diff --git a/python/ray/tests/test_basic.py b/python/ray/tests/test_basic.py
index c4a8e02a6..5a71bdd4e 100644
--- a/python/ray/tests/test_basic.py
+++ b/python/ray/tests/test_basic.py
@@ -105,6 +105,31 @@ def test_simple_serialization(ray_start_regular):
             assert type(obj) == type(new_obj_2)
 
 
+def test_fair_queueing(shutdown_only):
+    ray.init(
+        num_cpus=1, _internal_config=json.dumps({
+            "fair_queueing_enabled": 1
+        }))
+
+    @ray.remote
+    def h():
+        return 0
+
+    @ray.remote
+    def g():
+        return ray.get(h.remote())
+
+    @ray.remote
+    def f():
+        return ray.get(g.remote())
+
+    # This will never finish without fair queueing of {f, g, h}:
+    # https://github.com/ray-project/ray/issues/3644
+    ready, _ = ray.wait(
+        [f.remote() for _ in range(1000)], timeout=60.0, num_returns=1000)
+    assert len(ready) == 1000, len(ready)
+
+
 def test_complex_serialization(ray_start_regular):
     def assert_equal(obj1, obj2):
         module_numpy = (type(obj1).__module__ == np.__name__
diff --git a/python/ray/tests/test_signal.py b/python/ray/tests/test_signal.py
index 85e6cc6a5..066281d15 100644
--- a/python/ray/tests/test_signal.py
+++ b/python/ray/tests/test_signal.py
@@ -335,7 +335,9 @@ def test_receiving_on_two_returns(ray_start_regular):
             or (x == results[1][0] and y == results[0][0]))
 
 
-def test_serial_tasks_reading_same_signal(ray_start_regular):
+def test_serial_tasks_reading_same_signal(shutdown_only):
+    ray.init(num_cpus=2)
+
     @ray.remote
     def send_signal(value):
         signal.send(UserSignal(value))
diff --git a/src/ray/common/ray_config_def.h b/src/ray/common/ray_config_def.h
index e0720006a..db6547d3d 100644
--- a/src/ray/common/ray_config_def.h
+++ b/src/ray/common/ray_config_def.h
@@ -34,6 +34,12 @@ RAY_CONFIG(uint64_t, num_heartbeats_warning, 5)
 /// The duration between dumping debug info to logs, or -1 to disable.
 RAY_CONFIG(int64_t, debug_dump_period_milliseconds, 10000)
 
+/// Whether to enable fair queueing between task classes in raylet. When
+/// fair queueing is enabled, the raylet will try to balance the number
+/// of running tasks by class (i.e., function name). This prevents one
+/// type of task from starving other types (see issue #3664).
+RAY_CONFIG(bool, fair_queueing_enabled, true)
+
 /// The initial period for a task execution lease. The lease will expire this
 /// many milliseconds after the first acquisition of the lease. Nodes that
 /// require an object will not try to reconstruct the task until at least
diff --git a/src/ray/common/task/task_spec.cc b/src/ray/common/task/task_spec.cc
index 4512d4020..41b4f3542 100644
--- a/src/ray/common/task/task_spec.cc
+++ b/src/ray/common/task/task_spec.cc
@@ -5,6 +5,19 @@
 
