在Akka分布式数据中，可以使用Akka的akka.cluster.sharding模块来实现意外传闻间隔增长和消息大小增长的解决方法。下面是一个包含代码示例的解决方法：

首先，在application.conf文件中配置Akka集群和分片相关的设置：

akka {
  actor {
    provider = "cluster"
    warn-about-java-serializer-usage = off
  }

  remote {
    watch-failure-detector.acceptable-heartbeat-pause = 10s
    artery {
      transport = tcp
      canonical.port = 0
    }
  }

  cluster {
    sharding {
      retry-interval = 5s
      buffer-size = 100
      entity-restart-backoff = 10s
    }
  }
}

接下来，创建一个用于处理消息的Actor。在该Actor中，可以设置消息处理的超时时间，并通过withSupervisorStrategy方法设置意外传闻间隔增长和消息大小增长的策略。

import akka.actor.{Actor, ActorLogging, OneForOneStrategy, Props}
import akka.cluster.sharding.ShardRegion
import akka.cluster.sharding.ShardRegion.Passivate
import akka.cluster.sharding.ShardRegion.StartEntity
import akka.cluster.sharding.ShardRegion.StartEntityAck
import akka.cluster.sharding.ShardRegion.EntityIdExtractor
import akka.cluster.sharding.ShardRegion.EntityId
import akka.cluster.sharding.ShardRegion.EntityMessage
import akka.cluster.sharding.ShardRegion.ShardId

class MyActor extends Actor with ActorLogging {
  import MyActor._

  // 消息处理超时时间
  context.setReceiveTimeout(30.seconds)

  def receive: Receive = {
    case msg: MyMessage =>
      // 处理消息
      log.info("Received message: {}", msg)
    case ReceiveTimeout =>
      // 消息处理超时
      log.warning("Received timeout message")
    case _ =>
      log.warning("Received unknown message")
  }

  override def preStart(): Unit = log.info("MyActor started")
  override def postStop(): Unit = log.info("MyActor stopped")

  // 设置意外传闻间隔增长和消息大小增长的策略
  override def supervisorStrategy: OneForOneStrategy = OneForOneStrategy() {
    case _: Exception =>
      log.warning("Failure detected, escalating to supervisor")
      // 设置传递给上级Actor的消息，使其实现意外传闻间隔增长和消息大小增长
      self ! Passivate(stopMessage = Stop)
      OneForOneStrategy.Escalate
  }
}

object MyActor {
  def props(): Props = Props[MyActor]

  // 定义消息
  case class MyMessage(content: String)

  // 定义停止消息
  case object Stop

  // 定义实体Id提取器
  val entityIdExtractor: EntityIdExtractor = {
    case msg: MyMessage => msg.content.toString -> msg
    case StartEntity(entityId) => entityId -> entityId
  }

  // 定义实体消息提取器
  val messageExtractor: ShardRegion.MessageExtractor = {
    case msg: MyMessage => (msg.content.toString, msg)
    case msg: EntityMessage => (msg.entityId, msg.payload)
  }
}

最后，在应用程序的入口处，创建一个ClusterSharding实例，并通过ClusterSharding.start方法启动分片区域。

import akka.actor.ActorSystem
import akka.cluster.sharding.ClusterSharding
import akka.cluster.sharding.ClusterShardingSettings
import akka.cluster.sharding.ShardRegion

object MainApp extends App {
  implicit val system: ActorSystem = ActorSystem("MyActorSystem")

  // 创建实体类型名称
  val typeName = "MyActor"

  // 创建实体ShardId提取器
  val shardIdExtractor: ShardRegion.ShardIdExtractor = {
    case msg: MyActor.StartEntity => msg.entityId.toString
    case ShardRegion.StartEntity(id) => id.toString
  }

  // 创建分片区域
  val region: ClusterSharding = ClusterSharding(system)

  // 启动分片区域
  val settings: ClusterShardingSettings = ClusterShardingSettings(system)
  val myActorProps: Props = MyActor.props()
  val shardRegion: ActorRef = region.start(
    typeName = typeName,
    entityProps = myActorProps,