This implementation of java.util.AbstractQueue is bounded, but always accepts additional members, with the oldest members simply 'falling off' silently if the queue is full. I am neither a java low-level expert, nor a creative commons license expert, so any improvement, whether to execution or attribution, would be most helpful.

FalloffBoundedQueue.java

/*
 * Written by Doug Lea with assistance from members of JCP JSR-166
 * Expert Group and released to the public domain, as explained at
 * http://creativecommons.org/licenses/publicdomain
 */
package java.util;
import java.util.*;

/**
 * This class is heavily derived from the implementation of
 * {@linkplain ArrayBlockingQueue array blocking queue}, by
 * Doug Lea and JCP JSR-166, which is licensed as public domain.
 *
 * A bounded {@linkplain Queue queue} backed by an
 * array.  This queue orders elements FIFO (first-in-first-out).  The
 * <em>head</em> of the queue is that element that has been on the
 * queue the longest time.  The <em>tail</em> of the queue is that
 * element that has been on the queue the shortest time. New elements
 * are inserted at the tail of the queue, and the queue retrieval
 * operations obtain elements at the head of the queue.
 *
 * <p>This is a classic &quot;bounded buffer&quot;, in which a
 * fixed-sized array holds elements inserted by producers and
 * extracted by consumers.  Once created, the capacity cannot be
 * increased.  Attempts to <tt>put</tt> an element into a full queue
 * will result in the head element being discarded; attempts to
 * <tt>take</tt> an element from an empty queue will return null.
 *
 * <p>This class and its iterator implement all of the
 * <em>optional</em> methods of the {@link Collection} and {@link
 * Iterator} interfaces.
 *
 * <p>This class is a member of the
 * <a href="{@docRoot}/../technotes/guides/collections/index.html">
 * Java Collections Framework</a>.
 *
 * @author Mitch Connors and Doug Lea
 * @param <E> the type of elements held in this collection
 **/
@SuppressWarnings("unchecked")
public class FalloffBoundedQueue<E> extends AbstractQueue<E> {

    /** The queued items  */
    private final E[] items;
    /** items index for next take, poll or remove */
    private int takeIndex;
    /** items index for next put, offer, or add. */
    private int putIndex;
    /** Number of items in the queue */
    private int count;

    // Internal helper methods

    /**
     * Circularly increment i.
     */
    final int inc(int i) {
        return (++i == items.length)? 0 : i;
    }

    /**
     * Inserts element at current put position, advances, and signals.
     * Call only when holding lock.
     */
    private void insert(E x) {
        if (count == items.length) {
            extract();
        }
        items[putIndex] = x;
        putIndex = inc(putIndex);
        ++count;
    }

    /**
     * Extracts element at current take position, advances, and signals.
     * Call only when holding lock.
     */
    private E extract() {
        final E[] items = this.items;
        E x = items[takeIndex];
        items[takeIndex] = null;
        takeIndex = inc(takeIndex);
        --count;
        return x;
    }

    /**
     * Utility for remove and iterator.remove: Delete item at position i.
     * Call only when holding lock.
     */
    void removeAt(int i) {
        final E[] items = this.items;
        // if removing front item, just advance
        if (i == takeIndex) {
            items[takeIndex] = null;
            takeIndex = inc(takeIndex);
        } else {
            // slide over all others up through putIndex.
            for (;;) {
                int nexti = inc(i);
                if (nexti != putIndex) {
                    items[i] = items[nexti];
                    i = nexti;
                } else {
                    items[i] = null;
                    putIndex = i;
                    break;
                }
            }
        }
        --count;
    }

    /**
     * Creates an <tt>FalloffBoundedQueue</tt> with the given (fixed)
     * capacity and default access policy.
     *
     * @param capacity the capacity of this queue
     * @throws IllegalArgumentException if <tt>capacity</tt> is less than 1
     */
    public FalloffBoundedQueue(int capacity) {
        if (capacity <= 0)
            throw new IllegalArgumentException();
        this.items = (E[]) new Object[capacity];
    }