 namespace ray {
 
+std::unordered_map<SchedulingClassDescriptor, SchedulingClass>
+    TaskSpecification::sched_cls_to_id_;
+std::unordered_map<SchedulingClass, SchedulingClassDescriptor>
+    TaskSpecification::sched_id_to_cls_;
+int TaskSpecification::next_sched_id_;
+
+SchedulingClassDescriptor &TaskSpecification::GetSchedulingClassDescriptor(
+    SchedulingClass id) {
+  auto it = sched_id_to_cls_.find(id);
+  RAY_CHECK(it != sched_id_to_cls_.end()) << "invalid id: " << id;
+  return it->second;
+}
+
 void TaskSpecification::ComputeResources() {
   auto required_resources = MapFromProtobuf(message_->required_resources());
   auto required_placement_resources =
@@ -14,6 +27,25 @@ void TaskSpecification::ComputeResources() {
   }
   required_resources_.reset(new ResourceSet(required_resources));
   required_placement_resources_.reset(new ResourceSet(required_placement_resources));
+
+  // Map the scheduling class descriptor to an integer for performance.
+  auto sched_cls = std::make_pair(GetRequiredResources(), FunctionDescriptor());
+  auto it = sched_cls_to_id_.find(sched_cls);
+  if (it == sched_cls_to_id_.end()) {
+    sched_cls_id_ = ++next_sched_id_;
+    // TODO(ekl) we might want to try cleaning up task types in these cases
+    if (sched_cls_id_ > 100) {
+      RAY_LOG(WARNING) << "More than " << sched_cls_id_
+                       << " types of tasks seen, this may reduce performance.";
+    } else if (sched_cls_id_ > 1000) {
+      RAY_LOG(ERROR) << "More than " << sched_cls_id_
+                     << " types of tasks seen, this may reduce performance.";
+    }
+    sched_cls_to_id_[sched_cls] = sched_cls_id_;
+    sched_id_to_cls_[sched_cls_id_] = sched_cls;
+  } else {
+    sched_cls_id_ = it->second;
+  }
 }
 
 // Task specification getter methods.
@@ -33,6 +65,11 @@ std::vector<std::string> TaskSpecification::FunctionDescriptor() const {
   return VectorFromProtobuf(message_->function_descriptor());
 }
 
+const SchedulingClass TaskSpecification::GetSchedulingClass() const {
+  RAY_CHECK(sched_cls_id_ > 0);
+  return sched_cls_id_;
+}
+
 size_t TaskSpecification::NumArgs() const { return message_->args_size(); }
 
 size_t TaskSpecification::NumReturns() const { return message_->num_returns(); }
diff --git a/src/ray/common/task/task_spec.h b/src/ray/common/task/task_spec.h
index 31de3f704..e69241ec1 100644
--- a/src/ray/common/task/task_spec.h
+++ b/src/ray/common/task/task_spec.h
@@ -17,6 +17,10 @@ extern "C" {
 
 namespace ray {
 
+typedef std::vector<std::string> FunctionDescriptor;
+typedef std::pair<ResourceSet, FunctionDescriptor> SchedulingClassDescriptor;
+typedef int SchedulingClass;
+
 /// Wrapper class of protobuf `TaskSpec`, see `common.proto` for details.
 class TaskSpecification : public MessageWrapper<rpc::TaskSpec> {
  public:
@@ -78,6 +82,13 @@ class TaskSpecification : public MessageWrapper<rpc::TaskSpec> {
 
   size_t ArgMetadataSize(size_t arg_index) const;
 
+  /// Return the scheduling class of the task. The scheduler makes a best effort
+  /// attempt to fairly dispatch tasks of different classes, preventing
+  /// starvation of any single class of task.
+  ///
+  /// \return The scheduling class used for fair task queueing.
+  const SchedulingClass GetSchedulingClass() const;
+
   /// Return the resources that are to be acquired during the execution of this
   /// task.
   ///
@@ -137,16 +148,40 @@ class TaskSpecification : public MessageWrapper<rpc::TaskSpec> {
 
   std::string DebugString() const;
 
+  static SchedulingClassDescriptor &GetSchedulingClassDescriptor(SchedulingClass id);
+
  private:
   void ComputeResources();
+
   /// Field storing required resources. Initalized in constructor.
   /// TODO(ekl) consider optimizing the representation of ResourceSet for fast copies
   /// instead of keeping shared ptrs here.
   std::shared_ptr<ResourceSet> required_resources_;
   /// Field storing required placement resources. Initalized in constructor.
   std::shared_ptr<ResourceSet> required_placement_resources_;
+  /// Cached scheduling class of this task.
+  SchedulingClass sched_cls_id_;
+
+  /// Keep global static id mappings for SchedulingClass for performance.
+  static std::unordered_map<SchedulingClassDescriptor, SchedulingClass> sched_cls_to_id_;
+  static std::unordered_map<SchedulingClass, SchedulingClassDescriptor> sched_id_to_cls_;
+  static int next_sched_id_;
 };
 
