How to batch long process in serial using RxJava?

I have a big list of strings that needs to be checked against remote API.

Observable.from(List<String> strings) // let's say the `strings` has > 5000 items
   .buffer(50) // splitting the strings into 50-sized chunks, it returns Observable<List<String>> (fast)
   .flatMap((strings) -> {
       // checkPhoneNumbers is a network call using Retrofit's RxJava (slow)
       return mSyncApi.checkPhoneNumbers(strings);
   })
   .reduce( ... ) // aggregate all checking results
   .subscribe( ... );

The problem is buffer() seems to emit List<String> too fast that all of multiple .checkPhoneNumbers() get executed almost in the same time. What I would like to achieve is to enqueue .checkPhoneNumbers() to better support devices with slow connection.

Throttling the emitted List<String> by predefined time interval doesn't make sense since it will be a disadvantage for devices with lightning fast connection. I have tried RxJava's serialize() right after the flatMap() but it doesn't seems make any difference (although I don't know if it's the right use of serialize).

Any alternative approaches appreciated! Thanks.

As @zsxwing suggested, I think the maxConcurrent overload is what you're looking for if you're trying to limit the concurrency occurring inside flatMap.

For example: https://gist.github.com/benjchristensen/a0350776a595fd6e3810#file-parallelexecution-java-L78

private static void flatMapBufferedExampleAsync() {
    final AtomicInteger total = new AtomicInteger();
    Observable.range(0, 500000000)
            .doOnNext(i -> total.incrementAndGet())
            .buffer(100)
            .doOnNext(i -> System.out.println("emit " + i))
            .flatMap(i -> {
                return Observable.from(i).subscribeOn(Schedulers.computation()).map(item -> {
                    // simulate computational work
                        try {
                            Thread.sleep(10);
                        } catch (Exception e) {
                        }
                        return item + " processed " + Thread.currentThread();
                    });
            }, 2 /* limit concurrency to 2 */) // <--- note argument here
           .toBlocking().forEach(System.out::println);

    System.out.println("total emitted: " + total.get());
}