Nonblocking conditions for Clos fabrics with non-uniform switch radixes

Datacenter networks (DCNs) evolve over years and so comprise switches from different generations. Thus, each stage/layer of the Clos fabric may consist of switches with varying radixes (i.e., different port counts), leading to non-uniform stages. While optical circuit switches are increasingly deployed in DCNs to enhance transmission capacity and energy efficiency, the nonblocking condition, crucial for determining the performance of circuit-switched networks, has been established only for Clos fabrics with uniform stages. This study extends the nonblocking condition to Clos fabrics with non-uniform stages. To facilitate practicality, we formulate the condition using integer linear programming (ILP). Using our novel, to our knowledge, condition, we quantitatively demonstrate how much the nonblocking property is compromised under two practical scenarios, random link failures and network expansion, which would break network uniformity. In particular, we reveal that network expansion, common in DCN evolution, could significantly undermine the nonblocking property. Additionally, we assess the computational efficiency of our ILP formulation, which can successfully evaluate the nonblocking property of a large Clos fabric accommodating 32K terminals/uplinks in just 19 min.