Three Cache Hierarchy

Figure 13: On the x-axis is the size of each cache: $C_1$, $C_2$, and $C_3$. We present the total traffic between $C_1$ and $C_2$ (top-left), the aggregate hit ratio (top-right), and the average response time allowing unlimited bandwidth and free demotions (bottom-left) for a range of per-level cache sizes. In a limited bandwidth scenario ($200$ blocks per second: $2$ times that required if there were no hits or demotions), PROMOTE outperforms DEMOTE significantly (bottom-right).

Increasing the complexity of the hierarchies we study, we now turn to a three-level (three equal size caches) hierarchy.

As in the two-level case, we present detailed results for the first trace P1 in Figure 13. The other traces had similar results but we do not present plots for lack of space.

We observe that for the wide variety of traces and cache sizes, PROMOTE outperforms DEMOTE in three-level caches as well:

Inter-cache Bandwidth Usage: PROMOTE is $2$x more efficient than DEMOTE which uses $105$% ($111$% resp.) more bandwidth between $C_1$ and $C_2$ and $98$% ($113$% resp.) more bandwidth between $C_2$ and $C_3$, when compared to PROMOTE-LRU (PROMOTE-ARC, respectively).

Aggregate Hit Ratio: PROMOTE same as DEMOTE.

Hits in the Highest Cache: PROMOTE achieves $1.5$% and $10$% more hits in the top two caches than DEMOTE for the LRU and ARC variants, respectively.

Average Response Time: When bandwidth is not limited and demotions are free, PROMOTE beats DEMOTE by $0.2$% and $1.3$% on the average response time for LRU and ARC variants, respectively. For a limited bandwidth case, where we allow $200$ blocks per second ($2$x times $1/t_m = 100$), When we average the response time across all cache sizes, we observe that PROMOTE substantially outperforms DEMOTE by achieving lower response times, $5.61$ms (for ARC) and $5.93$ms (for LRU), as compared to DEMOTE with $8.04$ms (for ARC) and $7.57$ms (for LRU), respectively.