questions posed in [3]. They also showed the existence of graphs and protocols that are not universally stable. Greedy protocols In this paper, as in Borodin et al. 3] we only consider greedy protocols, those that advance a packet across an edge e whenever there is at least one packet waiting to traverse e. Some ....

[Article contains additional citation context not shown here]

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. Williamson. Adversarial queueing theory. Journal of the ACM, 48(1):13-38, 2001.

....some sort of ow control to make sure that the network does not become overloaded. Overloaded networks perform poorly) Typical ow control methods include: # Nodes must negotiate network bandwidth before they are allowed to inject packets. # Nodes must wait for a long deterministic adversarial [22, 6] or random [19, 16, 21, 25] duration between injections. # Nodes must await acknowledgments of previous packets before injecting new packets. Current real world ow control mechanisms use the rst and third approach. An overview of the current state of the art can be found in the books of Gouda ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory.In ########### ## ### ############# ###### ### ######### ## ### ###### ## #########, pages 376-385, Philadelphia, Pennsylvania, 22-24 May 1996.

....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 ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. Journal of the ACM, 48(1):13--38, January 2001.

....packets into the system, and it has to reveal their paths to the system. There is no need to do either routing or admission (input stream) control. Thus, it only remains to find the right switching strategy to send the packets to their destinations. This model was introduced by Borodin et al. in [9] and has subsequently been studied in several papers [5, 12, 13, 14, 17, 18] All previous results mentioned above (except for a result by Gamarnik for the special case that the adversary reveals the paths to the system [13] only manage to accomplish their task if the injection process is ....

....can handle. Even more, our upper bounds on the number of packets and flows (see Theorem 3.2) that are in the system at any time essentially match the lower bound given by Theorem 1.2 . Our algorithms are also bounded in the setting of (w; bounded adversaries introduced by Borodin et al. in [9]. For any w and 0, we call an adversary a discrete (w; bounded adversary if it selects paths for the injected packets so that for all edges e and all time intervals I of length w, e is contained in no more than w paths of packets injected during I . Analogously, we call an adversary a ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 376--385, 1996.

....the online algorithm does not know the distribution itself, it is given the information that this distribution belongs to a specific class of distributions. Other approaches to go beyond pure competitive analysis include the access graph model for paging [16, 17, 32] and the statistical adversary [18]. We refer to [24, Chapter 17] for a comprehensive survey. All of the extensions and alternatives to competitive analysis have been proven to be useful for some specific problem and powerful enough to obtain meaningful results. However, none of these approaches has yet succeeded in replacing ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson, Adversarial queueing theory, Proceedings of the 23rd Annual ACM Symposium on the Theory of Computing, 1996, pp. 376--385.

....is that of stability, i.e. the question of whether there is a bound on the total size of packets in the network at all times. The stability problem has been investigated under various models of packet routing, see for example [5, 6, 4, 7, 1] The adversarial queueing model of Borodin et al. [3], was developed as a robust model of queueing theory in network trac, and replaces stochastic by worst case inputs. Adversarial Queueing Theory considers the time evolution of a packet routing network as a game between an adversary and a protocol. The adversary, at each time step, may inject a set ....

....that b = 1. The motivation for study the behavior of packet communication networks, is to determine the conditions of stability, the fact that the number of packets in the system remains bounded, as the system dynamically evolves in time. Andrews et al. 2] solved several open questions posed in [3]. They also showed the existence of graphs and protocols that are not universally stable. In particular, they showed that for the network in Figure 2, the protocol FIFO is non stable for values of r 0:85. Later, Goel [8] proved that FIFO is not stable for the network in Figure 1. This result is ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. Williamson. Adversarial queueing theory. Journal of the ACM, 48(1):13-38, January 2001.

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BORODIN, A., KLEINBERG, J., RAGHAVAN, P., SUDAN, M., AND WILLIAMSON, D. P. 2001. Adversarial queueing theory. J. ACM 48, 1 (Jan.), 13--38.

No context found.

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proc. 28th ACM STOC, 1996.

No context found.

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. Williamson. Adversarial Queueing Theory. Journal version of [6]; to appear in JACM.

No context found.

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. Williamson. Adversarial Queueing Theory. Proceedings of the Twenty--Eighth Annual ACM Symposium on Theory of Computing, 376-385, 1996.

....routing has also been a major topic of study within the field of queueing theory [19; 18] Typical assumptions here are that packets are generated according to a Poisson process, and that the time to traverse an edge is an exponentiallydistributed random variable, rather than a fixed constant. See [5] for a review of previous work on these models. In this paper, we work within a model of continuous packet arrivals proposed by Borodin et al. 5] in which probabilistic assumptions are replaced by worst case inputs. The underlying goal is to determine whether it is feasible to prove stability ....

