STAMOULIS,G.D.,AND TSITSIKLIS, J. N. 1994. The efficiency of greedy routing in hypercubes and butterflies. IEEE Trans. Commun. 42, 11 (Nov.), 3051--3061.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....messaging protocol described in Chapter 5 implemented using both circuit switching and wormhole routing on three different network topologies. The literature contains a myriad of analytical models for dynamic network behaviour. Models have been proposed for specific network topologies ( Dally90] [Stamoulis91], Saleh96] Greenberg97] routing algorithms ( Draper94] Sceideler96] Ould98] and traffic patterns [Sarbazi00] While the vast majority of this work has focused on non discarding networks, discarding networks have also been considered ( Parviz79] Rehrmann96] Datta97] However, in ....

George D. Stamoulis, John N. Tsitsiklis, "The Efficiency of Greedy Routing in Hypercubes and Butterflies", Proc. SPAA '91, pp. 248-259.

....Many real world packet routing network algorithms in which packets are routed to random destinations can be modeled by Markovian Jackson Queueing Networks (M.J.Q.N. except for the fact that the real world networks require the service times at the servers to all be equal and constant [HBB94] [ST91]. In this paper we show that the average delay for a M.J.Q.N. with constant service times is upper bounded by the average delay for the corresponding traditional M.J.Q.N. with exponential service times) ST91] proved this result for layered networks. Our proof exactly parallels the [ST91] proof, ....

....networks require the service times at the servers to all be equal and constant [HBB94] ST91] In this paper we show that the average delay for a M.J.Q.N. with constant service times is upper bounded by the average delay for the corresponding traditional M.J.Q.N. with exponential service times) [ST91] proved this result for layered networks. Our proof exactly parallels the [ST91] proof, except that whereas their proof used induction on the layers of the network, we induct on time, thereby obviating the need for a layered network. 2 Proof Theorem 1 The average delay for a M.J.Q.N. where all ....

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George D. Stamoulis and John N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. Journal of the ACM, 1991.

....service time distribution for each of the following single queue networks: the M G 1 queue, the M G 1 queue with batch arrivals, the M G 1 queue with priorities, and the M G k queue [Whi83] Whi80] Ros89, pp. 353 356] With respect to networks of queues, HBW94] generalized an earlier result of [ST91] to show that for all Markovian networks N , N E,FCFS has greater average packet delay than N C,FCFS . There are also empirical studies of several non Markovian networks N (i.e. general classed networks) which show that the average packet delay measured is greater for N E,FCFS than for N C,FCFS ....

George D. Stamoulis and John N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. Journal of the ACM, 1991.

....server i moves next to server j with probability p ij . In the special case of Markovian routing, the queueing network N has only one class of packets. 3 But not all. 18 queueing network with Markovian routing fully describes the packet routing network. For a more detailed explanation see [72] and [56] The above result tells us that we can easily compute an upper bound on the average delay for any packet routing network which can be modeled by a queueing network with Markovian routing. In Chapter 4 , we find that we are able to prove much more general results for the case of light ....

....the ring was infinite, their Markov chain became tractable. Observe that the ring network with non Markovian routing where the destinations are random cannot be modeled by a Markovian queueing network. This is part of what makes the ring queueing network so intractable. Stamoulis and Tsitsiklis, [72], were the first to apply traditional queueing theory in delay analysis of problems from theoretical computer science, and their work has inspired our own. Their goal was to bound the average packet delay in the hypercube and butterfly 22 networks, where the packets are routed to random ....

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George D. Stamoulis and John N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. IEEE Transactions on Communications, 42(11):3051--3061, November 1994.

....aim to route some initially given set of packets along predetermined paths in a network as fast as possible. In practice however, networks are rarely used in this static fashion but packets are injected dynamically into the network. Since much less is known in the area of dynamic routing (see e.g. [5, 15, 17]) than in the area of static routing, it would be highly desirable to transfer the results gathered for static routing to dynamic routing. So far, however, not much is known about how to transform static routing protocols into stable dynamic protocols, or how efficient dynamic variants of ....

G.D. Stamoulis and J.N. Tsitsiklis. The Efficiency of Greedy Routing in Hypercubes and Butterflies. In Proc. of the 3rd Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 248-259, 1991.

....nature of these packet delay results seems beyond what we can hope to derive from applying general queuing theory results. On the other hand, the Leighton and Kahale Leighton results are specific to certain networks and utilize the assumption of random destinations. Stamoulis and Tsitsiklis [49] consider the case of layered networks under the assumption of Bernoulli routing. In queuing networks with Bernoulli routing, jobs are indistinguishable (i.e. a single class network) and the next server taken is a Markov process (i.e. a probabilistic function of the last server and independent of ....

....service time distributions, Meyn and Down [37] establish stability for such networks. These results apply to the more general case that each server has its own service time distribution. However, Harchol Balter and Wolfe [7] give evidence that it will not be a simple task to apply the approach in [49] to the general study of dynamic packet routing. First they show that the layered assumption in [49] is not necessary as they are able to derive the same results for any Bernoulli routing network. But they also show that without the Bernoulli network assumption, it is no longer necessarily true ....

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G. D. Stamoulis and J. N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. Proceedings of the Third Annual ACM Symposium on Parallel Algorithms and Architectures, 1991.

....done on converting the case where D is constant to the case where D is exponential. One example is Erlang s Method of Stages , described in [9] 1] which involves decomposing a constantdistributed service time into a collection of exponentially distributed service times. Stamoulis and Tsitsklis [18] use this method to analyze the routing problem on the hypercube in the case where D is constant. Mitra and Cieslak [14] use Kuehn s Method to approximate a general distributed edge traversal time by an exponentially distributed edge traversal time in order to obtain bounds on queue sizes for the ....

