diff --git a/dali/pipeline/executor/executor2/exec2.cc b/dali/pipeline/executor/executor2/exec2.cc
index 9821e086a7a..2f4e71f3624 100644
--- a/dali/pipeline/executor/executor2/exec2.cc
+++ b/dali/pipeline/executor/executor2/exec2.cc
@@ -48,6 +48,7 @@ void ApplyConcurrencyLimit(ExecGraph &graph, const Executor2::Config &config) {
       LimitBackendConcurrency(graph, OpType::CPU);
       break;  // other operators have no restrictions
     case OperatorConcurrency::Backend:
+      LimitBackendConcurrency(graph, OpType::CPU);
       LimitBackendConcurrency(graph, OpType::GPU);
       LimitBackendConcurrency(graph, OpType::MIXED);
       break;
@@ -70,6 +71,9 @@ class Executor2::Impl {
  public:
   explicit Impl(const Config &config) : config_(config) {
   }
+  ~Impl() {
+    Shutdown();
+  }
 
   enum class State {
     New = 0,
@@ -83,7 +87,6 @@ class Executor2::Impl {
   void Build(const graph::OpGraph &graph) {
     if (state_ != State::New)
       throw std::logic_error("Already built.");
-    std::cerr << "Building " << (void*)this << std::endl;
     state_ = State::Building;
     DeviceGuard dg(config_.device.value_or(CPU_ONLY_DEVICE_ID));
     graph_.Lower(graph);
@@ -154,7 +157,6 @@ class Executor2::Impl {
   void Shutdown() {
     if (state_ != State::Running)
       return;
-    std::cerr << "Shutting down " << (void*)this << std::endl;
     state_ = State::ShutdownRequested;
     if (exec_)
       exec_->Shutdown();
diff --git a/dali/pipeline/executor/executor2/exec2_test.cc b/dali/pipeline/executor/executor2/exec2_test.cc
index cdc9e894bbb..495612bbfcc 100644
--- a/dali/pipeline/executor/executor2/exec2_test.cc
+++ b/dali/pipeline/executor/executor2/exec2_test.cc
@@ -115,28 +115,30 @@ TEST_P(Exec2Test, Graph1_CPUOnly) {
   Executor2 exec(config_);
   graph::OpGraph graph = GetTestGraph1();
   exec.Build(graph);
-  exec.Run();
-  exec.Run();
+  for (int i = 0; i < 10; i++) {
+    exec.Run();
+  }
   Workspace ws;
-  exec.Outputs(&ws);
-  CheckTestGraph1Results(ws, config_.max_batch_size);
-  ws.Clear();
-  exec.Outputs(&ws);
-  CheckTestGraph1Results(ws, config_.max_batch_size);
+  for (int i = 0; i < 10; i++) {
+    ws.Clear();
+    exec.Outputs(&ws);
+    CheckTestGraph1Results(ws, config_.max_batch_size);
+  }
 }
 
 TEST_P(Exec2Test, Graph2_CPU2GPU) {
   Executor2 exec(config_);
   graph::OpGraph graph = GetTestGraph2();
   exec.Build(graph);
-  exec.Run();
-  exec.Run();
+  for (int i = 0; i < 10; i++) {
+    exec.Run();
+  }
   Workspace ws;
-  exec.Outputs(&ws);
-  CheckTestGraph2Results(ws, config_.max_batch_size);
-  ws.Clear();
-  exec.Outputs(&ws);
-  CheckTestGraph2Results(ws, config_.max_batch_size);
+  for (int i = 0; i < 10; i++) {
+    ws.Clear();
+    exec.Outputs(&ws);
+    CheckTestGraph2Results(ws, config_.max_batch_size);
+  }
 }
 
