Logical time: capturing causality in distributed systems

Causality is vital in distributed computations. Distributed systems can determine causality using logical clocks. Human beings use the concept of causality to plan, schedule, and execute an enterprise, or to determine a plan´s feasibility. In daily life, we use global time to deduce causality from loosely synchronized clocks such as wrist watches and wall clocks. But in distributed computing systems, the rate of event occurrence is several magnitudes higher, and the event-execution time several magnitudes smaller. If the physical clocks in these systems are not synchronized precisely the causality relation between events cannot be captured accurately. However, distributed systems have no built-in physical time and can only approximate it. This article presents a general framework of a system of logical clocks in distributed systems and discusses three methods: scalar, vector and matrix, for implementing logical time in these systems