可以用Promise实现。每个任务的结果用一个Promise保存，如果A依赖B则在B resolve之后才开始A.

const tasks = {
  a: {
    dep: ["b", "c"],
    run: (resultB, resultC) => resultB + resultC
  },
  b: {
    run: () => `B`
  },
  c: {
    dep: ["d"],
    run: resultD => `C` + resultD
  },
  d: {
    run: () => `D`
  },
};

const targetStack = [];

function run(taskTree, target, results = {}) {
  if (targetStack.indexOf(target) !== -1) {
    const err = new Error(`recursive dependicies: ${targetStack.concat([target]).join(" <- ")}`);
    targetStack.length = 0;
    throw err;
  }
  targetStack.push(target);
  const deps = (taskTree[target].dep || []).map(
    depName => results[depName] = results[depName] || run(taskTree, depName, results)
  );
  targetStack.pop();
  return Promise.all(deps).then(deps => taskTree[target].run.apply(undefined, deps));
}

run(tasks, "a").then(resultA => console.log(resultA));

(这个代码其实不需要任务是树形，只要求是无环图)

var p1 = new Promise(function (resolve, reject) {
  // ...
});

var p2 = new Promise(function (resolve, reject) {
  // ...
  resolve(p1);
})

这样p2就会在p1之后执行了。
可参考：promise

就是实现一个promise的polyfill么。可以看看一个非常精简的代买实现 promise-lie
如果有看不明白的地方可以交流。