Grzegorz Danilewicz

Wide-sense and strict-sense nonblocking operation of multicast multi-log/sub 2/ n switching networks

Multicast connections are used in broad-band switching networks as well as in parallel processing. We consider wide-sense and strict-sense nonblocking conditions for multi-log/sub 2/ N switching networks with multicast connections. We prove that such networks are wide-sense nonblocking if they are designed by vertically stacking at least t /spl middot/ 2/sup n-t-1/ + 2 /sup n-2t-1/ planes of a log/sub 2/ N networks together, where 1 /spl les/ t /spl les/ [n/2] and t defines the size of a blocking window K = 2/sup t/. For t = [n/2] and n even, and for [n/2] /spl les/ t /spl les/ n the number of planes must be at least t /spl middot/ 2/sup n-t-1/ + 1 and 2/sup t/ + (n - t - 1) /spl middot/ 2/sup n-t-1/ - 2/sup 2t-n-1/ + 1, respectively. In the case of strict-sense nonblocking switching networks, the number of planes is at least N/2. The results obtained in this paper show that in many cases number of planes in wide-sense nonblocking switching networks is less than those for t = [n/2] considered by Tscha and Lee (see ibid., vol.47, p.1425-31, Sept. 1999). The number of planes given in the paper is the minimum number of planes needed for wide-sense nonblocking operation provided that Algorithm 1 is used for setting up connections. The minimum number of planes for such operation in general is still open issue.

A New Control Algorithm for Wide-Sense Nonblocking Multiplane Photonic Banyan-Type Switching Fabrics with Zero Crosstalk

A new control algorithm for log2(N, 0, p) switching networks composed of 2 x 2 switching elements has been proposed recently. Under this algorithm, log2(N,0,p) switching networks with even number of stages are wide-sense nonblocking (WSNB) if p is the same as for the rearrangeable nonblocking (RNB) one. The considerred algorithm and WSNB conditions did not take into account crosstalk constraint, which is an important factor in photonic switching. This paper enhanced this algorithm to the case when crosstalk in the switching fabric is not allowed. WSNB conditions for this enhanced algorithm are also derived. It is shown, that the number of planes required is less than those derived earlier in other papers for WSNB multiplane banyan- type switching fabrics under crosstalk constraint. Under this algorithm, log2( N,0,p) switching networks with odd number of stages and with zero crosstalk are WSNB if p is the same as for RNB one.

The Architecture and Strict-Sense Nonblocking Conditions of a New Baseline-Based Optical Switching Network Composed of Symmetrical and Asymmetrical Switching Elements

In this paper, we introduce a new multiplane optical switching fabric structure based on a baseline type switching network. The new structure is built from symmetrical and asymmetrical optical switching elements. This new architecture can be extended to structures of greater size (it means capacity as a number of inputs and outputs). To compare different types of switching architectures, we define the cost of an appropriate structure as the number of its passive and active optical elements. Generally, structure with smallest number of these elements constitutes a cheaper solution. We also introduce a strict-sense nonblocking conditions for the proposed multiplane structure and compare them with an optical baseline multiplane switching networks of the same capacity. We show that for most capacities of the switching network, the new multiplane architecture is a cheaper solution than the multiplane baseline network even when the number of planes in the new architecture is greater than the number of one planes in the baseline structure — cost of the whole new structure expressed as the number of passive and active optical elements is fewer than baseline network of the same capacity.

Wide-Sense Nonblocking

Wide-sense nonblocking (WSNB) log2(N, 0, p) switching networks under the fixed-size blocking window algorithm have been proposed by Tscha and Lee. We have generalized this approach to the variable-size blocking window algorithm and shown that the minimum number of planes depends on the window size and the number of stages. We have also generalized this concept to log2(N, m, p) switching networks. Later, Hwang and Lin have proved that for m > 2, the number of required planes for WSNB operation under the blocking window algorithm is always greater than for m les 2, and determined the optimal window size and optimal m. In this paper, we further generalized these results to logd(N, 0, p) switching networks. In the paper, we prove that the minimum number of planes for any d is reached also for different sizes of blocking window depending on d and n.

