This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A General Theory for Deadlock-Free Adaptive Routing Using a Mixed Set of Resources
December 2001 (vol. 12 no. 12)
pp. 1219-1235

This paper presents a theoretical framework for the design of deadlock-free fully adaptive routing algorithms for a general class of network topologies and switching techniques in a single, unified theory. A general theory is proposed that allows the design of deadlock avoidance-based as well as deadlock recovery-based wormhole and virtual cut-through adaptive routing algorithms that use a homogeneous or a heterogeneous (mixed) set of resources. The theory also allows channel queues to be allocated nonatomically, utilizing resources efficiently. A general methodology for the design of fully adaptive routing algorithms applicable to arbitrary network topologies is also proposed. The proposed theory and methodology allow the design of efficient network routers that require minimal resources for handling infrequent deadlocks.

[1] C. Stunkel, D. Shea, B. Abali, M. Atkins, C. Bender, D. Grice, P. Hochshild, D. Joseph, B. Nathanson, R. Swetz, R. Stucke, M. Tsao, and P. Varker, “The SP2 High-Performance Switch,” IBM Systems J., vol. 34, no. 2,pp. 185–204, 1995.
[2] S.L. Scott and G.M. Thorson, “The Cray T3E Network: Adaptive Routing in a High Performance 3D Torus,” Proc. Symp. Hot Interconnects IV, pp. 147-156, Aug. 1996.
[3] J. Laudon and D. Lenoski, "The SGI Origin: A cc-NUMA Highly Scalable Server," Proc. 24th Ann. Int'l Symp. Computer Architecture, May 1997.
[4] M.D. Schroeder et al., “Autonet: A High-Speed, Self-Configuring Local Area Network Using Point-to-Point Links,” Technical Report SRC Research Report 59 (DEC), Apr. 1990.
[5] N. Boden et al., "Myrinet: A Gigabit-per-Second Local Area Network," IEEE Micro, Feb. 1995, pp. 29-36.
[6] D. Garcia, “ServerNet II,” Proc. 1997 Parallel Computing, Routing, and Comm. Workshop, June 1997.
[7] W.J. Dally and C.L. Seitz, “Deadlock-Free Message Routing in Multiprocessor Interconnection Networks,” IEEE Trans. Computers, Vol. C-36, No. 5, May 1987, pp. 547-553.
[8] P. Kermani and L. Kleinrock, “Virtual Cut-Through: A New Computer Communication Switching Technique,” Computer Networks, pp. 267-286, 1979.
[9] R. Horst, “ServerNet Deadlock Avoidance and Fractahedral Topologies,” Proc. Int'l Parallel Processing Symp., pp. 274–280, Apr. 1996.
[10] J. Carbonaro, “Cavallino: The Teraflops Router and NIC,” Proc. Symp. Hot Interconnects IV, pp. 157-160, Aug. 1996.
[11] M. Galles, “Spider: A High Speed Network Interconnect,” Proc. Symp. Hot Interconnects IV, pp. 141-146, Aug. 1996.
[12] S. L. Scott, J.R. Goodman, The Impact of Pipelined Channels on K-Ary N-Cube Networks IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 1, pp. 2-16, Jan. 1994.
[13] W.J. Dally, "Virtual-Channel Flow Control," IEEE Trans. Parallel and Distributed Systems, vol. 3, no. 2, pp. 194-205, Mar. 1992.
[14] F. Silla, M.P. Malumbres, A. Robles, P. López, and J. Duato, Efficient Adaptive Routing in Networks of Workstations with Irregular Topology Proc. Workshop Comm. and Architectural Support for Network-Based Parallel Computing, Feb. 1997.
[15] F. Silla and J. Duato, “On the Use of Virtual Channels in Networks of Workstations with Irregular Topology,” Proc. 1997 Parallel Computing, Routing, and Comm. Workshop, June 1997.
[16] S. Konstantinidou and L. Snyder, “Chaos Router: Architecture and Performance,” Proc. 18th Int'l Symp. Computer Architecture, pp. 212-221, May 1991.
[17] D.H. Linder and J.C. Harden, "An Adaptive and Fault Tolerant Wormhole Routing Strategy for k-Ary n-Cubes," IEEE Trans. Computers, vol. 40, no. 1, pp. 2-12, Jan. 1991.
[18] W.J. Dally and H. Aoki, "Deadlock-Free Adaptive Routing in Multicomputer Networks Using Virtual Channels," IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 4, pp. 466-475, Apr. 1993.
