Speculative prefetching has been proposed to improve the response time of network access. Previous studies in speculative prefetching focus on building and evaluating access models for the purpose of access prediction. This paper investigates a complementary area which has been largely ignored, that of performance modeling. We analyze the performance of a prefetcher that has uncertain knowledge about future accesses. Our performance metric is the improvement in access time, for which we derive a formula in terms of resource parameters (time available and time required for prefetching) and speculative parameters (probabilities for next access). We develop a prefetch algorithm to maximize the improvement in access time. The algorithm is based on finding the best solution to a stretch knapsack problem, using theoretically proven apparatus to reduce the search space. An integration between speculative prefetching and caching is also investigated.