可以使用Java中的ConcurrentLinkedQueue作为任务队列，每个任务都可以封装成一个Runnable对象，然后在另一个线程中执行这些任务。为了按照公平原则执行任务，可以在队列中使用Iterator遍历任务，并且为每个任务设置一个权重值，权重越高的任务会被先执行。

示例代码如下：

import java.util.Comparator;
import java.util.concurrent.ConcurrentLinkedQueue;
import java.util.concurrent.atomic.AtomicInteger;

public class FairTaskExecutor {

  private final ConcurrentLinkedQueue tasks = new ConcurrentLinkedQueue<>();
  private final AtomicInteger sequence = new AtomicInteger(0);

  /**
   * 添加任务到队列
   * @param task 任务
   * @param priority 权重值
   */
  public void addTask(Runnable task, int priority) {
    taskPriority = sequence.getAndIncrement() * 100 + priority;
    tasks.add(new PriorityRunnable(task, taskPriority));
  }

  /**
   * 执行任务
   */
  public void executeTasks() {
    Runnable task;
    while ((task = tasks.poll()) != null) {
      task.run();
    }
  }

  /**
   * 带有优先级的Runnable
   */
  private class PriorityRunnable implements Runnable, Comparable {
    private final Runnable task;
    private final int priority;

    public PriorityRunnable(Runnable task, int priority) {
      this.task = task;
      this.priority = priority;
    }

    @Override
    public void run() {
      task.run();
    }

    @Override
    public int compareTo(PriorityRunnable other) {
      return Integer.compare(priority, other.priority);
    }
  }

}

使用示例：

// 创建任务执行器
FairTaskExecutor executor = new FairTaskExecutor();

// 添加任务
executor.addTask(() -> System.out.println("Task 1 - Low Priority"), 1);
executor.addTask(() -> System.out.println("Task 2 - High Priority"), 10);
executor.addTask(() -> System.out.println("Task 3 - Medium Priority"), 5);

// 按照公平原则执行任务
executor.executeTasks();
``