    /**
     * Creates an <tt>FalloffBoundedQueue</tt> with the given (fixed)
     * capacity, the specified access policy and initially containing the
     * elements of the given collection,
     * added in traversal order of the collection's iterator.
     *
     * @param capacity the capacity of this queue
     * @param fair if <tt>true</tt> then queue accesses for threads blocked
     *        on insertion or removal, are processed in FIFO order;
     *        if <tt>false</tt> the access order is unspecified.
     * @param c the collection of elements to initially contain
     * @throws IllegalArgumentException if <tt>capacity</tt> is less than
     *         <tt>c.size()</tt>, or less than 1.
     * @throws NullPointerException if the specified collection or any
     *         of its elements are null
     */
    public FalloffBoundedQueue(int capacity,
                              Collection<? extends E> c) {
        this(capacity);
        if (capacity < c.size())
            throw new IllegalArgumentException();

        for (Iterator<? extends E> it = c.iterator(); it.hasNext();)
            add(it.next());
    }

    /**
     * Inserts the specified element at the tail of this queue if it is
     * possible to do so immediately without exceeding the queue's capacity,
     * returning <tt>true</tt> upon success and throwing an
     * <tt>IllegalStateException</tt> if this queue is full.
     *
     * @param e the element to add
     * @return <tt>true</tt> (as specified by {@link Collection#add})
     * @throws IllegalStateException if this queue is full
     * @throws NullPointerException if the specified element is null
     */
    public boolean add(E e) {
        return super.add(e);
    }

    /**
     * Inserts the specified element at the tail of this queue if it is
     * possible to do so immediately without exceeding the queue's capacity,
     * returning <tt>true</tt> upon success and <tt>false</tt> if this queue
     * is full.  This method is generally preferable to method {@link #add},
     * which can fail to insert an element only by throwing an exception.
     *
     * @throws NullPointerException if the specified element is null
     */
    public boolean offer(E e) {
        if (e == null) throw new NullPointerException();
        insert(e);
        return true;
    }

    /**
     * Inserts the specified element at the tail of this queue, pushing
     * the head off if the queue is full.
     *
     * @throws NullPointerException {@inheritDoc}
     */
    public void put(E e) {
        if (e == null) throw new NullPointerException();
        insert(e);
    }

    public E poll() {
        if (count == 0)
            return null;
        E x = extract();
        return x;
    }

    public E take() {
        E x = extract();
        return x;
    }

    public E peek() {
        return (count == 0) ? null : items[takeIndex];
    }

    // this doc comment is overridden to remove the reference to collections
    // greater in size than Integer.MAX_VALUE
    /**
     * Returns the number of elements in this queue.
     *
     * @return the number of elements in this queue
     */
    public int size() {
        return count;
    }

    // this doc comment is a modified copy of the inherited doc comment,
    // without the reference to unlimited queues.
    /**
     * Returns the number of additional elements that this queue can ideally
     * (in the absence of memory or resource constraints) accept without
     * blocking. This is always equal to the initial capacity of this queue
     * less the current <tt>size</tt> of this queue.
     *
     * <p>Note that you <em>cannot</em> always tell if an attempt to insert
     * an element will succeed by inspecting <tt>remainingCapacity</tt>
     * because it may be the case that another thread is about to
     * insert or remove an element.
     */
    public int remainingCapacity() {
        return items.length - count;
    }

    /**
     * Removes a single instance of the specified element from this queue,
     * if it is present.  More formally, removes an element <tt>e</tt> such
     * that <tt>o.equals(e)</tt>, if this queue contains one or more such
     * elements.
     * Returns <tt>true</tt> if this queue contained the specified element
     * (or equivalently, if this queue changed as a result of the call).
     *
     * @param o element to be removed from this queue, if present
     * @return <tt>true</tt> if this queue changed as a result of the call
     */
    public boolean remove(Object o) {
        if (o == null) return false;
        final E[] items = this.items;
        int i = takeIndex;
        int k = 0;
        for (;;) {
            if (k++ >= count)
                return false;
            if (o.equals(items[i])) {
                removeAt(i);
                return true;
            }
            i = inc(i);
        }
    }

