queued-axios.js

const axios = {
  get: (...args) => new Promise((resolve, reject) => {
    console.log('called', args.join(', '));
    setTimeout(() => resolve(args.join(', ')), 1500);
  }),
};

const api = {
  get: (...args) => new Promise((resolve, reject) => {
    queue.push(async () => {
      try {
        resolve(await axios.get(...args)); // 本物
      } catch (e) {
        reject(e);
      }
    });
    console.log('queued', args.join(', '));
    checkQueue();
  }),
};

const queue = [];
let current = null;  // 実行中の関数を入れとく

async function checkQueue() { // キューを頭から消化していく
  console.log('checkQueue');
  if (current || !queue.length) return;
  current = queue.shift();
  await current();
  current = null;
  checkQueue();
}

async function main() {
  const p1 = api.get('/hoge', 1);
  const p2 = api.get('/fuga', 2);
  p1.then(r1 => console.log('got', r1));
  p2.then(r2 => console.log('got', r2));
}

main();