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Bounds on Maximum Delay in Networks with Deflection Routing
July 1995 (vol. 6 no. 7)
pp. 724-732

Abstract—We consider the problem of finding the worst case packet transit delay in networks using deflection routing. Several classes of networks are studied, including many topologies for which deflection routing has been proposed or implemented (e.g., hypercube, Manhattan Street Network, shuffle-exchange network). We derive new upper bounds on the evacuation time of batch admissions, and present simple proofs for several existing bounds. Also derived are bounds on worst case transit delay for certain networks admitting packets continuously. To demonstrate the practical utility of our results, we compare a new delay bound to the maximum delay observed in simulations. The results have application in both protocol design and the determination of the required capacity of packet resequencing buffers.

[1] N.F. Maxemchuk,“The Manhattan Street Network,” IEEE Globecom 1985,New Orleans, La., pp. 255-261, Sept. 1985.
[2] J.T. Brassil, "Deflection Routing in Certain Regular Networks," PhD thesis, Univ. of California, San Diego, 1991.
[3] D.H. Lawrie and D.A. Padua,“Analysis of message switching with shuffle-exchanges in multiprocessors,” Proc. Workshop Interconnection Networks for Parallel and Distributed Processing, pp. 116-123, ACM, Apr. 1980.
[4] B. Hajek,“Bounds on evaluation time for deflection routing,” Distributed Computing, vol. 5, no. 1, pp. 1-5, 1991.
[5] S.A. Felperim,L. Gravana,G.D. Pifarre,, and J.L.C. Sanz,“Routing techniques for massively parallel communication,” Proc. IEEE, vol. 79-1, no. 4, pp. 488-503, Apr. 1991.
[6] N.F. Maxemchuk,“Regular mesh topologies in local and metropolitan area networks,” AT&T Technical J. vol. 64, no. 7 pp. 1,659-1,685, Sept. 1985.
[7] A.G. Greenberg and B. Hajek, "Deflection Routing in Hypercube Networks," IEEE Trans. Comm., vol. 35, no. 6, pp. 1,070-1,081, June 1992.
[8] J.Y. Ngai and C.L. Seitz, "A Framework For Adaptive Routing in Multicomputer Networks," Proc. ACM Symp. Parallel Algorithms Architectures, 1989.
[9] A. Krishna and B. Hajek,“Performance of shuffle-like switching networks with deflection,” Proc. IEEE INFOCOM’90, pp. 473-480, June, 1990.
[10] A.G. Greenberg and J. Goodman, "Sharp Approximate Models of Adaptive Routing in Mesh Networks," Teletraffic Analysis and Computer Performance Evaluation, J.W. Cohen, O.J. Boxma, and H.C. Tijms, eds., pp. 255-270.Amsterdam: Elsevier, 1988.
[11] T. Syzmanski,“An analysis of hot-potato routing in a fiber-optic packet switched hypercube,” IEEE INFOCOM’90 Proc., vol. 1, pp. 918-925, June 1990.
[12] J.T. Brassil and R.L. Cruz,“Nonuniform traffic in the Manhattan Street Network,” Proc. ICC’91, vol. 3, pp. 1,647-1651, June 1991.
[13] N.F. Maxemchuk,“Problems arising from deflection routing: Live-lock, lockout, congestion and message reassembly,” Proc. NATO Workshop on Architecture and High Performance Issues of High Capacity Local and MetropolitanArea Networks,France, June 1990.
[14] A.K. Choudhury and N.F. Maxemchuk,“Effect of a finite reassembly buffer on the performance of deflection routing,” Proc. ICC’91, vol. 3, pp. 1,637-1,646, June 1991.
[15] A. Borodin and J.E. Hopcroft,"Routing, merging and sorting on parallel models of comparison," J. Computer and System Science, vol. 30, pp. 130-145, 1985.
[16] K.E. Batcher,“Sorting networks and their applications,” AFIPS Spring Joint Computer Conf., vol. 32, pp. 307-314, 1968.

Index Terms:
Hot-potato routing, deflection networks, hypercube, Manhattan Street Network, shuffle-exchange, livelock, performance analysis.
Jack T. Brassil, Rene L. Cruz, "Bounds on Maximum Delay in Networks with Deflection Routing," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 7, pp. 724-732, July 1995, doi:10.1109/71.395401
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