Shared observable that will run a task. Every subscriber that subscribes while the task is running will share the same observable and receive the same result. When the tasks finishes the next subscriber will trigger a new task.

Main.java

public class Main {

    public static final long START_TIME = System.currentTimeMillis();

    public static void main(String[] args) throws InterruptedException {

        SingletonTask singletonTask = singletonTask();

        singletonTask.getObservable()
                .subscribeOn(Schedulers.newThread())
                .observeOn(Schedulers.single())
                .subscribe(timestamp -> System.out.println("[1] Got result: " + formatTimestamp(timestamp) + "ms"));
        System.out.println("[1] subscribed at " + (System.currentTimeMillis() - START_TIME) + "ms");

        Thread.sleep(1000);

        singletonTask.getObservable()
                .subscribeOn(Schedulers.newThread())
                .observeOn(Schedulers.single())
                .subscribe(timestamp -> System.out.println("[2] Got result: " + formatTimestamp(timestamp) + "ms"));
        System.out.println("[2] subscribed at " + (System.currentTimeMillis() - START_TIME) + "ms");

        Thread.sleep(1000);

        singletonTask.getObservable()
                .subscribeOn(Schedulers.newThread())
                .observeOn(Schedulers.single())
                .subscribe(timestamp -> System.out.println("[3] Got result: " + formatTimestamp(timestamp) + "ms"));
        System.out.println("[3] subscribed at " + (System.currentTimeMillis() - START_TIME) + "ms");

        Thread.sleep(1000);

        singletonTask.getObservable()
                .subscribeOn(Schedulers.newThread())
                .observeOn(Schedulers.single())
                .subscribe(timestamp -> System.out.println("[4] Got result: " + formatTimestamp(timestamp) + "ms"));
        System.out.println("[4] subscribed at " + (System.currentTimeMillis() - START_TIME) + "ms");

        Thread.sleep(1000);

        singletonTask.getObservable()
                .subscribeOn(Schedulers.newThread())
                .observeOn(Schedulers.single())
                .subscribe(timestamp -> System.out.println("[5] Got result: " + formatTimestamp(timestamp) + "ms"));
        System.out.println("[5] subscribed at " + (System.currentTimeMillis() - START_TIME) + "ms");

        Thread.sleep(20000);

    }

    private static String formatTimestamp(long timestamp) {
        return String.valueOf((timestamp - START_TIME) % 1000000);
    }
}

output.txt

[1] subscribed at 229ms
-> Started Task at 233ms
[2] subscribed at 1233ms
[3] subscribed at 2239ms
-> Finished Task at 3237ms
[1] Got result: 233ms
[2] Got result: 233ms
[3] Got result: 233ms
[4] subscribed at 3244ms
-> Started Task at 3244ms
[5] subscribed at 4248ms
-> Finished Task at 6246ms
[4] Got result: 3244ms
[5] Got result: 3244ms

SingletonTask.java

public enum SingletonTask {
    INSTANCE;

    private final Observable<Long> longRunningObservable = Observable.<Long>create(observableEmitter -> {
        long timestamp = System.currentTimeMillis();
        System.out.println("-> Started Task at " + (System.currentTimeMillis() - Main.START_TIME) + "ms");
        Thread.sleep(3000);
        System.out.println("-> Finished Task at " + (System.currentTimeMillis() - Main.START_TIME) + "ms");
        observableEmitter.onNext(timestamp);
        observableEmitter.onComplete();
    }).share();

    public static SingletonTask singletonTask() {
        return INSTANCE;
    }

    public Observable<Long> getObservable() {
        return longRunningObservable;
    }
}