Linearizable Read/Write Objects

We study the cost of using message passing to implement linearizable read write objects for shared memory multiprocessors under various assumptions on the available timing informa tion We take as cost measures the worst case response times for performing read and write operations in distributed implementations of virtual shared memory consisting of such objects and the sum of these response times It is assumed that processes have clocks that run at the same rate as real time and are within of each other for some known precision constant All messages incur a delay in the range d u d for some known constants u and d u d For the perfect clocks model where clocks are perfectly synchronized i e and every message incurs a delay of exactly d we present a linearizable implementation which achieves worst case response times for read and write operations of d and d respectively is a trade o parameter which may be tuned to account for the relative frequencies of read and write operations This implementation is optimal with respect to the sum of the worst case response times for read and write operations We next turn to the approximately synchronized clocks model where clocks are only ap proximately synchronized i e and message delays can vary i e u Our rst major result is the rst known linearizable implementation for this model which achieves worst case response times of less than d u minf ug and d u for read and write op erations respectively under a mild restriction on the trade o parameter u d is any arbitrary constant such that minf u d ug This implementation employs a novel use of approximately synchronized clocks in order to utilize the lower bound on message delay time and achieve bounds on worst case response times that depend on the message delay uncertainty u For a wide range of values of u these bounds improve upon previously known ones for implementations that support consistency conditions even weaker than linearizability Our next major result is a lower bound of d minf ug on the sum of the worst case response times for read and write operations for the approximately synchronized clocks model This bound applies to linearizable implementations possessing some natural symmetry properties the bound is shown using the technique of shifting executions Corresponding lower bounds but with no symmetry assumptions are shown on the individual worst case response times for read and write operations Our bounds for the approximately synchronized clocks model extend naturally to the im perfect clocks model where clocks may be arbitrarily far from each other i e