Technical Report

It is usually believed that the blocking probability of a switching network will increase with the increase of the failure rate of building components (e.g., links, switching elements, etc.) in the switch. In this report, we propose a mathematical model for evaluating the maximum blocking probability of optical banyan networks on vertical stacking when the link failures are considered. Based on our model, some surprising results are observed. We found that when the link failure rate is significantly low (say, less than 0.01), the blocking probability of a banyan-based switching network will increase with the increase of the link failure rate. Surprisingly, however, if we increase the link failure rate to be larger than some value (say, 0.01), the blocking probability of the network will decrease rather than increase with the increase of the link failure rate. This decreasing trend of blocking probability with the increase of the link failure rate will continue until the link failure rate reaches a threshold value (say, 0.16). After reaching the minimum blocking probability at a threshold value of link failure rate, the blocking probability of the network will increase again with the increase of link failure rate. As far as we know that for switching networks, such fluctuating variation of blocking probability with the increase of component (link here) failure rate is firstly observed and deserves special attention in switch design. I. Vertically Stacked Optical Banyan Networks (VSOB) A large-scale optical switch is usually composed of numerous basic switching elements (SEs) grouped in multiple stages along with the optical links arranged in a specified interconnection pattern. The basic SEs and the interconnecting optical links in an optical switching device will perform a pre-defined switching function such that the optical flow at an input can be transported to a specific output of the switch. Here we refer to the interconnection pattern of the optical links, the basic SEs, and the input/output ports of the switch, as network of the optical switch. The basic 2×2 SE in optical switching systems is usually a directional-coupler (DC) that is made of two waveguides close to each other [1][2][3]. DC can pass multiple-wavelength optical signals and this makes it ideal for optical cross-connects (OXCs). A large-scale optical switch is usually composed of numerous basic switching elements (SEs) grouped in multiple stages along with the optical links arranged in a specified interconnection pattern. The basic SEs and the interconnecting optical links in an optical switching device will perform a pre-defined switching function such that the optical flow at an input can be transported to a specific output of the switch. Here we refer to the interconnection pattern of the optical links, the basic SEs, and the input/output ports of the switch, as network of the optical switch. The basic 2×2 SE in optical switching systems is usually a directional-coupler (DC) that is made of two waveguides close to each other [1][2][3]. DC can pass multiple-wavelength optical signals and this makes it ideal for optical cross-connects (OXCs). It is notable that DC suffers from an intrinsic crosstalk problem [1][4], in which a portion of optical power in one waveguide of a DC will be coupled into the other waveguide unintentionally when two input optical flows pass through the DC at the same time no matter it is in a BAR or CROSS status. This undesirable coupling effect is called firstorder crosstalk, which may propagate downstream stage by stage, leading to a higher order crosstalk in each downstream stage with a decreasing magnitude. A cost-effective solution to the crosstalk problem is to make sure that only one signal passes through a DC at a time such that the first-order crosstalk can be eliminated. The topology of banyan type networks [5][6][7][8] is a very popular structure for building communication switches. This class of networks is characterized by having a small depth, absolute loss uniformity (each path goes through exactly the same number of SEs) and a simple switch setting ability (self-routing). These characteristics have made the banyan topology promising in serving as the architecture for the DC-based optical switches because the amount of loss and attenuation experienced by an input optical flow is proportional to the number of DC’s it traverses. However, with the banyan topology only a unique path can be found from each network input to each network output, in which the network is simply degraded as a blocking one. To deal with this situation, it is an effective approach of keeping the whole network nonblocking by vertical stacking multiple copies of an optical banyan network [9]. This class of networks is called vertically stacked optical banyan (VSOB) networks (Fig.1), which preserves the nonblocking characteristic while neither increasing the number of stages nor sacrificing the selfrouting property intrinsically possessed by the banyan network structures. Fi ne In this report, we fo each SE (this is also re for the VSOB networ number of planes req that the adoption of th the hardware cost. It h a network that does n initiating a compromis Due to the increasin large mesh WDM n probability of compo networks in the curren probability of VSOB n O u tp u ts B a n y a n n e tw o r k P la n e 1 B a n y a n n e tw o r k P la n e 2 B a n y a n n e tw o r k P la n e m : . In p u ts