It is analog of [Bluebird.map with concurency](http://bluebirdjs.com/docs/api/promise.map.html) But with [correct start order](https://github.com/petkaantonov/bluebird/issues/847).

order-correct-async-map.js

function ownMap(arr, cb, {concurrency} = {}) {
    if (!concurrency || concurrency < 1) {
        return ownMap(arr, cb, {concurrency: Number.POSITIVE_INFINITY})
    }
    const arrLength = arr.length;
    const batchPromises = new Array(arrLength);
    let currentTaskNumber = 0;
    return new Promise((resolve, reject) => {
        function endOneMore(result) {
            if (currentTaskNumber === arrLength) {
                Promise.all(batchPromises)
                    .then(resolve);
            }
            if (currentTaskNumber < arrLength) {
                startOneMore();
            }
            return result;
        }

        function startOneMore() {
            batchPromises[currentTaskNumber] = cb(arr[currentTaskNumber])
                .then(endOneMore, reject);
            currentTaskNumber++;
        }
        arr.slice(0, concurrency)
            .map((v, i) => startOneMore(i));
    });
}

// test

const array = (new Array(10)).fill(0).map((v, k) => k);

ownMap(
    array,
    (numb) => {
        console.error(numb, 'started', numb);
        const time = Math.round(Math.random() * 900) + 100;
        return (new Promise(resolve => setTimeout(resolve, time)))
            // .then(() => console.error(numb, 'ended', numb))
            .then(() => `${numb} - ${time}`);
    },
    {concurrency: 3}
).then((arr) => console.log('finished all', arr.length, arr));

output.txt

0 'started' 0
1 'started' 1
2 'started' 2
3 'started' 3
4 'started' 4
5 'started' 5
6 'started' 6
7 'started' 7
8 'started' 8
9 'started' 9
finished all 10 [ '0 - 284',
  '1 - 327',
  '2 - 316',
  '3 - 900',
  '4 - 643',
  '5 - 167',
  '6 - 708',
  '7 - 622',
  '8 - 870',
  '9 - 536' ]

interface IAsyncMapWorker<TArg, TRes>{
    (arg: TArg): Promise<TRes>;
}

interface IAsyncMap<TArg, TRes>{
    (
        array: TArg[],
        callback: IAsyncMapWorker<TArg, TRes>,
        numberOfWorkers: number
    ): Promise<TRes[]>;
}