What is the happened-before relation?

We’re used to thinking of time as a total order: given two events, one happened before the other. At my desk, I sit down before I turn on my computer. All the things happening to you have a total order, because you’re a timeline. Sitting down at my desk and turning on my computer happened at the same place (my desk). Because of this, they have a total order. This total order is nicely tracked by the clock on my desk. If you compared the reading of that clock at both events, you would find that the time at which I sat at my desk was less than the time I turned on my computer.

But once we look at “distributed systems”, where events can happen in multiple places, it gets weird. Do I sit down at my desk before Eve sits down at hers in New York? It seems hard to tell. Distributed systems literature says it’s not necessarily the case that one happened before the other. It’s not just that it’s hard to tell whether I sat down before Eve: the events can happen “concurrently”, or “at the same time”.

What does “concurrent” mean? It does not mean that “the clock on my wall read the same as the clock on the New York office wall”. “Time” in distributed systems is not about wall clocks!

Instead, “time” in distributed systems is all about causality. Let’s say I sit down, then phone Eve; and Eve only sits down after I call her. We then know that I sat down first, because I caused Eve to sit down (if you squint). Typically, cause-and-effect is modelled as “message-passing”. If I send Eve a message, then my sending the message causes Eve to receive the message. In the “distributed systems” definition, Jim calling Eve “happened before” Eve picking up.

So we have two ways to determine whether A happened before B:

  1. A and B happened at the same place, and the wall clock says A happened before B.
  2. A was a “send message”, and B was the corresponding “receive message”.

Let’s apply this to our example, where we have four events:

Because A and B happened in the same place (Jim’s desk), we can use Rule 1 to say that A happened before B. Because B was a “send message” and C was a “receive message”, we can use Rule 2 to say that B happened before C. Because C and D happened in the same place (Eve’s desk), we can use Rule 1 again to say that C happened before D.

So, A happened before D! Well, actually, we need one more rule for this:

  1. (Transitivity) If A happened before B, and B happened before C, then A happened before C.

We now have all the pieces of the “happened-before relation” (as originally defined by Leslie Lamport). This relation is supposed to capture our sense of time, or our sense of causality, and basically asserts that time and causality are the same things.

To visualize such events in “time”, we usually draw diagrams like this:

message-passing processes

Here, P, Q and R are “processes”. In our example, “Jim’s desk” and “Eve’s desk” are processes: things fixed in position. The arrows are messages being passed between processes. In our example, Jim calling Eve would be modelled as a message.

It’s important to understand that these “processes” and “messages” are really not specific to computing! The happened-before relation is more a model of physics. Computers, being part of the same world, are of course subject to the same rules.

Tagged #concurrency, #programming, #computer-science.

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