George D. Stamoulis and John N. Tsitsiklis. The Efficiency of Greedy Routing in Hypercubes and Butterflies. Journal of the ACM, 1991.

....All generated packets are routed in parallel. Dynamic routing using shortest path routing has good performance on buffered meshes [14] The performance of dynamic shortest path routing on a buffered binary hypercube using randomly chosen shortest paths has been theoretically analyzed in [17]. Approximate models aim at giving intuitive support for simulation results. Abraham and Padmanabhan s interesting analysis for the buffered and unbuffered binary hypercube is based on the approximation that each packet moves independently of other packets [1] This model was later modified to ....

G.D. Stamoulis and T.N. Tsitsiklis, The efficiency of greedy routing in hypercubes and butterflies, IEEE Trans. Commun. 42 (11) (1994) 3051--3061.

....models where service times are exponentially distributed (as these results are often easier to obtain) and it is assumed that the behavior when service times are constant (with the same mean) is similar. In some cases there are even provable relationships between the two models (see, for example, [11, 16]) In this case, however, changing the distribution of the random variable X causes a dramatic change in behavior. 10 Board Z seconds behind, Z uniform on [0,2T] Update interval T Average Time 0 2 4 6 8 10 12 14 0 5 10 15 20 25 1 Choice 2 Choices 3 Choices Shortest l=0.9, 1.0 ....

G. D. Stamoulis and J. N. Tsitsiklis, "The Efficiency of Greedy Routing in Hypercubes and Butterflies", IEEE Transactions on Communications, Vol. 42(11), 1994, pp. 3051--3061.

.... process and are routed to random destinations [47, 34, 14, 13] Another question that has attracted interest is whether or not it is possible to use results from queueing theory concerning exponential edgetraversal times to derive results in networks where the edge traversal times are con16 stant [63, 29, 30, 49]. We consider a model that does not make any statistical assumptions, i.e. we assume that the packets are injected into the network by an adversary. By this we mean that both the times at which packets are injected and the routes that they must follow are chosen by an adversary. However we cannot ....

G. Stamoulis and J. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. IEEE Transactions on Communications, 42(11):3051--3061, November 1994.

....former approach. Usually, packet injection is viewed as a probabilistic model; for example, assuming Poisson arrivals at each node with destinations chosen uniformly and independently. In such cases the performance is measured in terms of the expected latency and queue size. See, for example, [BU, BFU, HB, HW, SV, STs]. The first attempt to develop a model of dynamic routing for analyzing the queue size and latency in the worst case was made by Cruz [C, C2] In his model, one assumes arbitrary virtual circuits are established each with a source of fixed rate (with bounded bursts allowed) subject to the ....

G. Stamoulis and J. Tsitsiklis, "The Efficiency of Greedy Routing in Hypercubes and Butterflies," IEEE Transactions on Communications, 42 (11), pp. 3051--208, 1994.

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STAMOULIS,G.D.,AND TSITSIKLIS, J. N. 1994. The efficiency of greedy routing in hypercubes and butterflies. IEEE Trans. Commun. 42, 11 (Nov.), 3051--3061.

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STAMOULIS,G.D.,AND TSITSIKLIS, J. N. 1991. The efficiency of greedy routing in hypercubes and butterflies. In Proceedings of the 3rd Annual ACM Symposium on Parallel Algorithms and Architectures (Hilton Head, S.C., July 21--24). ACM, New York, pp. 248 --260.

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George D. Stamoulis and John N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. Journal of the ACM, 1991.

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George D. Stamoulis and John N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. Journal of the ACM, 1991.

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G. D. Stamoulis and J. N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. IEEE Trans. on Communications, 42(11):3051--3061, Nov. 1994.

No context found.

G. Stamoulis and J. Tsitsiklis, "The Efficiency of Greedy Routing in Hypercubes and Butterflies," IEEE Transactions on Communications, 42 (11), pp. 3051--208, 1994.

No context found.

G. Stamoulis and J. Tsitsiklis, "The Efficiency of Greedy Routing in Hypercubes and Butterflies," IEEE Transactions on Communications, 42 (11), pp. 3051--208, 1994.

No context found.

G. Stamoulis and J. Tsitsiklis, "The Efficiency of Greedy Routing in Hypercubes and Butterflies," IEEE Transactions on Communications, 42 (11), pp. 3051--208, 1994.

No context found.

G. Stamoulis and J. Tsitsiklis, "The Efficiency of Greedy Routing in Hypercubes and Butterflies," IEEE Transactions on Communications, 42 (11), pp. 3051--208, 1994.

No context found.

G.D. Stamoulis and J.N. Tsitsiklis. The Efficiency of Greedy Routing in Hypercubes and Butterflies. In Proc. of the 3rd Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 248-259, 1991.

No context found.

Stamoulis, G.D. and J.N. Tsitsiklis, "The efficiency of greedy routing in hypercubes and butterflies," IEEE Trans. Communications, vol. 42, no. 11, Nov. 1994, pp. 3051-3061.

No context found.

G. D. Stamoulis and J. N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. In Proceedings of the 3rd Annual ACM Symposium on Parallel Algorithms and Architectures, pages 248--259, July 1991.

No context found.

G. D. Stamoulis and J. N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. IEEE Transactions on Communications, 42(11):3051--3061, November 1994.

No context found.

G. D. Stamoulis and J. N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. IEEE Trans. on Communications, 42(11):3051--3061, Nov. 1994.

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