    /**
     * Returns <tt>true</tt> if this queue contains the specified element.
     * More formally, returns <tt>true</tt> if and only if this queue contains
     * at least one element <tt>e</tt> such that <tt>o.equals(e)</tt>.
     *
     * @param o object to be checked for containment in this queue
     * @return <tt>true</tt> if this queue contains the specified element
     */
    public boolean contains(Object o) {
        if (o == null) return false;
        final E[] items = this.items;
        int i = takeIndex;
        int k = 0;
        while (k++ < count) {
            if (o.equals(items[i]))
                return true;
            i = inc(i);
        }
        return false;
    }

    /**
     * Returns an array containing all of the elements in this queue, in
     * proper sequence.
     *
     * <p>The returned array will be "safe" in that no references to it are
     * maintained by this queue.  (In other words, this method must allocate
     * a new array).  The caller is thus free to modify the returned array.
     *
     * <p>This method acts as bridge between array-based and collection-based
     * APIs.
     *
     * @return an array containing all of the elements in this queue
     */
    public Object[] toArray() {
        final E[] items = this.items;
        Object[] a = new Object[count];
        int k = 0;
        int i = takeIndex;
        while (k < count) {
            a[k++] = items[i];
            i = inc(i);
        }
        return a;
    }

    /**
     * Returns an array containing all of the elements in this queue, in
     * proper sequence; the runtime type of the returned array is that of
     * the specified array.  If the queue fits in the specified array, it
     * is returned therein.  Otherwise, a new array is allocated with the
     * runtime type of the specified array and the size of this queue.
     *
     * <p>If this queue fits in the specified array with room to spare
     * (i.e., the array has more elements than this queue), the element in
     * the array immediately following the end of the queue is set to
     * <tt>null</tt>.
     *
     * <p>Like the {@link #toArray()} method, this method acts as bridge between
     * array-based and collection-based APIs.  Further, this method allows
     * precise control over the runtime type of the output array, and may,
     * under certain circumstances, be used to save allocation costs.
     *
     * <p>Suppose <tt>x</tt> is a queue known to contain only strings.
     * The following code can be used to dump the queue into a newly
     * allocated array of <tt>String</tt>:
     *
     * <pre>
     *     String[] y = x.toArray(new String[0]);</pre>
     *
     * Note that <tt>toArray(new Object[0])</tt> is identical in function to
     * <tt>toArray()</tt>.
     *
     * @param a the array into which the elements of the queue are to
     *          be stored, if it is big enough; otherwise, a new array of the
     *          same runtime type is allocated for this purpose
     * @return an array containing all of the elements in this queue
     * @throws ArrayStoreException if the runtime type of the specified array
     *         is not a supertype of the runtime type of every element in
     *         this queue
     * @throws NullPointerException if the specified array is null
     */
    public <T> T[] toArray(T[] a) {
        final E[] items = this.items;
        if (a.length < count)
            a = (T[])java.lang.reflect.Array.newInstance(
                a.getClass().getComponentType(),
                count
                );

        int k = 0;
        int i = takeIndex;
        while (k < count) {
            a[k++] = (T)items[i];
            i = inc(i);
        }
        if (a.length > count)
            a[count] = null;
        return a;
    }

    /**
     * Atomically removes all of the elements from this queue.
     * The queue will be empty after this call returns.
     */
    public void clear() {
        final E[] items = this.items;
        int i = takeIndex;
        int k = count;
        while (k-- > 0) {
            items[i] = null;
            i = inc(i);
        }
        count = 0;
        putIndex = 0;
        takeIndex = 0;
    }

