Abstract

In this paper, we consider four-stage multicast switching networks with different types of nonblocking capability. The goal of the paper is multifold. First, we evaluate and summarize various nonblocking conditions of four-stage multicast switching networks in recent work [Y. Yang and J. Wang, “A New Design for Wide-Sense Nonblocking Multicast Switching Networks,” IEEE Trans. Commun., vol. 53, no. 3, pp. 497–504, Mar. 2005, and F. Yan , “Nonblocking Four-Stage Multicast Network for Mulicast-Capable Optical Cross Connects,” J. Lightw. Technol., vol. 27, no. 17, pp. 3923–2932, Sep. 2009], and then propose a locally-rearrangeable nonblocking (LRNB) multicast switching network as a trade-off for nonblocking capability and network hardware cost between wide-sense nonblocking (WSNB) networks and rearrangeable nonblocking (RNB) networks. We further derive optimized network parameters and present a comprehensive cost analysis for different types of four-stage nonblocking multicast switching networks. Using the terms defined in F. Yan , our results show that for an N × N network, a 4(2 <i>m</i>)-stage WSNB network and a 4(2 <i>m</i>)-stage LRNB network have 16.114 N<sup>3/2</sup> and 12.669 N<sup>3/2</sup> crosspoints, respectively; 4(3 <i>m</i>)-stage WSNB and LRNB networks have the same number of crosspoints, $11.657 N<sup>3/2</sup>; and 4(2 <i>m</i>)-stage RNB network has 7.447 N<sup>3/2</sup> crosspoints.

© 2011 IEEE

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  1. C. Clos, "A study of non-blocking switching networks," Bell Syst. Tech. J. 32, 406-424 (1953).
  2. Y. Yang, G. M. Masson, "Nonblocking broadcast switching networks," IEEE Trans. Comput. 40, 1005-1015 (1991).
  3. Y. Yang, G. M. Masson, "The necessary conditions for Clos-type nonblocking multicast networks," IEEE Trans. Comput. 48, 1214-1227 (1999).
  4. F. K. Hwang, The Mathematical Theory of Nonblocking Switching Networks (World Scientific, 2004).
  5. Y. Yang, J. Wang, "A new design for wide-sense nonblocking multicast switching networks," IEEE Trans. Commun. 53, 497-504 (2005).
  6. F. Yan, "Nonblocking four-stage multicast network for multicast-capable optical cross connects," J. Lightw. Technol. 27, 3923-3932 (2009).
  7. V. E. Benes, Mathematical Theory of Connecting Networks and Telephone Traffic (Academic, 1965).
  8. J. Duato, S. Yalamanchili, L. M. Ni, Interconnection Networks: An Engineering Approach (Morgan Kaufmann, 2003).
  9. D. Nassimi, S. Sahni, "Parallel permutation and sorting algorithms and a new generalized connection network," J. ACM 29, 642-667 (1982).
  10. G. M. Masson, B. W. Jordan, "Generalized multi-stage connection networks," Networks 2, 191-209 (1972).
  11. F. K. Hwang, A. Jajszczyk, "On nonblocking multiconnection networks," IEEE Trans. Commun. 34, 1038-1041 (1986).
  12. P. Feldman, J. Friedman, N. Pippenger, "Wide-sense nonblocking networks," SIAM J. Discrete Math. 1, 158-173 (1988).
  13. C. Lee, A. Y. Oruç, "Design of efficient and easily routable generalized connectors," IEEE Trans. Commun. 43, 646-650 (1995).
  14. T. T. Lee, "Nonblocking copy networks for multicast packet switching," IEEE J. Sel. Areas Commun. 6, 1455-1467 (1988).
  15. Y. Yang, J. Wang, "A new self-routing multicast network," IEEE Trans. Parallel Distrib. Syst. 10, 1299-1316 (1999).
  16. Y. Yang, J. Wang, C. Qiao, "Nonblocking WDM multicast switching networks," IEEE Trans. Parallel Distrib. Syst. 11, 1274-1287 (2000).
  17. Y. Yang, J. Wang, "Nonblocking $k$-fold multicast networks," IEEE Trans. Parallel Distrib. Syst. 14, 131-141 (2003).

2009 (1)

F. Yan, "Nonblocking four-stage multicast network for multicast-capable optical cross connects," J. Lightw. Technol. 27, 3923-3932 (2009).

2005 (1)

Y. Yang, J. Wang, "A new design for wide-sense nonblocking multicast switching networks," IEEE Trans. Commun. 53, 497-504 (2005).

