A global virtual time (GVT) estimation algorithm, called pGVT, is designed for time warp systems that operate in an environment where reliable and first in, first out message delivery is not guaranteed. As a result, pGVT relies on message acknowledgment. A central GVT manager process calculates GVT values from information reported by the local processes. The key issue that the author is trying to solve is accurate GVT estimation with minimum reports from the local processes. The idea is that the local processes decide for themselves when to report new GVT information, instead of asking the GVT manager. A statistical method is used to assist the local processes in deciding. The method uses two statistical values. One is the average GVT increment for the last k increases of the GVT, δGVT, and the other is the ratio of the time for a message to be sent and acknowledged to the GVT manager and the average time between successive GVT broadcasts. A local process reports its local GVT ( LGVT ) only when a straggler message is received or the last broadcast GVT approaches the current LGVT, that is, whenever  GVT + K * δGVT ≥ LGVT  holds. Effectively, only those local processes that are executing on or near the critical path will report to the GVT manager.