Google pagerank and alexa rank are the two famous ranking system which give a clear view of a site with its rank. Many bloggers are believing that alexa rank will help a site to get pagerank. But the fact is alexa rank is completely based on the traffic that recieves to the site. After the adding and claiming of the site the alexa will observe that site for about 3 months after they give a rank which is based on the traffic that recieved to the site during that period. Alexa rank helps a site to compete with other sites. But on the other hand the page rank system is not on that basis. Google gives a page rank to a site according to the performs of that site which is including the traffic and daily update of the site. There are many sites that have pagerank of 2 or 3 but doesn't have alexa rank. This case is entiraly same in the case of alexa rank also. Increase in alexa rank never provide a good result in search engine and it only increases the rank according to the flow of traffic. Through alexa one can find complete details about the sites including the daily traffic, daily income of the site and worth of the site etc.
In the fact google pagerank will help the site to come top in the search results. As the pagerank increases the traffic recieves to the site also increases. While the real fun as the pagerank increases huge traffics may come so alexa rank also get increased. Both the ranking system has there own benefits but it never helps each other page rank is the important thing needed for a site while alexa rank shows the status of the site. All the best.