 }  // namespace ray
 
+/// We must define the hash since it's not auto-defined for vectors.
+namespace std {
+template <>
+struct hash<ray::SchedulingClassDescriptor> {
+  size_t operator()(ray::SchedulingClassDescriptor const &k) const {
+    size_t seed = std::hash<ray::ResourceSet>()(k.first);
+    for (const auto &str : k.second) {
+      seed ^= std::hash<std::string>()(str);
+    }
+    return seed;
+  }
+};
+}  // namespace std
+
 #endif  // RAY_COMMON_TASK_TASK_SPEC_H
diff --git a/src/ray/raylet/main.cc b/src/ray/raylet/main.cc
index bdc67ba4c..b4e4b744a 100644
--- a/src/ray/raylet/main.cc
+++ b/src/ray/raylet/main.cc
@@ -123,6 +123,8 @@ int main(int argc, char *argv[]) {
       RayConfig::instance().heartbeat_timeout_milliseconds();
   node_manager_config.debug_dump_period_ms =
       RayConfig::instance().debug_dump_period_milliseconds();
+  node_manager_config.fair_queueing_enabled =
+      RayConfig::instance().fair_queueing_enabled();
   node_manager_config.max_lineage_size = RayConfig::instance().max_lineage_size();
   node_manager_config.store_socket_name = store_socket_name;
   node_manager_config.temp_dir = temp_dir;
diff --git a/src/ray/raylet/node_manager.cc b/src/ray/raylet/node_manager.cc
index fdd6b9fcf..1b2074a9f 100644
--- a/src/ray/raylet/node_manager.cc
+++ b/src/ray/raylet/node_manager.cc
@@ -1,5 +1,6 @@
 #include "ray/raylet/node_manager.h"
 
+#include <cctype>
 #include <fstream>
 
 #include "ray/common/status.h"
@@ -78,6 +79,7 @@ NodeManager::NodeManager(boost::asio::io_service &io_service,
       heartbeat_timer_(io_service),
       heartbeat_period_(std::chrono::milliseconds(config.heartbeat_period_ms)),
       debug_dump_period_(config.debug_dump_period_ms),
+      fair_queueing_enabled_(config.fair_queueing_enabled),
       temp_dir_(config.temp_dir),
       object_manager_profile_timer_(io_service),
       initial_config_(config),
@@ -755,24 +757,46 @@ void NodeManager::ProcessNewClient(LocalClientConnection &client) {
   client.ProcessMessages();
 }
 
-// A helper function to create a mapping from resource shapes to
-// tasks with that resource shape from a given list of tasks.
-std::unordered_map<ResourceSet, ordered_set<TaskID>> MakeTasksWithResources(
+// A helper function to create a mapping from task scheduling class to
+// tasks with that class from a given list of tasks.
+std::unordered_map<SchedulingClass, ordered_set<TaskID>> MakeTasksByClass(
     const std::vector<Task> &tasks) {
-  std::unordered_map<ResourceSet, ordered_set<TaskID>> result;
+  std::unordered_map<SchedulingClass, ordered_set<TaskID>> result;
   for (const auto &task : tasks) {
     auto spec = task.GetTaskSpecification();
-    result[spec.GetRequiredResources()].push_back(spec.TaskId());
+    result[spec.GetSchedulingClass()].push_back(spec.TaskId());
   }
   return result;
 }
 
