Rearrangeable f-cast multi-log2 N networks

Multi-log2 N networks (or vertically stacked banyan networks) have been an attractive class of switching networks due to their small depth O(log N), absolute signal loss uniformity and good fault tolerance property. Recently, F.K.Hwang extended the study of multi-log2 N networks to the general f-cast case, which covers the unicast case (f = 1) and multicast case (f = N) as special cases, and determined the conditions for these networks to be f-cast strictly nonblocking when the fan-out capability is available at both the input stage and middle banyan stage. In this paper, we study the rearrangeable f-cast multilog2 N networks under both node-blocking scenario (relevant to photonic switches) and link-blocking scenario (relevant to electronic switches). In particular, we consider the following three fan-out cases in our study: (1) no restriction on fan-out capability; (2) input stage has no fan-out capability; (3) middle banyan stage has no fan-out capability. We determine the necessary conditions for the first two cases while obtaining the necessary and also sufficient condition for the third one.

[1]  Chin-Tau A. Lea,et al.  Strictly nonblocking directional-coupler-based switching networks under crosstalk constraint , 2000, IEEE Trans. Commun..

[2]  Frank K. Hwang,et al.  On Multicast Rearrangeable 3-stage Clos Networks Without First-Stage Fan-Out , 2006, SIAM J. Discret. Math..

[3]  Pin-Han Ho,et al.  Performance modeling for all-optical photonic switches based on the vertical stacking of banyan network structures , 2005, IEEE Journal on Selected Areas in Communications.

[4]  Frank K. Hwang,et al.  Wide-sense nonblocking multicast Log2(N, m, p) networks , 2003, IEEE Trans. Commun..

[5]  M. Ackroyd.  Call Repacking in Connecting Networks , 1979, IEEE Trans. Commun..

[6]  G. Jack Lipovski,et al.  Banyan networks for partitioning multiprocessor systems , 1973, ISCA '73.

[7]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[8]  T. C. Huang,et al.  Crosstalk in a lossy directional coupler switch , 1995 .

[9]  Chin-Tau A. Lea,et al.  Wide-sense nonblocking Banyan-type switching systems based on directional couplers , 1998, IEEE J. Sel. Areas Commun..

[10]  W. Kabacinski,et al.  Simultaneous connections routing in multi-log/sub 2/N switching fabrics , 2004, 2004 Workshop on High Performance Switching and Routing, 2004. HPSR..

[11]  Frank Hwang,et al.  The Mathematical Theory of Nonblocking Switching Networks , 1998 .

[12]  Yeonghwan Tscha,et al.  Yet another result on multi-log2N networks , 1999, IEEE Trans. Commun..

[13]  Achille Pattavina,et al.  Nonblocking conditions of multicast three-stage interconnection networks , 2005, Networks.

[14]  Chin-Tau A. Lea,et al.  Multi-log2N networks and their applications in high-speed electronic and photonic switching systems , 1990, IEEE Trans. Commun..

[15]  Wojciech Kabacinski,et al.  Wide-sense and strict-sense nonblocking operation of multicast multi-log2 n switching networks , 2002, IEEE Trans. Commun..

[16]  Wojciech Kabacinski,et al.  Comments on "Wide-sense nonblocking multicast Log/sub 2/(N, m, p) Networks" , 2006, IEEE Trans. Commun..

[17]  Achille Pattavina,et al.  Switching theory : architectures and performance in broadband ATM networks , 1998 .

[18]  Dejie Li.  Elimination of crosstalk in directional coupler switches , 1993 .

[19]  Frank K. Hwang.  A unifying approach to determine the necessary and sufficient conditions for nonblocking multicast 3-stage Clos networks , 2005, IEEE Transactions on Communications.

[20]  Wojciech Kabacinski,et al.  A New Control Algorithm for Wide-Sense Nonblocking Multiplane Photonic Banyan-Type Switching Fabrics with Zero Crosstalk , 2006, IEEE Journal on Selected Areas in Communications.

[21]  Guido Maier,et al.  Design of photonic rearrangeable networks with zero first-order switching-element-crosstalk , 2001, IEEE Trans. Commun..

[22]  Xiaohong Jiang,et al.  Blocking behaviors of crosstalk-free optical Banyan networks on vertical stacking , 2003, TNET.

[23]  Chin-Tau A. Lea,et al.  Log2 (N, m, p) strictly nonblocking networks , 1991, IEEE Trans. Commun..

[24]  Chin-Tau A. Lea,et al.  Tradeoff of horizontal decomposition versus vertical stacking in rearrangeable nonblocking networks , 1991, IEEE Trans. Commun..

[25]  D. König.  Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre , 1916 .

[26]  Frank K. Hwang,et al.  Necessary and Sufficient Conditions for Rearrangeable Log , 2005 .

[27]  Frank K. Hwang,et al.  Choosing the best logk(N, m, P) strictly nonblocking networks , 1998, IEEE Trans. Commun..

[28]  Achille Pattavina,et al.  Nonblocking conditions of multicast three-stage interconnection networks , 2005 .

[29]  Wojciech Kabacinski.  Nonblocking Electronic and Photonic Switching Fabrics , 2005 .