2003 (1)

Y. Yang, J. Wang, "Nonblocking $k$-fold multicast networks," IEEE Trans. Parallel Distrib. Syst. 14, 131-141 (2003).

2000 (1)

Y. Yang, J. Wang, C. Qiao, "Nonblocking WDM multicast switching networks," IEEE Trans. Parallel Distrib. Syst. 11, 1274-1287 (2000).

1999 (2)

Y. Yang, J. Wang, "A new self-routing multicast network," IEEE Trans. Parallel Distrib. Syst. 10, 1299-1316 (1999).

Y. Yang, G. M. Masson, "The necessary conditions for Clos-type nonblocking multicast networks," IEEE Trans. Comput. 48, 1214-1227 (1999).

1995 (1)

C. Lee, A. Y. Oruç, "Design of efficient and easily routable generalized connectors," IEEE Trans. Commun. 43, 646-650 (1995).

1991 (1)

Y. Yang, G. M. Masson, "Nonblocking broadcast switching networks," IEEE Trans. Comput. 40, 1005-1015 (1991).

1988 (2)

P. Feldman, J. Friedman, N. Pippenger, "Wide-sense nonblocking networks," SIAM J. Discrete Math. 1, 158-173 (1988).

T. T. Lee, "Nonblocking copy networks for multicast packet switching," IEEE J. Sel. Areas Commun. 6, 1455-1467 (1988).

1986 (1)

F. K. Hwang, A. Jajszczyk, "On nonblocking multiconnection networks," IEEE Trans. Commun. 34, 1038-1041 (1986).

1982 (1)

D. Nassimi, S. Sahni, "Parallel permutation and sorting algorithms and a new generalized connection network," J. ACM 29, 642-667 (1982).

1972 (1)

G. M. Masson, B. W. Jordan, "Generalized multi-stage connection networks," Networks 2, 191-209 (1972).

1953 (1)

C. Clos, "A study of non-blocking switching networks," Bell Syst. Tech. J. 32, 406-424 (1953).

Bell Syst. Tech. J. (1)

C. Clos, "A study of non-blocking switching networks," Bell Syst. Tech. J. 32, 406-424 (1953).

IEEE J. Sel. Areas Commun. (1)

T. T. Lee, "Nonblocking copy networks for multicast packet switching," IEEE J. Sel. Areas Commun. 6, 1455-1467 (1988).

IEEE Trans. Commun. (3)

F. K. Hwang, A. Jajszczyk, "On nonblocking multiconnection networks," IEEE Trans. Commun. 34, 1038-1041 (1986).

Y. Yang, J. Wang, "A new design for wide-sense nonblocking multicast switching networks," IEEE Trans. Commun. 53, 497-504 (2005).

C. Lee, A. Y. Oruç, "Design of efficient and easily routable generalized connectors," IEEE Trans. Commun. 43, 646-650 (1995).

IEEE Trans. Comput. (2)

Y. Yang, G. M. Masson, "Nonblocking broadcast switching networks," IEEE Trans. Comput. 40, 1005-1015 (1991).

Y. Yang, G. M. Masson, "The necessary conditions for Clos-type nonblocking multicast networks," IEEE Trans. Comput. 48, 1214-1227 (1999).

IEEE Trans. Parallel Distrib. Syst. (3)

Y. Yang, J. Wang, "A new self-routing multicast network," IEEE Trans. Parallel Distrib. Syst. 10, 1299-1316 (1999).

Y. Yang, J. Wang, C. Qiao, "Nonblocking WDM multicast switching networks," IEEE Trans. Parallel Distrib. Syst. 11, 1274-1287 (2000).

Y. Yang, J. Wang, "Nonblocking $k$-fold multicast networks," IEEE Trans. Parallel Distrib. Syst. 14, 131-141 (2003).

J. ACM (1)

D. Nassimi, S. Sahni, "Parallel permutation and sorting algorithms and a new generalized connection network," J. ACM 29, 642-667 (1982).

J. Lightw. Technol. (1)

F. Yan, "Nonblocking four-stage multicast network for multicast-capable optical cross connects," J. Lightw. Technol. 27, 3923-3932 (2009).

Networks (1)

G. M. Masson, B. W. Jordan, "Generalized multi-stage connection networks," Networks 2, 191-209 (1972).

SIAM J. Discrete Math. (1)

P. Feldman, J. Friedman, N. Pippenger, "Wide-sense nonblocking networks," SIAM J. Discrete Math. 1, 158-173 (1988).

Other (3)

V. E. Benes, Mathematical Theory of Connecting Networks and Telephone Traffic (Academic, 1965).

J. Duato, S. Yalamanchili, L. M. Ni, Interconnection Networks: An Engineering Approach (Morgan Kaufmann, 2003).

F. K. Hwang, The Mathematical Theory of Nonblocking Switching Networks (World Scientific, 2004).

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