over the same interval skew t is a variable representing the hit rates of index values representing the ratio of frequently hit values to values that are hit infrequently or not at all action t is a variable that will be used to incorporate the result of tests into a tentative action taken by the system and refaction t is a variable that will be used to incorporate the action into a refined action taken by the system both action and refaction are intermediate mathematical variables that are only actually manifest in the subsequent update of the value of cache size at times t u2212 2 dt and u2212 dt all of the algorithm variables are defined as 0 an increment value for triggering measurement of variables is fixed and is denoted dt dt can be in units of time cycles or instructions measurement times are cache size c is updated every dt interval the value c t is that held over the interval t u2212 dt t the value c t dt is that held over the interval t t dt and so on for example c t dt is computed instantaneously at times t 0 lt c min lt c t lt c max also c min lt c max the miss rate m t is the rate per dt of references to main memory caused by cache misses m t is deduced from data collected over the interval t u2212 dt t performance threshold m max is a target performance limit value for m skew t is a binary signal representing.