Flexible Routing Criteria for Circuit-Switched Hypercubes

Chiu, Ge-Ming; Chalasani, Suresh; Raghavendra, C.S.

doi:10.1006/jpdc.1994.1087

Cited by 4 publications

(10 citation statements)

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“…This algorithm has the drawback that it causes the node whose address is all ones to become a hotspot, creating a critical problem in system performance [Chiu et al 1994]. Another algorithm, presented by Li [1994], allows k ϩ 1 simultaneous disjoint paths from a source to a destination node that is a Hamming distance k from the source.…”

Section: Existing Hypercube Routing Algorithmsmentioning

confidence: 99%

“…Of the known existing, minimal, circuit-switched routing algorithms, the Turn Model [Glass and Ni 1994] and the UP (or DOWN) Preference [Chiu et al 1994] algorithms have previously shown the greatest flexibility in providing deadlock-free paths from a source to its destination. The Turn Model algorithm [Glass and Ni 1994] is developed by analyzing the directions in which packets can turn in a network and the cycles they form.…”

Section: Existing Hypercube Routing Algorithmsmentioning

confidence: 99%

“…A nonminimal algorithm has the potential to cause infinite-length paths known as livelocks, and thus some mechanism is needed to avoid these. Although it has been shown that the chaos router reduces network congestion [Bolding et al 1994;Fulgham 1993], the livelock prevention implementation has been difficult for circuit-switched applications [Chiu et al 1994]. Thus in this work we focus only on minimal algorithms.…”

Section: Existing Hypercube Routing Algorithmsmentioning

confidence: 99%

“…The UP Preference algorithm [Chiu et al 1994] specifies that any up transition U i can be made at any point in the order of required transitions, but a down transition D i can be made only after all lower-dimension transitions have been completed. Table I shows all possible paths from node 3 to node 4 and whether or not each path is allowed by the UP Preference and the TURN Model algorithms.…”

Section: Existing Hypercube Routing Algorithmsmentioning

confidence: 99%

“…Hypercubes, i.e., binary n-cube interconnection systems, have been extensively studied in recent years [Chiu et al 1994;Choi and Somani 1993;Gaughan and Yalamanchili 1993;Kim and Das 1994;Ohring and Das 1996;Seitz 1985]. An n-dimensional (n-D) hypercube network has N ϭ 2 n nodes with each node assigned an n-bit address ( x nϪ1 , x nϪ2 , .…”

Section: Introductionmentioning

confidence: 99%

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Optimally adaptive, minimum-distance, circuit-switched routing in hypercubes

Mahmood

Lynch

Shaffer

1997

ACM Trans. Comput. Syst.

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In circuit-switched routing, the path between a source and its destination is established by incrementally reserving all required links before the data transmission can begin. If the routing algorithm is not carefully designed, deadlocks can occur in reserving these links. Deadlock-free algorithms based on dimension-ordered routing, such as the E-cube, exist. However, E-cube does not provide any flexibility in choosing a path from a source to its destination and can thus result in long latencies under heavy or uneven traffic. Adaptive, minimum-distance routing algorithms, such as the Turn Model and the UP Preference algorithms, have previously been reported. In this article, we present a new class of adaptive, provably deadlock-free, minimum-distance routing algorithms. We prove that the algorithms developed here are optimally adaptive in the sense that any further flexibility in communication will result in deadlock. We show that the Turn Model is actually a member of our new class of algorithms that does not perform as well as other algorithms within the new class. It creates artificial hotspots in routing the traffic and allows fewer total paths. We present an analytical comparison of the flexibility and balance in routing provided by various algorithms and a comparison based on uniform and nonuniform traffic simulations. The Extended-UP Preference algorithm developed in this article is shown to have improved performance with respect to existing algorithms. The methodology and the algorithms developed here can be used to develop routing for other schemes such as wormhole routing, and for other recursively defined networks such as k-ary n-cubes.

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Section: Existing Hypercube Routing Algorithmsmentioning

confidence: 99%

Section: Existing Hypercube Routing Algorithmsmentioning

confidence: 99%

Section: Existing Hypercube Routing Algorithmsmentioning

confidence: 99%

Section: Existing Hypercube Routing Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimally adaptive, minimum-distance, circuit-switched routing in hypercubes

Mahmood

Lynch

Shaffer

1997

ACM Trans. Comput. Syst.

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A fault-tolerant routing strategy in hypercube multicomputers

Chiu

1996

IEEE Trans. Comput.

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Circuit switching with input queuing: an analysis for the d-dimensional wraparound mesh and the hypercube

Sharma

Varvarigos

1997

IEEE Trans. Parallel Distrib. Syst.

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We analyze circuit switching in a multiprocessor network, where connection requests (or sessions) arrive at each node of the network according to a Poisson process with rate 1. Each session joins the appropriate input-queue at its source node, and, upon advancing to the head of the queue, transmits a setup packet to establish a connection. If the setup packet is successful, it reserves the links on the path for the duration of the session, and the session is served without interruptions. Otherwise, the connection request remains queued at the source, and subsequent attempts are made to establish the circuit. We analyze the queue of connection requests at the input-buffer of a network link, and obtain analytic expressions for the stability region, the average queuing delay, the average connection time, the average waiting time, and the average total delay, which show how these parameters depend on system variables, such as network dimension and session arrival rate. The queuing analysis focuses on the input-queue of a particular link, and accounts for the interactions with queues of other links through the retrial attempts and the associated probability of success. The queuing analysis is independent of the particular network topology under consideration, as long as the probability that a session arriving at a random time successfully establishes a connection can be calculated for that network. Simulations demonstrate the close agreement between the observed network behavior and that predicted by the analysis.

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Flexible Routing Criteria for Circuit-Switched Hypercubes

Cited by 4 publications

References 0 publications

Optimally adaptive, minimum-distance, circuit-switched routing in hypercubes

Optimally adaptive, minimum-distance, circuit-switched routing in hypercubes

A fault-tolerant routing strategy in hypercube multicomputers

Circuit switching with input queuing: an analysis for the d-dimensional wraparound mesh and the hypercube

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