How to Calculate Miss Rate of Direct-mapped Cache

Optional: Performance Metrics (for AMAT)

How to Calculate Miss Rate of Direct-Mapped Cache

In computer architecture, the efficiency of a cache memory system is primarily determined by how frequently the processor can find the data it needs within the high-speed cache rather than accessing the slower main memory. For a direct-mapped cache, where each block of main memory maps to exactly one cache line, calculating the miss rate is a fundamental step in performance analysis.

The Miss Rate Formula

The miss rate represents the fraction of memory accesses that are not found in the cache. It is calculated using the following formula:

Miss Rate = (Number of Misses / Total Memory Accesses) × 100%

Conversely, the Hit Rate is the fraction of accesses found in the cache:

Hit Rate = 1 – Miss Rate

Input Definitions

• Total Memory Accesses: The total number of times the processor attempts to read or write data from/to memory. This is often the sum of hits and misses.
• Cache Misses: The count of accesses where the requested data was not present in the cache, requiring a fetch from the lower-level memory.
• Hit Time: The time required to access data in the cache (usually 1-2 clock cycles for L1 cache).
• Miss Penalty: The additional time required to fetch a block from main memory when a miss occurs.

Example Calculation

Consider a CPU executing a program that generates 5,000 memory references. Performance counters indicate that 250 of these references resulted in cache misses.

To find the miss rate:

1. Identify Total Accesses = 5,000
2. Identify Miss Count = 250
3. Calculation: 250 / 5,000 = 0.05
4. Convert to percentage: 0.05 × 100 = 5% Miss Rate

This implies a 95% Hit Rate.

Average Memory Access Time (AMAT)

While the miss rate is a percentage, the actual impact on performance is measured in time (cycles or nanoseconds), known as Average Memory Access Time (AMAT). The formula depends heavily on the miss rate calculated above:

AMAT = Hit Time + (Miss Rate × Miss Penalty)

Using the example above, if the Hit Time is 1 cycle and the Miss Penalty is 100 cycles:

AMAT = 1 + (0.05 × 100) = 1 + 5 = 6 cycles.

Why Direct-Mapped Caches Have Higher Miss Rates

In a direct-mapped cache, a specific memory block can only be stored in one specific cache line determined by the index bits of the address (Address Modulo Cache Blocks). If multiple active memory blocks map to the same cache line, they will repeatedly evict each other. This phenomenon is known as a conflict miss.

While direct-mapped caches are simpler and have faster hit times than set-associative caches, they generally suffer from higher conflict miss rates, making the calculation and monitoring of these rates crucial for system optimization.