The emerging high-capacity optical networks make it urgent to design large-scale flexible mesh optical cross-connect (OXC). Though Clos networks are the theory for building scalable and cost-effective switching fabrics, the nonblocking conditions for flex-grid optical Clos networks without wavelength conversion remain unknown. This paper studies the nonblocking conditions for the flex-grid OXC-Clos network, which is constructed from a number of small-size standard OXCs. We first show that a strictly nonblocking (SNB) OXC-Clos network will incur a high cost, as small-granularity lightpaths may abuse central modules (CMs), rendering them unavailable for large-granularity requests due to frequency conflicts. Hence, we propose a granularity differential routing (GDR) strategy, the idea of which is to restrict the set of CMs that can be utilized by the lightpaths of each granularity. Under the GDR strategy, we investigate two system models, called granularity-port binding and unbinding models, and prove the wide-sense nonblocking (WSNB) conditions. We show that the cost of WSNB network is remarkably smaller than that of SNB network, and find that the granularity-port unbinding model can offer more flexible network-bandwidth utilization compared to the binding model, with a slight cost associated with switching fabrics.

The emerging high-capacity optical networks makes it urgent to design large-scale flexible mesh optical cross-connects (OXCs). Though Clos network is the theory for building scalable and cost-effective switching fabrics, the nonblocking conditions of flex-grid optical Clos networks without wavelength conversion remain unknown. This paper studies the nonblocking conditions for the flex-grid OXC-Clos network, which is constructed from a number of small-size standard OXCs. We first show that a strictly nonblocking (SNB) OXC-Clos network will incur a high cost, as small-granularity lightpaths may abuse central modules, rendering them unavailable for large-granularity requests due to frequency conflicts. We thus propose a granularity differential routing (GDR) strategy, the idea of which is to restrict the set of CMs that can be used by the lightpaths of each granularity. Under the GDR strategy, we investigate two system models, granularity-port binding and unbinding models, and prove the wide-sense nonblocking (WSNB) conditions for OXC-Clos network. We show that the cost of WSNB network is remarkably smaller than that of SNB network, and find that the second model can lead to more flexible network-bandwidth utilization than the first model only at a small cost of switching fabrics.