An accurate, tractable, analytic cache model for time-shared systems is presented, which estimates the overall cache miss-rate of a multiprocessing system with any cache size and time quanta. The input to the model consists of the isolated miss-rate curves for each process, the time quanta for each of the executing processes, and the total cache size. The output is the overall miss-rate. Trace-driven simulations demonstrate that the estimated miss-rate is very accurate. Since the model provides a fast and accurate way to estimate the effect of context switching, it is useful for both understanding the effect of context switching on caches and optimizing cache performance for time-shared systems. A cache partitioning mechanism is also presented and is shown to improve the cache miss-rate up to 25% over the normal LRU replacement policy.