SomeActorTest.scala

import java.util.{Timer, TimerTask}

import akka.actor.{Actor, ActorSystem, Props}
import akka.testkit.{ImplicitSender, TestKit}
import org.scalatest.{BeforeAndAfterAll, Matchers, WordSpecLike}

import scala.concurrent.{Future, Promise}
import scala.util.Try

class SomeActorTest()
    extends TestKit(ActorSystem("MySpec"))
    with ImplicitSender
    with WordSpecLike
    with Matchers
    with BeforeAndAfterAll {

  override def afterAll: Unit = {
    TestKit.shutdownActorSystem(system)
  }

  "An actor" must {
    "begin process another message before previous future complete" in {
      class SomeActor extends Actor {

        import context.dispatcher

        def delay(delay: Long): Future[Long] = {
          val promise = Promise[Long]()
          val t = new Timer()
          t.schedule(new TimerTask {
            override def run(): Unit = {
              promise.complete(Try(delay))
            }
          }, delay)
          promise.future
        }

        override def receive: Receive = {
          case "first" =>
            val s = sender()
            delay(1000).map { _ =>
              s ! "first"
            }
          case "second" =>
            val s = sender()
            delay(500).map { _ =>
              s ! "second"
            }
        }
      }

      val a = system.actorOf(Props(new SomeActor()))
      a ! "first"
      a ! "second"
      expectMsg("second")
      expectMsg("first")
    }
  }
}