Distributed time-stamping enables tolerance to distributed denial of service attacks. However, they involve high cost due to the requirement that all time-stamping units (TSUs), whose number could be numerous, must be audited by trusted third parties. We propose a distributed multi-generation time-stamping scheme with predictable expectation time of notary and minimizing the cost of administration. The scheme is called the "Time-Stamping Authority Grid" with "K = L + M among N in G generations scheme", where K is the number of issued requests, L is the number of requests to reliable TSUs, M is the number of requests to randomly chosen TSUs, N is the total number of TSUs, and G is the number of the generation that the requests are propagated. Our scheme solves the problems involving both centralized and previous distributed time-stamping schemes by constructing a peer-to-peer network of TSUs, thereby attaining the scalability and dramatically reduced cost.