As I mentioned in response to this question, MGL ch. 85§ 11B gives bikers the right to ride anywhere that a car can legally drive. However, it goes on to say that that right can be limited on state highways where posted signs specifically prohibit cycling.
The Alewife Brook Parkway is a part of Route 16, which is a state highway. That means the DOT can limit bike access to all or portions of the route, if they post signs.