Question

In a two-level cache system, the access times of L₁ and L₂ caches are 1 and 8 clock cycles, respectively. The miss penalty from the L₂ cache to main memory is 18 clock cycles. The miss rate of L₁ cache is twice that of L₂. The average memory access time (AMAT) of this cache system is 2 cycle. The miss rates of L₁ and L­₂ respectively are:

1. 0.111 and 0.056
2. 0.056 and 0.111
3. 0.0892 and 0.1784
4. 0.1784 and 0.0892

Answer 1

Correct Answer - Option 1 : 0.111 and 0.056

Data:

Access time of L₁ = T₁ = 1 clock cycle

Access time of L₂ = T₂ = 8 clock cycle

L₂ miss penalty = T₃ = 18 clock cycle

L₁ miss rate = 2 × L₂ miss rate

Average memory access time = AMAT = 2 clock cycle

Let, L₂ miss rate = a

∴ L₁ miss rate = 2a

Formula:

 AMAT = (T₁ + 2a × T₂ + 2a × a × T₃)

Calculation:

2 = 1 + 2a × 8 + 2a × a × 18

2 = 1 + 16a + 36a²

36a² + 16a -1 = 0

36a² + 18a – 2a + 1 = 0

18a (2a + 1) – 1(2a + 1) = 0

\(a = \frac{{ - 1}}{2},\frac{1}{{18}}\)

So, miss rate of L₂ = 0.056 and Miss rate of L₁ = 0.111