 void NodeManager::DispatchTasks(
-    const std::unordered_map<ResourceSet, ordered_set<TaskID>> &tasks_with_resources) {
+    const std::unordered_map<SchedulingClass, ordered_set<TaskID>> &tasks_by_class) {
   std::unordered_set<TaskID> removed_task_ids;
-  for (const auto &it : tasks_with_resources) {
-    const auto &task_resources = it.first;
-    for (const auto &task_id : it.second) {
+
+  // Dispatch tasks in priority order by class. This avoids starvation problems where
+  // one class of tasks become stuck behind others in the queue, causing Ray to start
+  // many workers. See #3644 for a more detailed description of this issue.
+  std::vector<const std::pair<const SchedulingClass, ordered_set<TaskID>> *> fair_order;
+  for (auto &it : tasks_by_class) {
+    fair_order.emplace_back(&it);
+  }
+  // Prioritize classes that have fewer currently running tasks. Note that we only
+  // sort once per round of task dispatch, which is less fair then it could be, but
+  // is simpler and faster.
+  if (fair_queueing_enabled_) {
+    std::sort(
+        std::begin(fair_order), std::end(fair_order),
+        [this](const std::pair<const SchedulingClass, ordered_set<ray::TaskID>> *&a,
+               const std::pair<const SchedulingClass, ordered_set<ray::TaskID>> *&b) {
+          return local_queues_.NumRunning(a->first) < local_queues_.NumRunning(b->first);
+        });
+  }
+  // Approximate fair round robin between classes.
+  for (const auto &it : fair_order) {
+    const auto &task_resources =
+        TaskSpecification::GetSchedulingClassDescriptor(it->first).first;
+    // FIFO order within each class.
+    for (const auto &task_id : it->second) {
       const auto &task = local_queues_.GetTaskOfState(task_id, TaskState::READY);
       if (!local_available_resources_.Contains(task_resources)) {
         // All the tasks in it.second have the same resource shape, so
@@ -985,7 +1009,7 @@ void NodeManager::HandleWorkerAvailable(
   cluster_resource_map_[local_client_id].SetLoadResources(
       local_queues_.GetResourceLoad());
   // Call task dispatch to assign work to the new worker.
-  DispatchTasks(local_queues_.GetReadyTasksWithResources());
+  DispatchTasks(local_queues_.GetReadyTasksByClass());
 }
 
 void NodeManager::ProcessDisconnectClientMessage(
@@ -1090,7 +1114,7 @@ void NodeManager::ProcessDisconnectClientMessage(
                    << "job_id: " << worker->GetAssignedJobId();
 
     // Since some resources may have been released, we can try to dispatch more tasks.
-    DispatchTasks(local_queues_.GetReadyTasksWithResources());
+    DispatchTasks(local_queues_.GetReadyTasksByClass());
   } else if (is_driver) {
     // The client is a driver.
     const auto job_id = worker->GetAssignedJobId();
@@ -1684,7 +1708,7 @@ void NodeManager::HandleTaskBlocked(const std::shared_ptr<LocalClientConnection>
       worker->MarkBlocked();
 
       // Try dispatching tasks since we may have released some resources.
-      DispatchTasks(local_queues_.GetReadyTasksWithResources());
+      DispatchTasks(local_queues_.GetReadyTasksByClass());
     }
   } else {
     // The client is a driver. Drivers do not hold resources, so we simply mark
@@ -1782,7 +1806,7 @@ void NodeManager::EnqueuePlaceableTask(const Task &task) {
   // (See design_docs/task_states.rst for the state transition diagram.)
   if (args_ready) {
     local_queues_.QueueTasks({task}, TaskState::READY);
-    DispatchTasks(MakeTasksWithResources({task}));
+    DispatchTasks(MakeTasksByClass({task}));
   } else {
     local_queues_.QueueTasks({task}, TaskState::WAITING);
   }
@@ -1881,8 +1905,8 @@ void NodeManager::FinishAssignedTask(Worker &worker) {
       task_resources.ToResourceSet());
   worker.ResetTaskResourceIds();
 