    /**
     * @throws UnsupportedOperationException {@inheritDoc}
     * @throws ClassCastException            {@inheritDoc}
     * @throws NullPointerException          {@inheritDoc}
     * @throws IllegalArgumentException      {@inheritDoc}
     */
    public int drainTo(Collection<? super E> c) {
        if (c == null)
            throw new NullPointerException();
        if (c == this)
            throw new IllegalArgumentException();
        final E[] items = this.items;
        int i = takeIndex;
        int n = 0;
        int max = count;
        while (n < max) {
            c.add(items[i]);
            items[i] = null;
            i = inc(i);
            ++n;
        }
        if (n > 0) {
            count = 0;
            putIndex = 0;
            takeIndex = 0;
        }
        return n;
    }

    /**
     * @throws UnsupportedOperationException {@inheritDoc}
     * @throws ClassCastException            {@inheritDoc}
     * @throws NullPointerException          {@inheritDoc}
     * @throws IllegalArgumentException      {@inheritDoc}
     */
    public int drainTo(Collection<? super E> c, int maxElements) {
        if (c == null)
            throw new NullPointerException();
        if (c == this)
            throw new IllegalArgumentException();
        if (maxElements <= 0)
            return 0;
        final E[] items = this.items;
        int i = takeIndex;
        int n = 0;
        int sz = count;
        int max = (maxElements < count)? maxElements : count;
        while (n < max) {
            c.add(items[i]);
            items[i] = null;
            i = inc(i);
            ++n;
        }
        if (n > 0) {
            count -= n;
            takeIndex = i;
        }
        return n;
    }


    /**
     * Returns an iterator over the elements in this queue in proper sequence.
     * The returned <tt>Iterator</tt> is a "weakly consistent" iterator that
     * will never throw {@link ConcurrentModificationException},
     * and guarantees to traverse elements as they existed upon
     * construction of the iterator, and may (but is not guaranteed to)
     * reflect any modifications subsequent to construction.
     *
     * @return an iterator over the elements in this queue in proper sequence
     */
    public Iterator<E> iterator() {
        return new Itr();
    }

    /**
     * Iterator for FalloffBoundedQueue
     */
    private class Itr implements Iterator<E> {
        /**
         * Index of element to be returned by next,
         * or a negative number if no such.
         */
        private int nextIndex;

        /**
         * nextItem holds on to item fields because once we claim
         * that an element exists in hasNext(), we must return it in
         * the following next() call even if it was in the process of
         * being removed when hasNext() was called.
         */
        private E nextItem;

        /**
         * Index of element returned by most recent call to next.
         * Reset to -1 if this element is deleted by a call to remove.
         */
        private int lastRet;

        Itr() {
            lastRet = -1;
            if (count == 0)
                nextIndex = -1;
            else {
                nextIndex = takeIndex;
                nextItem = items[takeIndex];
            }
        }

        public boolean hasNext() {
            /*
             * No sync. We can return true by mistake here
             * only if this iterator passed across threads,
             * which we don't support anyway.
             */
            return nextIndex >= 0;
        }

        /**
         * Checks whether nextIndex is valid; if so setting nextItem.
         * Stops iterator when either hits putIndex or sees null item.
         */
        private void checkNext() {
            if (nextIndex == putIndex) {
                nextIndex = -1;
                nextItem = null;
            } else {
                nextItem = items[nextIndex];
                if (nextItem == null)
                    nextIndex = -1;
            }
        }

        public E next() {
            if (nextIndex < 0)
                throw new NoSuchElementException();
            lastRet = nextIndex;
            E x = nextItem;
            nextIndex = inc(nextIndex);
            checkNext();
            return x;
        }

        public void remove() {
            int i = lastRet;
            if (i == -1)
                throw new IllegalStateException();
            lastRet = -1;

            int ti = takeIndex;
            removeAt(i);
            // back up cursor (reset to front if was first element)
            nextIndex = (i == ti) ? takeIndex : i;
            checkNext();
        }
    }
}