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Traffic splitting is a required functionality in networks, for example forload balancing over paths or servers, or by the source's access restrictions.The capacities of the servers (or the number of users with particular accessrestrictions) determine the sizes of the parts into which traffic should besplit. A recent approach implements traffic splitting within the ternarycontent addressable memory (TCAM), which is often available in switches. It isimportant to reduce the amount of memory allocated for this task since TCAMsare power consuming and are often also required for other tasks such asclassification and routing. Recent works suggested algorithms to compute asmallest implementation of a given partition in the longest prefix match (LPM)model. In this paper we analyze properties of such minimal representations andprove lower and upper bounds on their size. The upper bounds hold for generalTCAMs, and we also prove an additional lower-bound for general TCAMs. We alsoanalyze the expected size of a representation, for uniformly random orderedpartitions. We show that the expected representation size of a random partitionis at least half the size for the worst-case partition, and is linear in thenumber of parts and in the logarithm of the size of the address space.

Codes for Load Balancing in TCAMs: Size Analysis