-  if (task.GetTaskSpecification().IsActorCreationTask() ||
-      task.GetTaskSpecification().IsActorTask()) {
+  const auto &spec = task.GetTaskSpecification();
+  if (spec.IsActorCreationTask() || spec.IsActorTask()) {
     // If this was an actor or actor creation task, handle the actor's new
     // state.
     FinishAssignedActorTask(worker, task);
@@ -1898,8 +1922,7 @@ void NodeManager::FinishAssignedTask(Worker &worker) {
   // Unset the worker's assigned task.
   worker.AssignTaskId(TaskID::Nil());
   // Unset the worker's assigned job Id if this is not an actor.
-  if (!task.GetTaskSpecification().IsActorCreationTask() &&
-      !task.GetTaskSpecification().IsActorTask()) {
+  if (!spec.IsActorCreationTask() && !spec.IsActorTask()) {
     worker.AssignJobId(JobID::Nil());
   }
 }
@@ -2227,7 +2250,7 @@ void NodeManager::HandleObjectLocal(const ObjectID &object_id) {
     // Queue and dispatch the tasks that are ready to run (i.e., WAITING).
     auto ready_tasks = local_queues_.RemoveTasks(ready_task_id_set);
     local_queues_.QueueTasks(ready_tasks, TaskState::READY);
-    DispatchTasks(MakeTasksWithResources(ready_tasks));
+    DispatchTasks(MakeTasksByClass(ready_tasks));
   }
 }
 
@@ -2464,7 +2487,7 @@ void NodeManager::FinishAssignTask(const TaskID &task_id, Worker &worker, bool s
     // assigned to a worker once one becomes available.
     // (See design_docs/task_states.rst for the state transition diagram.)
     local_queues_.QueueTasks({assigned_task}, TaskState::READY);
-    DispatchTasks(MakeTasksWithResources({assigned_task}));
+    DispatchTasks(MakeTasksByClass({assigned_task}));
   }
 }
 
diff --git a/src/ray/raylet/node_manager.h b/src/ray/raylet/node_manager.h
index 2afd90460..58b4b381a 100644
--- a/src/ray/raylet/node_manager.h
+++ b/src/ray/raylet/node_manager.h
@@ -52,6 +52,8 @@ struct NodeManagerConfig {
   uint64_t heartbeat_period_ms;
   /// The time between debug dumps in milliseconds, or -1 to disable.
   uint64_t debug_dump_period_ms;
+  /// Whether to enable fair queueing between task classes in raylet.
+  bool fair_queueing_enabled;
   /// the maximum lineage size.
   uint64_t max_lineage_size;
   /// The store socket name.
@@ -304,7 +306,7 @@ class NodeManager : public rpc::NodeManagerServiceHandler {
   /// \param tasks_with_resources Mapping from resource shapes to tasks with
   /// that resource shape.
   void DispatchTasks(
-      const std::unordered_map<ResourceSet, ordered_set<TaskID>> &tasks_with_resources);
+      const std::unordered_map<SchedulingClass, ordered_set<TaskID>> &tasks_by_class);
 
   /// Handle a task that is blocked. This could be a task assigned to a worker,
   /// an out-of-band task (e.g., a thread created by the application), or a
@@ -512,6 +514,8 @@ class NodeManager : public rpc::NodeManagerServiceHandler {
   std::chrono::milliseconds heartbeat_period_;
   /// The period between debug state dumps.
   int64_t debug_dump_period_;
+  /// Whether to enable fair queueing between task classes in raylet.
+  bool fair_queueing_enabled_;
   /// Whether we have printed out a resource deadlock warning.
   bool resource_deadlock_warned_ = false;
   /// The path to the ray temp dir.
diff --git a/src/ray/raylet/scheduling_queue.cc b/src/ray/raylet/scheduling_queue.cc
index 8e20aacfa..85b2efba1 100644
--- a/src/ray/raylet/scheduling_queue.cc
+++ b/src/ray/raylet/scheduling_queue.cc
@@ -95,23 +95,23 @@ const ResourceSet &TaskQueue::GetCurrentResourceLoad() const {
 }
 
