[Alexandroppolus]

см. в консольку

function run(limit, func, params) {
    'use strict';
    if (typeof limit !== 'number' || limit < 1 || typeof func !== 'function' || !params || !params.length) {
        return Promise.resolve([]);
    }

    return new Promise(function (resolve) {
        var result = new Array(params.length);
        var pos = 0;
        var rcount = 0;
        function ok(data) {
            end(this, false, data);
        }
        function err(data) {
            end(this, true, data);
        }
        function end(idx, error, data) {
            result[idx] = {
                data: error ? null : data,
                error: error ? data : null
            };
            rcount++;
            if (pos < params.length) {
                Promise.resolve(func(params[pos])).then(ok.bind(pos), err.bind(pos));
                ++pos;
            } else {
                if (rcount >= params.length) {
                    resolve(result);
                }
            }
        }
        var m = Math.min(limit, params.length);
        while (pos < m) {
            Promise.resolve(func(params[pos])).then(ok.bind(pos), err.bind(pos));
            ++pos;
        }
    });
}


run(3, function(p) {
    console.log('start: ', p);
    return new Promise(function(r) { setTimeout(function(v) { console.log(v); r(v); }, p * 1000, 'result ' + p); });
}, [5, 3, 7, 2, 6]).then(console.log);