....according to a Poisson process, and that the time to traverse an edge is an exponentiallydistributed random variable, rather than a fixed constant. See [5] for a review of previous work on these models. In this paper, we work within a model of continuous packet arrivals proposed by Borodin et al. [5], in which probabilistic assumptions are replaced by worst case inputs. The underlying goal is to determine whether it is feasible to prove stability results even when packets are injected by an adversary, rather than an oblivious randomized process. The framework was termed adversarial queueing ....

[Article contains additional citation context not shown here]

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proc. 28th ACM STOC, 1996.

....such dynamic algorithms have been studied in a probabilistic framework, where one assumes an underlying randomized process that generates job arrivals and departures; see e.g. 9, 17] and the references therein. An Adversarial Model. Motivated by work in the related area of packet routing [5, 6, 7, 3], Muthukrishnan and Rajaraman proposed an adversarial framework for studying dynamic load balancing in the token based model we have been discussing [18] Rather than considering a probabilistic process that generates tokens, they posit an adversary that is allowed at the beginning of each round ....

....adversary if there is a constant B such that h t (v) a t # B for all nodes v and rounds t. Note that stability in this context imposes a bound on deviation from the average; it is not required that the actual number of tokens in the system remains bounded. As in the case of packet routing [7, 3], one needs to find a suitable restriction on the adversary: an arbitrarily powerful adversary could flood a particular set of nodes S # V with tokens much faster than these nodes can spread the tokens out to the rest of the graph, and thereby prevent any algorithm from maintaining stability. ....

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, D. Williamson, "Adversarial Queueing Theory," Proc. 28th ACM Symp. on Theory of Computing, 1996.

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Borodin, A., Kleinberg, J., Raghavan, P., Sudan, M., and Williamson, D. P. Adversarial queueing theory, Journal of the ACM, Vol. 48, No 1, January 2001, pp. 13-38

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Borodin, A., Kleinberg, J., Raghavan, P., Sudan, M., and Williamson, D. P. Adversarial queueing theory, Journal of the ACM, Vol. 48, No 1, January 2001, pp. 13-38

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pages 376 -- 385, Philadelphia, PA, May 1996.

No context found.

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson, "Adversarial queueing theory," Journal of the ACM, vol. 48, no. 1, pp. 13--38, Jan. 2001.

No context found.

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. Journal of the ACM, 48(1):13--38, Jan. 2001.

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. Journal of the ACM, 48(1):13--38, January 2001.

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Borodin, A., Kleinberg, J., Raghavan, P., Sudan, M., and Williamson, D. P. Adversarial queueing theory, Journal of the ACM, Vol. 48, No 1, January 2001, pp. 13-38

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D.P. Williamson. Adversarial queueing theory. In Proc. STOC '96.

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan and D. Williamson. Adversarial queueing theory. Journal of the ACM, 48(1), pp. 13-38, 2001. Previously at STOC'96, pp. 376-385.

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proceedings of the 28th ACM Symposium on Theory of Computing (STOC), pages 376--385, 1996.

No context found.

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson, "Adversarial queueing theory," Journal of the ACM, vol. 48, no. 1, pp. 13--38, Jan. 2001.

No context found.

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 376--385, 1996.

No context found.

A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson, "Adversarial queueing theory," Journal of the ACM, vol. 48, no. 1, pp. 13--38, Jan. 2001.

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D.P. Williamson. Adversarial queueing theory. In these proceedings.

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. Williamson, "Adversarial queueing theory," J. Assoc. Comput. Mach. , vol. 48, no. 1, pp. 13--38, 2001.

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Allan Borodin, Jon Kleinberg, Prabhakar Raghavan, Madhu Sudan, and David P. Williamson, "Adversarial queueing theory," (Journal version) Submitted for publication.

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Allan Borodin, Jon Kleinberg, Prabhakar Raghavan, Madhu Sudan, and David P. Williamson, "Adversarial queueing theory," in Symposium on Computer Science, 1996.

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 376-385, 1996.

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Borodin, A., Kleinberg, J., Raghavan, P., Sudan, M., and Williamson, D.P. (1998). Adversarial queueing theory. In preparation.

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Borodin, A., Kleinberg, J., Raghavan, P., Sudan, M., and Williamson, D.P. (1996). Adversarial queueing theory. Proc. 28th Ann. ACM Sympos. on Theory of Computing, 376--385.

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. P. Williamson. Adversarial queueing theory. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 376--385, 1996.

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A.Borodin, J.Kleimberg, P.Raghavan, M.Sudan, D.P.Williamson, "Adversarial Queueing Theory", Journal of the ACM, Vol. 48, n. 1, January 2001.

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. Williamson. Adversarial queueing theory. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pages 376-385, May 1996.

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A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan, and D. Williamson. Adversarial queueing theory. In ACM Symposium on Theory of Computing, pages 376-385, 1996.

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