
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Emmanouel A. Varvarigos, Ayan Banerjee, "Routing Schemes for Multiple Random Broadcasts in Arbitrary Network Topologies," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 8, pp. 886895, August, 1996.  
BibTex  x  
@article{ 10.1109/71.532119, author = {Emmanouel A. Varvarigos and Ayan Banerjee}, title = {Routing Schemes for Multiple Random Broadcasts in Arbitrary Network Topologies}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {7}, number = {8}, issn = {10459219}, year = {1996}, pages = {886895}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.532119}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Routing Schemes for Multiple Random Broadcasts in Arbitrary Network Topologies IS  8 SN  10459219 SP886 EP895 EPD  886895 A1  Emmanouel A. Varvarigos, A1  Ayan Banerjee, PY  1996 KW  General graphs KW  edgedisjoint trees KW  dynamic broadcasting KW  queuing systems. VL  7 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Abstract—We consider the problem where packets are generated at each node of a network according to a Poisson process with rate λ, and each of them has to be broadcast to all the other nodes. The network topology is assumed to be an arbitrary bidirectional graph. We derive upper bounds on the maximum achievable broadcast throughput, and lower bounds on the average time required to complete a broadcast. These bounds apply to any network topology, independently of the scheme used to perform the broadcasts. We also propose two dynamic broadcasting schemes, called the indirect and the direct broadcasting scheme, that can be used in a general topology, and we evaluate analytically their throughput and average delay. The throughput achieved by the proposed schemes is equal to the maximum possible, if a halfduplex link model is assumed, and is at least equal to one half of the maximum possible, if a fullduplex model is assumed. The average delay of both schemes is of the order of the diameter of the trees used to perform the broadcasts. The analytical results obtained do not use any approximating assumptions.
[1] D. Bertzekas and R. Gallager, Data Networks, second ed. PrenticeHall, 1992.
[2] D.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computation.Englewood Cliffs, N.J.: Prentice Hall International, 1989.
[3] D. Bertsekas, C. Ozveren, G. Stamoulis, P. Tseng, and J. Tsitsiklis, "Optimal Communication Algorithms for Hypercubes," J. Parallel and Distributed Computing, vol. 11, pp. 263275, 1991.
[4] S.L. Brumelle, "Some Inequalities for ParallelServer Queues," Operations Research, vol. 19, pp. 402413, 1971.
[5] C.J. Colbourn, The Combinatorics of Network Reliability, Oxford Univ. Press, 1987.
[6] 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. 255270.Amsterdam: Elsevier, 1988.
[7] A.G. Greenberg and B. Hajek, "Deflection Routing in Hypercube Networks," IEEE Trans. Comm., vol. 35, no. 6, pp. 1,0701,081, June 1992.
[8] A. Krishna, "Communication with Few Buffers: Analysis and Design," PhD thesis, Dept. of Electrical and Computer Eng., Univ. of Illinois at UrbanaChampaign, Dec. 1990.
[9] F.T. Leighton,Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes.San Mateo, Calif.: Morgan Kaufmann, 1992.
[10] Y. Lan, A.H. Esfahanian, and L.M. Ni, "Multicast in Hypercube Multiprocessors," J. Parallel and Distributed Computing, vol. 8, pp. 3041, Jan. 1990.
[11] N.F. Maxemchuk, "Comparison of Deflection and StoreandForward Techniques in the Manhattan Street and ShuffleExchange Networks," Proc. INFORCOM '89, vol. 3, pp. 800809, Apr. 1989.
[12] C.J.A. NashWilliams, "EdgeDisjoint Spanning Trees of Finite Graphs," J. London Math. Soc., vol. 36, 1961.
[13] Y. Shiloach, "EdgeDisjoint Branching in Directed Multigraphs," Information Processing Letters, 1979.
[14] G. Stamoulis and J. Tsitsiklis, "Efficient Routing Schemes for Multiple Broadcasts in Hypercubes," IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 7, pp. 725739, July 1993.
[15] G.D. Stamoulis and J.N. Tsitsiklis, "Greedy Routing in Hupercubes and Butterflies," IEEE Trans. Comm., vol. 44, no. 11, pp. 3,0513,061, 1994.
[16] R.E. Tarjan, "A Good Algorithm for EdgeDisjoint Branching," Information Processing Letters, 1974.
[17] E.A. Varvarigos and D.P. Bertsekas, "Multinode Broadcast in Hypercubes and Rings with Randomly Distributed Length of Packets," IEEE Trans. Parallel and Distributed Systems, vol. 4, pp. 144154, 1993.
[18] E. A. Varvarigos and D. P. Bertsekas,“Partial multinode broadcast and partial exchange in$d$dimensional wraparound meshes,”to appear inJ. Parallel Distrib. Comput.
[19] E.A. Varvarigos and D.P. Bertsekas, "Performance of Hypercube Routing Schemes With or Without Buffering," IEEE/ACM Trans. Networking, vol. 2, no. 3, pp. 299311, June 1994.
[20] E.A. Varvarigos and D.P. Bertsekas, "Dynamic Broadcasting in Parallel Computing" IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 2, pp. 120131, Feb. 1995.