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multithreading - Run java thread at specific times

I have a web application that synchronizes with a central database four times per hour. The process usually takes 2 minutes. I would like to run this process as a thread at X:55, X:10, X:25, and X:40 so that the users knows that at X:00, X:15, X:30, and X:45 they have a clean copy of the database. It is just about managing expectations. I have gone through the executor in java.util.concurrent but the scheduling is done with the scheduleAtFixedRate which I believe provides no guarantee about when this is actually run in terms of the hours. I could use a first delay to launch the Runnable so that the first one is close to the launch time and schedule for every 15 minutes but it seems that this would probably diverge in time. Is there an easier way to schedule the thread to run 5 minutes before every quarter hour?

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You can let the Runnable schedule its "next run".

Such as,

class Task implements Runnable {
    private final ScheduledExecutorService service;

    public Task(ScheduledExecutorService service){
        this.service = service;
    }

    public void run(){
        try{
             //do stuff
        }finally{
            //Prevent this task from stalling due to RuntimeExceptions.
            long untilNextInvocation = //calculate how many ms to next launch
            service.schedule(new Task(service),untilNextInvocation,TimeUnit.MILLISECONDS);
        }
    }
}

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