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BRICK: A Novel Exact Active Statistics Counter ArchitectureAuthor: Nan Hua, Bill Lin, Jun (Jim) Xu, Haiquan (Chuck) ZhaoPublisher: ANCS’08Presenter: Yun-Yan ChangDate:2011/02/23

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Introduction Design of BRICK

◦ Basic idea◦ Rank indexing◦ Handling increment◦ Handling overflow

Performance evaluation Conclusion

Outline

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Present a novel active statistics counter architecture called BRICK (Bucketized Bank Indexed Counter).

BRICK◦ Store variable width counters entirely in SRAM

while supporting fast access.◦ Exploit statistical multiplexing technique.

Group a fixed number of randomly selected counters into a bucket by an indexing scheme.

Introduction

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◦ Figure 1 shows the effect of statistical multiplexing Each horizontal layer of bricks corresponds to a

bucket The length of bricks corresponds to the real counter

widths.

Introduction

Figure 1: BRICK wall (conceptual baseline scheme)

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Randomly bundle N counters into h buckets, B1, B2, ..., Bh, where each bucket holds k counters and N = hk.

Basic idea

Figure2: (b) Bucket structure

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When access the yth counter, apply the index y to permuted index i by a permutation function π : {1...N} →{1. . .N}.

The corresponding counter Ci can then be found in the lth bucket Bl , where l = .

Basic idea

Figure2:(a) index permutation

ki

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Each bucket contains p sub-counter arrays A1, A2, ..., Ap to store the 1st, 2nd, ..., pth sub-counters.

◦ Assume the worst-case counter width is divided into p parts, which refer to as “sub-counters".

Basic idea

Figure 3: (a) Within a bucket, segmentation of variable-width counters into sub-counter arrays.

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For each counter, use indexing scheme to identify locations of sub-counters across the different sub-counter arrays.

Rank indexing

Figure3: (b) Compact representation of variable-width counters.

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Algorithm for get the value of ith counter.

Rank indexing

※ rank(Ij, a): return the number of 1 in bit-string Ij, count form Ij[1] to Ij[a].

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Increment algorithm

Handle increment

※ varshift(s, j, c): bit-string s, start from jth bit, shift right c times.

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Handle increment

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※ varshift(s, j, c): bit-string s, start from jth bit, shift right c times.

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Extend data structure with full-size buckets F1, F2, ... , FJ , each bucket Ft is organized as k full-size counters.

◦ When a bucket overflow occurs for some Bl , the next available full-size bucket Ft is allocated to store its k counters, where t is just +1 of the last allocated full-size bucket.

◦ Use a flag fl to set to indicate the overflowed buckets.

◦ The index of the full-size bucket Ft is stored in a field labeled t, which is associated with Bl .

Handle overflow

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Memory costs and lower bounds

Sl :memory cost of each bucket S : total memory cost

◦ Lower bound of memory

Performance evaluation

NMlg (1) MCi

Ni 1 (2)

Ci: denote counter and counter valueM: sum of counter valuesN: number of counters

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Numerical results with various configurations

The number of entries decreases exponentially as we go to the higher sub-counter arrays. (main compression)

Performance evaluation

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Numerical results with various configurations

The amount of extra storage only decreases slightly with additional levels in the BRICK implementation.

Performance evaluation

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Performance evaluation

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Results for real Internet trace USC: around 18.9 million packets, 1.1 million flows. UNC: around 32.6 million packets, 1.24 million flows.

Performance evaluation

Worst-case counter width

Total storage requirementUSC UNC

Naïve 25 bits/counter 3.85 MB 4.40 MBBRICK 10 bits/counter 1.39 MB 1.63 MB

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BRICK is SRAM-efficient yet allows for fast counter lookup and increment.

Index filed only requires small number of extra bits per bucket.

Conclusion