Allow invoker pools to overlap for small N. (#3751)

For small N, allow the managed invokers to overlap with blackbox invokers.
As an example, for a blackbox fraction of 10%, and two invokers, the blackbox
pool will have size 1, but the managed pool will utilize both invokers.

core/controller/src/main/scala/whisk/core/loadBalancer/ShardingContainerPoolBalancer.scala

@@ -424,12 +424,14 @@ case class ShardingContainerPoolBalancerState(
     val oldSize = _invokers.size
     val newSize = newInvokers.size
 
-    val blackboxes = Math.max(1, (newSize.toDouble * blackboxFraction).toInt)
-    val managed = Math.max(1, newSize - blackboxes)
+    // for small N, allow the managed invokers to overlap with blackbox invokers, and
+    // further assume that blackbox invokers << managed invokers
+    val managed = Math.max(1, Math.ceil(newSize.toDouble * (1 - blackboxFraction)).toInt)
+    val blackboxes = Math.max(1, Math.floor(newSize.toDouble * blackboxFraction).toInt)
 
     _invokers = newInvokers
-    _blackboxInvokers = _invokers.takeRight(blackboxes)
     _managedInvokers = _invokers.take(managed)
+    _blackboxInvokers = _invokers.takeRight(blackboxes)
 
     if (oldSize != newSize) {
       _managedStepSizes = ShardingContainerPoolBalancer.pairwiseCoprimeNumbersUntil(managed)

tests/src/test/scala/whisk/core/loadBalancer/test/ShardingContainerPoolBalancerTests.scala

@@ -83,6 +83,33 @@ class ShardingContainerPoolBalancerTests extends FlatSpec with Matchers with Str
     state.blackboxStepSizes shouldBe Seq(1)
   }
 
+  it should "allow managed partition to overlap with blackbox for small N" in {
+    Seq(0.1, 0.2, 0.3, 0.4, 0.5).foreach { bf =>
+      val state = ShardingContainerPoolBalancerState()(ShardingContainerPoolBalancerConfig(bf, 1))
+
+      (1 to 100).toSeq.foreach { i =>
+        state.updateInvokers((1 to i).map(_ => healthy(1)))
+
+        withClue(s"invoker count $bf $i:") {
+          state.managedInvokers.length should be <= i
+          state.blackboxInvokers should have size Math.max(1, (bf * i).toInt)
+
+          val m = state.managedInvokers.length
+          val b = state.blackboxInvokers.length
+          bf match {
+            // written out explicitly for clarity
+            case 0.1 if i < 10 => m + b shouldBe i + 1
+            case 0.2 if i < 5  => m + b shouldBe i + 1
+            case 0.3 if i < 4  => m + b shouldBe i + 1
+            case 0.4 if i < 3  => m + b shouldBe i + 1
+            case 0.5 if i < 2  => m + b shouldBe i + 1
+            case _             => m + b shouldBe i
+          }
+        }
+      }
+    }
+  }
+
   it should "update the cluster size, adjusting the invoker slots accordingly" in {
     val slots = 10
     val state = ShardingContainerPoolBalancerState()(ShardingContainerPoolBalancerConfig(0.5, slots))