 bool ReadyQueue::AppendTask(const TaskID &task_id, const Task &task) {
-  const auto &resources = task.GetTaskSpecification().GetRequiredResources();
-  tasks_with_resources_[resources].push_back(task_id);
+  const auto &scheduling_class = task.GetTaskSpecification().GetSchedulingClass();
+  tasks_by_class_[scheduling_class].push_back(task_id);
   return TaskQueue::AppendTask(task_id, task);
 }
 
 bool ReadyQueue::RemoveTask(const TaskID &task_id, std::vector<Task> *removed_tasks) {
   if (task_map_.find(task_id) != task_map_.end()) {
-    const auto &resources =
-        task_map_[task_id]->GetTaskSpecification().GetRequiredResources();
-    tasks_with_resources_[resources].erase(task_id);
+    const auto &scheduling_class =
+        task_map_[task_id]->GetTaskSpecification().GetSchedulingClass();
+    tasks_by_class_[scheduling_class].erase(task_id);
   }
   return TaskQueue::RemoveTask(task_id, removed_tasks);
 }
 
-const std::unordered_map<ResourceSet, ordered_set<TaskID>>
-    &ReadyQueue::GetTasksWithResources() const {
-  return tasks_with_resources_;
+const std::unordered_map<SchedulingClass, ordered_set<TaskID>>
+    &ReadyQueue::GetTasksByClass() const {
+  return tasks_by_class_;
 }
 
 const std::list<Task> &SchedulingQueue::GetTasks(TaskState task_state) const {
@@ -119,9 +119,9 @@ const std::list<Task> &SchedulingQueue::GetTasks(TaskState task_state) const {
   return queue->GetTasks();
 }
 
-const std::unordered_map<ResourceSet, ordered_set<TaskID>>
-    &SchedulingQueue::GetReadyTasksWithResources() const {
-  return ready_queue_->GetTasksWithResources();
+const std::unordered_map<SchedulingClass, ordered_set<TaskID>>
+    &SchedulingQueue::GetReadyTasksByClass() const {
+  return ready_queue_->GetTasksByClass();
 }
 
 const Task &SchedulingQueue::GetTaskOfState(const TaskID &task_id,
@@ -223,6 +223,10 @@ void SchedulingQueue::RemoveTasksFromQueue(ray::raylet::TaskState task_state,
     if (queue->RemoveTask(task_id, removed_tasks)) {
       RAY_LOG(DEBUG) << "Removed task " << task_id << " from "
                      << GetTaskStateString(task_state) << " queue";
+      if (task_state == TaskState::RUNNING) {
+        num_running_tasks_
+            [removed_tasks->back().GetTaskSpecification().GetSchedulingClass()] -= 1;
+      }
       it = task_ids.erase(it);
     } else {
       it++;
@@ -351,6 +355,9 @@ void SchedulingQueue::QueueTasks(const std::vector<Task> &tasks, TaskState task_
   for (const auto &task : tasks) {
     RAY_LOG(DEBUG) << "Added task " << task.GetTaskSpecification().TaskId() << " to "
                    << GetTaskStateString(task_state) << " queue";
+    if (task_state == TaskState::RUNNING) {
+      num_running_tasks_[task.GetTaskSpecification().GetSchedulingClass()] += 1;
+    }
     queue->AppendTask(task.GetTaskSpecification().TaskId(), task);
   }
 }
@@ -417,6 +424,15 @@ const std::unordered_set<TaskID> &SchedulingQueue::GetDriverTaskIds() const {
   return driver_task_ids_;
 }
 