 
diff --git a/dali/pipeline/executor/executor2/exec2_test.h b/dali/pipeline/executor/executor2/exec2_test.h
index a1e01ade128..ca6efaef69c 100644
--- a/dali/pipeline/executor/executor2/exec2_test.h
+++ b/dali/pipeline/executor/executor2/exec2_test.h
@@ -45,18 +45,27 @@ class DummyOpCPU : public Operator<CPUBackend> {
   void RunImpl(Workspace &ws) override {
     int N = ws.GetRequestedBatchSize(0);
     addend_.Acquire(spec_, ws, N);
+    sample_sums_.resize(N);
+    auto &tp = ws.GetThreadPool();
     for (int s = 0; s < N; s++) {
-      int sum = *addend_[s].data + s;
-      for (int i = 0; i < ws.NumInput(); i++) {
-        sum += *ws.Input<CPUBackend>(i)[s].data<int>();
-      }
-      *ws.Output<CPUBackend>(0)[s].mutable_data<int>() = sum;
+      auto sample_sum = [&, s](int) {
+        int sum = *addend_[s].data + s;
+        for (int i = 0; i < ws.NumInput(); i++) {
+          sum += *ws.Input<CPUBackend>(i)[s].data<int>();
+        }
+        sample_sums_[s] = sum;
+      };
+      tp.AddWork(sample_sum);
     }
+    tp.RunAll(true);
+    for (int s = 0; s < N; s++)
+      *ws.Output<CPUBackend>(0)[s].mutable_data<int>() = sample_sums_[s];
   }
 
   bool CanInferOutputs() const override { return true; }
   ArgValue<int> addend_{"addend", spec_};
 
+  std::vector<int> sample_sums_;
   std::string instance_name_;
 };
 
diff --git a/dali/pipeline/executor/executor2/exec_graph.h b/dali/pipeline/executor/executor2/exec_graph.h
index b4d2a401361..f654f40a115 100644
--- a/dali/pipeline/executor/executor2/exec_graph.h
+++ b/dali/pipeline/executor/executor2/exec_graph.h
@@ -129,6 +129,8 @@ class DLL_PUBLIC ExecNode {
    * from being executed concurrently.
    */
   std::shared_ptr<tasking::Semaphore> concurrency;
+  std::atomic_int actual_concurrency{0};
+
   /** Limits the number of output buffers for the operator.
    *
    * If the graph is scheduled multiple times ahead, the operator would produce multiple results,
diff --git a/dali/pipeline/executor/executor2/exec_graph_test.cc b/dali/pipeline/executor/executor2/exec_graph_test.cc
index 000c5667624..a285edb7dac 100644
--- a/dali/pipeline/executor/executor2/exec_graph_test.cc
+++ b/dali/pipeline/executor/executor2/exec_graph_test.cc
@@ -24,6 +24,16 @@ namespace dali {
 namespace exec2 {
 namespace test {
 
+namespace {
+void LimitBackendConcurrency(ExecGraph &graph, OpType backend, int max_concurrency = 1) {
+  auto sem = std::make_shared<tasking::Semaphore>(max_concurrency);
+  for (auto &n : graph.Nodes()) {
+    if (n.backend == backend)
+        n.concurrency = sem;
+  }
+}
+}  // namespace
+
 TEST(ExecGraphTest, SimpleGraph) {
   int batch_size = 32;
   OpSpec spec0(kTestOpName);
@@ -62,6 +72,7 @@ TEST(ExecGraphTest, SimpleGraph) {
   g.Link(n0, 0, n2, 0);
   g.Link(n1, 0, n2, 1);
   g.Link(n2, 0, no, 0);
+  LimitBackendConcurrency(g, OpType::CPU);
 