{\rm log}_{d}(N, 0, p)

Recently, Hwang and Lin derived nonblocking conditions for multicast connections in Log2(N,m,p) networks. They improved some conditions obtained earlier by Kabacinacuteski and Danilewicz. In this letter, we identify some inaccuracy in present results concerning wide-sense nonblocking Log2(N,m,p) multicast networks, and give the correct results

Multicast Switching Networks

Non-blocking operation of log/sub 2/(N.m.p.) multicast switching networks is considered. A modified algorithm proposed Tscha and Lee (1992) and by Danilewicz and Kabacinski (see IEEE International Conference on Communications ICC 2000, New Orleans, LA, USA, p.1440-4, 2000) is used for setting up connections. Conditions under which log/sub 2/(N.m.p.) switching networks are non-blocking in the wide-sense are derived and proved. It is shown that wide-sense non-blocking log/sub 2/(N.m.p.) multicast switching networks require less vertically stacked copies of log/sub 2/(N.m.l.) networks and less 2/spl middot/2 switches than multi-log/sub 2/N networks considered by Danilewicz et al.

Comments on "Wide-sense nonblocking multicast Log/sub 2/(N,m,p) Networks"

A new control algorithm for log2(N, 0, p) switching networks composed of 2 x 2 switching elements has been proposed recently. Under this algorithm, log2(N,0,p) switching networks with even number of stages are wide-sense nonblocking (WSNB) if p is the same as for the rearrangeable nonblocking (RNB) one. The considerred algorithm and WSNB conditions did not take into account crosstalk constraint, which is an important factor in photonic switching. This paper enhanced this algorithm to the case when crosstalk in the switching fabric is not allowed. WSNB conditions for this enhanced algorithm are also derived. It is shown, that the number of planes required is less than those derived earlier in other papers for WSNB multiplane banyan- type switching fabrics under crosstalk constraint. Under this algorithm, log2( N,0,p) switching networks with odd number of stages and with zero crosstalk are WSNB if p is the same as for RNB one.

Log/sub 2/(N.m.p) broadcast switching networks

Performance evaluation of the MOQ switch recently proposed by us is discussed in this paper. In the MOQ switch both the switch fabric and buffers can operate at the same speed as input and output ports. This solution does not need any speedup in the switch fabric as well as any matching algorithms between inputs and outputs. The description and the first evaluation were presented earlier. In this paper new performance measures for the proposed MOQ switch are evaluated. The simulation studies have been carried out for switches of capacity 4times4, 8times8, 16times16 and 32times32, and under different traffic patterns. The simulations results are also compared with OQ switches and VOQ switches of the same sizes and under different scheduling algorithms: iSLIP, PIM, iRRM, MMRRS, HRRM

Wide-Sense Nonblocking Multiplane Photonic Banyan-Type Switching Fabrics With Zero Crosstalk

In this article we present the new algorithm Maximal Size Matching with Permanent Selection (MSMPS). This algorithm offers high efficiency with minimal MTD (Mean Time Delay). This algorithm based on permanent connections between inputs and outputs. When at least two connections without packets to send are found (empty connections), algorithm tries to convert them into better matching with the longest VOQ from the available. Simulations confirm that for large load our algorithm provides better efficiency than other algorithms.

Performance evaluation of the multiple output queueing switch under different traffic patterns

In this article, we introduce a new space-division optical switching fabric architecture based on baseline switching networks. The new structure is built from optical switching elements (OSE) 2 × 2, 3 × 3, 2 × 3, and 3 × 2. The new structure is called the log2 N-1 switching network and consists of fewer numbers of active and passive optical elements than traditional baseline switching networks composed of symmetrical OSEs. In the paper, we investigate space-division multiplane strict-sense and rearrangeable log2 N-1 nonblocking switching networks and compare these with space-division multiplane baseline switching networks. The new structure has lower cost than other architectures for strict-sense nonblocking (SSNB) conditions and for rearrangeable (RNB) networks with odd number of stages. For RNB networks, when the number of stages is even, the cost of the multiplane log2 N-1 optical switching network is equal to or higher than traditional networks.