[19] J. Duato, "A New Theory of Deadlock-Free Adaptive Routing in Wormhole Networks," IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 12, pp. 1,320-1,331, Dec. 1993.
[20] J.H. Kim, Z. Liu, and A.A. Chien, "Compressionless Routing: A Framework for Adaptive and Fault Tolerant Routing," Proc. 21st Ann. Int'l Symp. Computer Architecture, pp. 289-300, Apr. 1994.
[21] K.V. Anjan and T.M. Pinkston, “An Efficient, Fully Adaptive Deadlock Recovery Scheme: Disha,” Proc. 22nd Ann. Int'l Symp. Computer Architecture, pp. 201-210, June 1995.
[22] P. Palazzari and M. Coli, “Virtual Cut-Through Implementation of the Hole-Based Packet Switching Routing Algorithm,” Proc. Sixth Euromicro Workshop Parallel and Distributed Processing, pp. 416-421, Jan. 1998.
[23] W.J. Dally, L.R. Dennison, D. Harris, K. Kan, and T. Xanthopoulos, “Architecture and implementation of the Reliable Router,” Proc. Hot Interconnects II, Aug. 1994.
[24] T.M. Pinkston, Y. Choi, and M. Raksapatcharawong, “Architecture and Optoelectronic Implementation of the WARRP Router,” Proc. Fifth Symp. Hot Interconnects, pp. 181-189, Aug. 1997.
[25] J. Duato, “A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 10, pp. 1,055–1,067, Oct. 1995.
[26] K.V. Anjan, T.M. Pinkston, and J. Duato, Generalized Theory for Deadlock-Free Adaptive Routing and Its Application to Disha Concurrent Proc. 10th Int'l Parallel Processing Symp., Apr. 1996.
[27] T.M. Pinkston, “Flexible and Efficient Routing Based on Progressive Deadlock Recovery,” IEEE Trans. Computers, vol. 48, no. 7, pp. 649-669, July 1999.
[28] S.L. Scott and G. Thorson, “Optimized Routing in the Cray T3D,” Proc. Workshop Parallel Computer Routing and Comm., pp. 281–294, May 1994.
[29] L.-S. Peh and W. Dally, “A Delay Model for Router Microarchitectures,” IEEE Micro, vol. 21, no. 1, pp. 26-34, Jan./Feb. 2001.
[30] J. Duato, S. Yalamanchili, and L.M. Ni, Interconnection Networks: An Engineering Approach. Los Alamitos, Calif.: IEEE CS Press, 1997.
[31] S. Warnakulasuriya and T.M. Pinkston, “Characterization of Deadlocks in Irregular Networks,” Proc. 1999 Int'l Conf. Parallel Processing, Sept. 1999.
[32] T.M. Pinkston and S. Warnakulasuriya, Characterization of Deadlocks in K-Ary N-Cube Networks IEEE Trans. Parallel and Distributed Systems, vol. 10, no. 9, pp 38-49, Sept. 1999.
[33] P. López, J.M. Martínez, and J. Duato, A Very Efficient Distributed Deadlock Detection Mechanism for Wormhole Networks Proc. High Performance Computer Architecture Symp., Feb. 1998.
[34] T.M. Pinkston and S. Warnakulasuriya, “On Deadlocks in Interconnection Networks,” Proc. 24th Int'l Symp. Computer Architecture, June 1997.
[35] J.M. Martínez, P. López, J. Duato, and T.M. Pinkston, “Software-Based Deadlock Recovery Technique for True Fully Adaptive Routing in Wormhole Networks,” Proc. Int'l Conf. Parallel Processing, pp. 182-189, Aug. 1997.
[36] Y. Tamir and G.L. Frazier, "Dynamically-Allocated Multi-Queue Buffers for VLSI Communication Switches," IEEE Trans. Computers, vol. 41, no. 6, pp. 725-737, June 1992.
[37] J. Duato, “A Necessary and Sufficient Condition for Deadlock-Free Routing in Cut-Through and Store-and-Forward Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 8, pp. 841-854, Aug. 1996.
[38] S. Warnakulasuriya and T.M. Pinkston, A Formal Model of Message Blocking and Deadlock Resolution in Interconnection Networks IEEE Trans. Parallel and Distributed Systems, vol. 11, no. 2, pp. 212-229, Mar. 2000.
[39] J. Duato, “A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks,” Proc. 1994 Int'l Conf. Parallel Processing, vol. 1, pp. 142-149, Aug. 1994.
