On the surface these methods do the same thing in Java; Thread.yield(), Thread.sleep(0), Object.wait(0,1) and LockSupport.parkNanos(1) They all wait a sort period of time, but how much that is varies a surprising amount and between platforms.

Timing a short delay

The following code times how long it takes to repeatedly call those methods.

import java.util.concurrent.locks.LockSupport;

public class Pausing {
    public static void main(String... args) throws InterruptedException {
        int repeat = 10000;
        for (int i = 0; i < 3; i++) {
            long time0 = System.nanoTime();
            for (int j = 0; j < repeat; j++)
                Thread.yield();
            long time1 = System.nanoTime();
            for (int j = 0; j < repeat; j++)
                Thread.sleep(0);
            long time2 = System.nanoTime();
            synchronized (Thread.class) {
                for (int j = 0; j < repeat/10; j++)
                    Thread.class.wait(0, 1);
            }
            long time3 = System.nanoTime();
            for (int j = 0; j < repeat/10; j++)
                LockSupport.parkNanos(1);
            long time4 = System.nanoTime();

            System.out.printf("The average time to yield %.1f μs, sleep(0) %.1f μs, " +
                    "wait(0,1) %.1f μs and LockSupport.parkNanos(1) %.1f μs%n",
                    (time1 - time0) / repeat / 1e3, (time2 - time1) / repeat / 1e3, 
                    (time3 - time2) / (repeat/10) / 1e3, (time4 - time3) / (repeat/10) / 1e3);
        }
    }
}

On Windows 7

The average time to yield 0.3 μs, sleep(0) 0.6 μs, wait(0,1) 999.9 μs and LockSupport.parkNanos(1) 1000.0 μs
The average time to yield 0.3 μs, sleep(0) 0.6 μs, wait(0,1) 999.5 μs and LockSupport.parkNanos(1) 1000.1 μs
The average time to yield 0.2 μs, sleep(0) 0.5 μs, wait(0,1) 1000.0 μs and LockSupport.parkNanos(1) 1000.1 μs

On RHEL 5.x

The average time to yield 1.1 μs, sleep(0) 1.1 μs, wait(0,1) 2003.8 μs and LockSupport.parkNanos(1) 3.8 μs
The average time to yield 1.1 μs, sleep(0) 1.1 μs, wait(0,1) 2004.8 μs and LockSupport.parkNanos(1) 3.4 μs
The average time to yield 1.1 μs, sleep(0) 1.1 μs, wait(0,1) 2005.6 μs and LockSupport.parkNanos(1) 3.1 μs

In summary

If you want to wait for a short period of time, you can't assume that all these methods do the same thing, nor will be the same between platforms.