You can use reentrant locks with a fairness policy or timeout to avoid thread starvation. You can apply a thread fairness policy. it will help avoid a thread waiting forever to get to your resources.
private final ReentrantLock lock = new ReentrantLock(true);
//the param true turns on the fairness policy.
The "fairness policy" picks the next runnable thread to execute. It is based on priority, time since last run, blah blah
also, Synchronize can block indefinitely if it cant escape the block. Reentrantlock can have timeout set.