+int SchedulingQueue::NumRunning(const SchedulingClass &cls) const {
+  auto it = num_running_tasks_.find(cls);
+  if (it == num_running_tasks_.end()) {
+    return 0;
+  } else {
+    return it->second;
+  }
+}
+
 std::string SchedulingQueue::DebugString() const {
   std::stringstream result;
   result << "SchedulingQueue:";
@@ -426,6 +442,30 @@ std::string SchedulingQueue::DebugString() const {
            << " tasks: " << GetTaskQueue(task_state)->GetTasks().size();
   }
   result << "\n- num tasks blocked: " << blocked_task_ids_.size();
+  result << "\nScheduledTaskCounts:";
+  size_t total = 0;
+  for (const auto &pair : num_running_tasks_) {
+    result << "\n- ";
+    auto desc = TaskSpecification::GetSchedulingClassDescriptor(pair.first);
+    for (const auto &str : desc.second) {
+      // Only print the ASCII parts of the function descriptor.
+      bool ok = str.size() > 0;
+      for (char c : str) {
+        if (!isprint(c)) {
+          ok = false;
+        }
+      }
+      if (ok) {
+        result << str;
+        result << ".";
+      }
+    }
+    result << desc.first.ToString();
+    result << ": " << pair.second;
+    total += pair.second;
+  }
+  RAY_CHECK(total == GetTaskQueue(TaskState::RUNNING)->GetTasks().size())
+      << total << " vs " << GetTaskQueue(TaskState::RUNNING)->GetTasks().size();
   return result.str();
 }
 
diff --git a/src/ray/raylet/scheduling_queue.h b/src/ray/raylet/scheduling_queue.h
index 2c503dc38..3bea64911 100644
--- a/src/ray/raylet/scheduling_queue.h
+++ b/src/ray/raylet/scheduling_queue.h
@@ -132,12 +132,11 @@ class ReadyQueue : public TaskQueue {
   /// \brief Get a mapping from resource shape to tasks.
   ///
   /// \return Mapping from resource set to task IDs with these resource requirements.
-  const std::unordered_map<ResourceSet, ordered_set<TaskID>> &GetTasksWithResources()
-      const;
+  const std::unordered_map<SchedulingClass, ordered_set<TaskID>> &GetTasksByClass() const;
 
  private:
-  /// Index from resource shape to tasks that require these resources.
-  std::unordered_map<ResourceSet, ordered_set<TaskID>> tasks_with_resources_;
+  /// Index from task description to tasks queued of that type.
+  std::unordered_map<SchedulingClass, ordered_set<TaskID>> tasks_by_class_;
 };
 
 /// \class SchedulingQueue
@@ -183,7 +182,7 @@ class SchedulingQueue {
   /// Get a reference to the queue of ready tasks.
   ///
   /// \return A reference to the queue of ready tasks.
-  const std::unordered_map<ResourceSet, ordered_set<TaskID>> &GetReadyTasksWithResources()
+  const std::unordered_map<SchedulingClass, ordered_set<TaskID>> &GetReadyTasksByClass()
       const;
 
   /// Get a task from the queue of a given state. The caller must ensure that
@@ -302,6 +301,11 @@ class SchedulingQueue {
   /// \return Aggregate resource demand from ready tasks.
   ResourceSet GetReadyQueueResources() const;
 
+  /// Returns the number of running tasks in this class.
+  ///
+  /// \return int.
+  int NumRunning(const SchedulingClass &cls) const;
+
   /// Returns debug string for class.
   ///
   /// \return string.
@@ -331,6 +335,8 @@ class SchedulingQueue {
 
   // A pointer to the ready queue.
   const std::shared_ptr<ReadyQueue> ready_queue_;
+  /// Track the breakdown of tasks by class in the RUNNING queue.
+  std::unordered_map<SchedulingClass, int32_t> num_running_tasks_;
   // A pointer to the task queues. These contain all tasks that have a task
   // state < TaskState::kNumTaskQueues.
   std::array<std::shared_ptr<TaskQueue>, static_cast<int>(TaskState::kNumTaskQueues)>