[40] F. Petrini and M. Vanneschi, “Performance Analysis of Minimal Adaptive Wormhole Routing with Time-Dependent Deadlock Recovery,” Proc. 11th Int'l Parallel Processing Symp., pp. 589-595, Apr. 1997.
[41] K.V. Anjan and T.M. Pinkston, "DISHA: An Efficient Fully Adaptive Deadlock Recovery Scheme," Proc. Ninth Int'l Parallel Processing Symp., Apr. 1995.
[42] X. Lin and L. M. Ni,“Multicast communication in multicomputer networks,”IEEE Trans. Parallel, Distrib. Syst.,vol. 4, pp. 1105–1117, Oct. 1993.
[43] G.D. Pifarré, L. Gravano, S.A. Felperin, and J.L.C. Sanz, "Fully Adaptive Minimal Deadlock-Free Packet Routing in Hypercubes, Meshes and Other Networks: Algorithms and Simulations," IEEE Trans. Parallel Distributed Systems, vol. 5, no. 3, pp. 247-263, Mar. 1994.
[44] X. Lin, P.K. McKinley, L.M. Ni, “The Message Flow Model for Routing in Wormhole-Routed Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 7, pp. 755–760, July 1995.
[45] L. Schwiebert and D.N. Jayasimha, “A Universal Proof Technique for Deadlock-Free Routing in Interconnection Networks,” Proc. Symp. Parallel Algorithms and Architectures, pp. 175–184, July 1995.
[46] L. Schwiebert and D.N. Jayasimha, "A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing," J. Parallel and Distributed Computing, vol. 32, no. 1, pp. 103-117, Jan. 1996.
[47] B. Abali, “A Deadlock Avoidance Method for Computer Networks,” Proc. First Int'l Workshop Comm. and Architectural Support for Network-Based Parallel Computing (CANPC '97), pp. 61-72, Feb. 1997.
[48] W. Qiao and L.M. Ni, “Adaptive Routing in Irregular Networks Using Cut-Through Switches,” Proc. 1996 Int'l Conf. Parallel Processing, Aug. 1996.
[49] P.M. Merlin and P.J. Schweitzer, “Deadlock Avoidance in Store-and-Forward Networks—I: Store-and-Forward Deadlock,” IEEE Trans. Comm., vol. 3, pp. 345-354, Mar. 1980.
[50] K.D. Gunther, “Prevention of Deadlocks in Packet-Switched Data Transport Systems,” IEEE Trans. Comm., vol. 4, pp. 512-524, Apr. 1981.
[51] E. Fleury and P. Fraigniaud, “A General Theory for Deadlock Avoidance in Wormhole-Routed Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 7, pp. 626-638, July 1998.
[52] P.T. Gaughan and S. Yalamanchili, "A Family of Fault-Tolerant Routing Protocols for Direct Multiprocessor Networks," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 6, pp. 482-487, May 1995.
[53] C.R. Hesshope, P.R. Miller, and J.T. Yanchev, "High Performance Communications in Processor Networks," Proc. Int'l Symp. Computer Architecture, pp. 150-157, 1989.
[54] D.S. Reeves, E.F. Gehringer, and A. Chandiramani, “Adaptive Routing and Deadlock Recovery: A Simulation Study,” Proc. Fourth Conf. Hypercube Concurrent Computers and Applications, Mar. 1989.
[55] J.H. Kim, Z. Liu, and A.A. Chien., "Compressionless Routing: A Framework for Fault-Tolerant Routing," IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 3, pp. 229-244, Mar. 1997.
[56] M. Coli and P. Palazzari, “An Adaptive Deadlock and Livelock Free Routing Algorithm,” Proc. Third Euromicro Workshop Parallel and Distributed Processing, pp. 288-295 Jan. 1995.
[57] C. Carrion, R. Beivide, J.A. Gregorio, and F. Vallejo, “A Flow Control Mechanism to Prevent Message Deadlock in k-Ary n-Cube Networks,” Proc. 1997 Int'l Conf. High Performance Computing, Dec. 1997.

Index Terms:
General theory for deadlock-free fully adaptive routing, regular networks, irregular networks, nonatomic queue allocation
Citation:
J. Duato, T.M. Pinkston, "A General Theory for Deadlock-Free Adaptive Routing Using a Mixed Set of Resources," IEEE Transactions on Parallel and Distributed Systems, vol. 12, no. 12, pp. 1219-1235, Dec. 2001, doi:10.1109/71.970556
Usage of this product signifies your acceptance of the Terms of Use.