Edit in JSFiddle

;(function($) {
    function AjaxQueue(override) {
        this.override = !!override;
    };
    
    AjaxQueue.prototype = {
        
        requests: new Array(),
        
        offer: function(options) {
            var _self = this;
            
            var xhrOptions = $.extend({}, options, {
                complete: function(jqXHR, textStatus) {

                    if($.isArray(options.complete)) {
                        
                        var funcs = options.complete;
                        for(var i = 0, len = funcs.length; i < len; i++)
                            funcs[i].call(this, jqXHR, textStatus);
                    
                    } else {
                        
                        if(options.complete)
                            options.complete.call(this, jqXHR, textStatus);            
                    }
                    _self.poll();
                },
               
                beforeSend: function(jqXHR, settings) {
                   if(options.beforeSend)
                       var ret = options.beforeSend.call(this, jqXHR, settings);
                   
                   if(ret === false) {
                       _self.poll();
                       return ret;
                   }
                }
            });
            
            if(this.override) {
                console.log('go override');
                this.replace(xhrOptions);
            } else {
                console.log('go queue');
                this.requests.push(xhrOptions);
        
                if(this.requests.length == 1) {
                    $.ajax(xhrOptions);
                }
            }
        },
        
        replace: function(xhrOptions) {
            var prevRet = this.peek();
            if(prevRet != null) {
                prevRet.abort();
            }
            
            this.requests.shift();
            this.requests.push($.ajax(xhrOptions));
        },
        
        poll: function() {
            if(this.isEmpty()) {
                return null;    
            }
    
            var processedRequest = this.requests.shift();
            var nextRequest = this.peek();
            if(nextRequest != null) {
                $.ajax(nextRequest);
            }
    
            return processedRequest;
        },
        
        peek: function() {
            if(this.isEmpty()) {
                return null;
            }
            
            var nextRequest = this.requests[0];
            return nextRequest;
        },
        
        isEmpty: function() {
            return this.requests.length == 0;
        }
    };
    
    var queue = {};
        
    var AjaxManager = {     
        createQueue: function(name, override) {
            return queue[name] = new AjaxQueue(override);
        },
        
        destroyQueue: function(name) {
            if(queue[name]) {
                queue[name] = null;
                delete queue[name];
            }
        },
        
        getQueue: function(name) {
            return ( queue[name] ? queue[name] : null); 
        }
    };
    
    $.AM = AjaxManager;
})(jQuery);

var newQueue = $.AM.createQueue('queue');

$('#ajaxBtn').click(function() {
    var count = parseInt($(this).attr('data-count'));
    $(this).attr('data-count', ++count);
    $(this).html('trigger ajax ' + count);
    newQueue.offer({
        url: '/echo/html/',
        type: 'post',
        data: {
            html: '<p>This is demo ' + count + ' </p>',
            delay: 3
        },
        beforeSend: function(jqXHR, settings) {
            // for whatever reason
            // var num = Math.floor(Math.random() * 100);
            // $('#log').append(num);
            // if(num % 2 !== 0) {
               // return false;
            // }
        },
        success: function(data, textStatus, jqXHR) {
           $('#log').append(data);
        }
    })
});

<div id="log"></div>
<button id="ajaxBtn" data-count="0">trigger ajax</button>