What kind of problems are commonly solved via priority queues:

• If you need to handle something with a higher priority first, regardless of what order the items arrive, you use a PQ
• Minimum Spanning Tree (MST) algorithms
• Lossless data compression algorithms
• Sweep Line algorithm
• Get "next best/worst" element
• Event-Driven simulations
• Dijkstra's shortest path algorithm

• java.util.PriorityQueue, not thread-safe, based on natural order (example) or explicit Comparator (example)
• java.util.concurrent.PriorityBlockingQueue, thread-safe, based on natural or explicit Comparator, example