queue.js

const delay = () => (Math.floor(Math.random() * 6) + 1) * 1000;

const callback1 = () =>
  new Promise((resolve) =>
    setTimeout(() => resolve(console.log({ callback: 1 })), delay())
  );

const callback2 = () =>
  new Promise((resolve) =>
    setTimeout(() => resolve(console.log({ callback: 2 })), delay())
  );

const callback3 = () =>
  new Promise((resolve) =>
    setTimeout(() => resolve(console.log({ callback: 3 })), delay())
  );

const callback4 = () =>
  new Promise((resolve) =>
    setTimeout(() => resolve(console.log({ callback: 4 })), delay())
  );

class QueueProcessingCallback {
  static MAX_CONCURRENTLY_EXECUTING = 5;

  static FIFO = "FIFO";

  static LIFO = "LIFO";

  constructor(type = this.constructor.FIFO) {
    this.poll = 0;
    this.queue = [];
    this.type = type;

    return this;
  }

  debug = () => {
    const { poll, queue, type } = this;

    return console.log({ poll, queue, type });
  };

  flush = () => {
    const {
      constructor: { FIFO, LIFO },
      poll,
      process,
      queue,
      type,
    } = this;
    const { [type]: index } = { [FIFO]: 0, [LIFO]: -1 };
    const [promise] = queue.splice(index, 1);

    this.poll = poll - 1;
    this.queue = queue;

    return promise ? process(promise) : this;
  };

  process = (promise) => {
    const {
      constructor: { MAX_CONCURRENTLY_EXECUTING: limit },
      flush,
      poll,
      queue,
    } = this;
    const full = poll >= limit - 1;

    this.poll = poll + (full ? 0 : 1);
    this.queue = queue.concat(full ? promise : []);

    return full ? this : promise().then(flush);
  };
}

const fifo = new QueueProcessingCallback();

fifo.process(callback1);
fifo.process(callback2);
fifo.process(callback3);
fifo.process(callback4);
fifo.process(callback1);
fifo.process(callback2);
fifo.process(callback3);
fifo.process(callback4);

const lifo = new QueueProcessingCallback(QueueProcessingCallback.LIFO);

lifo.process(callback1);
lifo.process(callback2);
lifo.process(callback3);
lifo.process(callback4);
lifo.process(callback1);
lifo.process(callback2);
lifo.process(callback3);
lifo.process(callback4);

setTimeout(() => {
  fifo.debug();
  lifo.debug();
}, 10000);

https://codesandbox.io/p/sandbox/bold-yalow-x48l6v