# ADAPTIVE DISTRIBUTED CACHING WITH MINIMAL MEMORY USAGE

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3 OBJ-ID PROXY LAST AVG HITS Proxy[5] Proxy[4] Proxy[1] Proxy[2] Proxy[1] Proxy[7] Proxy[4] In our previous algorithm, each newly created entry will remain in the mapping table forever, leading to a growing mapping table. Depending on the amount of unique requested objects, the system will eventually run out of memory. In the case of a limited-size mapping table, it will fill up over time and existing entries will sooner or later be replaced by new requests. As described earlier, we use the average time between two requests to decide whether an object should be stored or discarded. Therefore, each newly created entry should stay long enough in the mapping table so that a repeat request can occur to allow the algorithm to compute the average request time New Algorithm Figure 3. A Sample Single Table To deal with the above problem, we found it useful to part the mapping table into a section for objects that are requested more than once and another one for new objects that are only requested once. The underlying idea can be stated as follows Single Table The single table is used to simply keep track of the current flow of requests. Each unknown object will receive a new entry on the top of the table and displacing the oldest entry at the bottom of the table the well-known LRU algorithm. It is a requirement of the single table that it is large enough so that requests with at least two hits can occur. Preliminary studies have shown that the minimum table size is highly dependent on the experienced request pattern and more work is necessary to characterize this relationship. When an existing entry in the mapping table experiences another hit, the time difference between the two requests will be used as a first approximation of the average object request frequency and the object will move from the single table to the multiple table (described below). The LAST column represents the local time value, for the last time when the specific object was requested while the AVG value represents the average time between two requests of the same type (Figure 3). OBJ-ID PROXY LAST AVG HITS Proxy[8] This Proxy[1] This Proxy[4] Proxy[8] Proxy[4] Figure 4. A Sample Multiple Table Multiple Table The multiple table is also restricted in its size and contains only objects that were requested more than once ordered by their average request time. Once the table is filled, newly arriving objects from the single table have to have a lower average value than the worst case currently residing in the table before it will be placed at the appropriate position. Removed objects from the multiple table will be placed into the single table as a regular entry, giving it the chance to be hit again later. The forwarding address for elements with the THIS value marks objects for which this proxy itself is responsible when future requests arrive and unresolved queries need to be forwarded to the origin server. The general structure of the multiple table is the same as that of the single table and it should be pointed out that the table is always ordered in ascending order of the fourth column (average request time). This order allows the simple identification of the object with the worst average time and quick insertions/deletions based using binary search Cached Table The cached table in a proxy within the ADC architecture keeps track of all currently cached objects there. This table is very similar to the previously described multiple table, with the exception that the table entries represent actually stored objects. Similar to the multiple table, this table is also ordered by the average request value in column four and new objects have to outperform at least the worst case in (the last row) the table and will be placed in the appropriate position within it. Elements that drop out of the bottom of this table move back to the multiple table which gives them the chance to be hit again in the near future or to drop out completely over time Noisy Hits Splitting up the mapping table from our previous work into a single and a multiple table has overcome the obstacle of limited resources but has introduced a new problem of Noisy Hits. When we order the mapping table based on the average request time, an object that has been requested only two times but within a very short time frame and never again will be wrongly placed into the mapping table (or even the caching part in the worst case)

4 and uses up resources that could otherwise be assigned to more frequently requested objects. Different approaches have been tried out to filter out the noisy hits. When considering simplicity of the algorithm and computational cost, we decided that each object has to be hit at least twice to enter the multiple table, and at least three times before moving them into the caching table. With this approach, we are losing a small percentage of the overall hit-rate by compromising objects that were requested only once or twice, but it allows the algorithm to focus on the more important, well-established objects. 4. EXPERIMENTATION To validate/verify the new algorithm described above, we ran multiple simulations over a set of artificially created request patterns based on the polygraph test bed [15] and compared the results to those of a common hashing based algorithm ZIPF Test Set In our previous paper [3], we introduced a simple artificially created request pattern based on ZIPF distribution over a set of 10,000 unique objects with 500,000 requests. We simulated a set of 10 proxies with a total cache size of 1,000 objects (each proxy is able to store 100 objects). For the simulation with the ZIPF data, we select 1000 entries as the average multiple table size, a value that was chosen based on preliminary studies, and compare the results of ADC to the two hashing algorithms. Figure 8 shows that for our own ZIPF distribution, the ADC algorithm is well able to compete with both hashing approaches POLYGRAPH Test Set For the second session of experimentations, we tried to create artificial data that represents closer the request patterns experienced on a real system and used the widely used Polygraph tool to build a file with 2.3 million requests. Figure 5 shows the source code of the polygraph language. We used the standard Polymix 4 file without the initial fill-phase. Essentially, the final request file pattern contains two peak request rates over a set of approximately 1.5 million requests with some request gaps in between Hit-Rate We ran the Polymix 4 file against ADC and both hashing algorithms, and describe in this section the observed hit rate. REQUESTS HITS [%] ALGORITHM COMPARISON HASH ALL HASH SELL ADC HIT RATE Figure 5. Algorithm comparison /* PolyMix-4 workload */ TheBench.peak_req_rate = 100/sec; FillRate = TheBench.peak_req_rate; ProxyCacheSize = 1MB; 301 Figure 6. Polygraph Settings HIT - RATE - POLYGRAPH MA-5000 MA AVERAGE Figure 6 shows the hit rates in three sections. The first part covers the hashing algorithm with always caching; the second part the hashing with selective caching and the last part the ADC based approach. All three sections come with three graphs, a moving average over that 5,000 and 50,000 and all requests. It is clear that the updated version of the ADC algorithm (with single, multiple and caching tables) outperforms both hashing algorithms over the set of 2.3 million requests. It is also clear that the new ADC algorithm requires a certain learning phase, which comes with an additional overhead as can be observed in the slowly increasing graph of the total average hit-rate Hops Rate & Execution Time In the second part of this section we take a look at the average hops rate, which represents the effort to search for a specific cached object. One hop is defined by the request Figure 7. Hit Rate Polygraph

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