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The size of a single-hop cross-bar fabric is still limited by the technology, and the fabrics available on the market do not exceed the terabit capacity. A multihop fabric such as Clos network provides the higher capacity by using the smaller switching elements (SE). When the traffic load is balanced over the switches in a middle stage, all the traffic would get through the fabric, as long as the switch outputs are not overloaded. However, the delay that packets experience through the Clos switch depends on the granularity of flows that are balanced. We examine the maximum fabric utilization under which a tolerable delay is provided for various load balancing algorithms, and derive the general formula for this utilization in terms of the number of flows that are balanced. We show that the algorithms which balance flows with sufficiently coarse granularity provide both high fabric utilization and delay guarantees to the most sensitive applications. Since no admission control should be performed within the switch, the fast traffic-pattern changes can be accommodated in the proposed scalable architecture.