   WorkspaceParams params = {};
   auto tp = std::make_unique<ThreadPool>(std::thread::hardware_concurrency(), 0, false, "test");
@@ -114,14 +125,15 @@ TEST(ExecGraphTest, SimpleGraphRepeat) {
        .AddOutput("op2e0", "cpu")
        .AddArg("name", "op2");
   auto op2 = std::make_unique<DummyOpCPU>(spec2);
-  ExecGraph def;
-  ExecNode *n2 = def.AddNode(std::move(op2));
-  ExecNode *n1 = def.AddNode(std::move(op1));
-  ExecNode *n0 = def.AddNode(std::move(op0));
-  ExecNode *no = def.AddOutputNode();
-  def.Link(n0, 0, n2, 0);
-  def.Link(n1, 0, n2, 1);
-  def.Link(n2, 0, no, 0);
+  ExecGraph g;
+  ExecNode *n2 = g.AddNode(std::move(op2));
+  ExecNode *n1 = g.AddNode(std::move(op1));
+  ExecNode *n0 = g.AddNode(std::move(op0));
+  ExecNode *no = g.AddOutputNode();
+  g.Link(n0, 0, n2, 0);
+  g.Link(n1, 0, n2, 1);
+  g.Link(n2, 0, no, 0);
+  LimitBackendConcurrency(g, OpType::CPU);
   ThreadPool tp(4, 0, false, "test");
   WorkspaceParams params = {};
   ExecEnv env;
@@ -135,8 +147,8 @@ TEST(ExecGraphTest, SimpleGraphRepeat) {
     ex.Start();
     auto start = dali::test::perf_timer::now();
     for (int i = 0; i < N; i++) {
-      def.PrepareIteration(std::make_shared<IterationData>(), params);
-      auto fut = def.Launch(ex);
+      g.PrepareIteration(std::make_shared<IterationData>(), params);
+      auto fut = g.Launch(ex);
       auto &pipe_out = fut.Value<const PipelineOutput &>();
       auto &ws = pipe_out.workspace;
       auto &out = ws.Output<CPUBackend>(0);
@@ -179,14 +191,16 @@ TEST(ExecGraphTest, SimpleGraphScheduleAhead) {
        .AddOutput("op2e0", "cpu")
        .AddArg("name", "op2");
   auto op2 = std::make_unique<DummyOpCPU>(spec2);
-  ExecGraph def;
-  ExecNode *n2 = def.AddNode(std::move(op2));
-  ExecNode *n1 = def.AddNode(std::move(op1));
-  ExecNode *n0 = def.AddNode(std::move(op0));
-  ExecNode *no = def.AddOutputNode();
-  def.Link(n0, 0, n2, 0);
-  def.Link(n1, 0, n2, 1);
-  def.Link(n2, 0, no, 0);
+  ExecGraph g;
+  ExecNode *n2 = g.AddNode(std::move(op2));
+  ExecNode *n1 = g.AddNode(std::move(op1));
+  ExecNode *n0 = g.AddNode(std::move(op0));
+  ExecNode *no = g.AddOutputNode();
+  g.Link(n0, 0, n2, 0);
+  g.Link(n1, 0, n2, 1);
+  g.Link(n2, 0, no, 0);
+  LimitBackendConcurrency(g, OpType::CPU);
+
   ThreadPool tp(4, 0, false, "test");
   WorkspaceParams params = {};
   ExecEnv env;
@@ -200,8 +214,8 @@ TEST(ExecGraphTest, SimpleGraphScheduleAhead) {
   std::vector<tasking::TaskFuture> fut;
   fut.reserve(N);
   for (int i = 0; i < N; i++) {
-    def.PrepareIteration(std::make_shared<IterationData>(), params);
-    fut.push_back(def.Launch(ex));
+    g.PrepareIteration(std::make_shared<IterationData>(), params);
+    fut.push_back(g.Launch(ex));
   }
 
   int ctr = 0;
@@ -330,6 +344,7 @@ TEST(ExecGraphTest, LoweredExec) {
   graph::OpGraph def = GetTestGraph1();
   ExecGraph g;
   g.Lower(def);
+  LimitBackendConcurrency(g, OpType::CPU);
 
   ThreadPool tp(std::thread::hardware_concurrency(), 0, false, "test");
   WorkspaceParams params = {};
diff --git a/dali/pipeline/executor/executor2/op_task.cc b/dali/pipeline/executor/executor2/op_task.cc
index 0a5561962b0..4ad8c21f841 100644
--- a/dali/pipeline/executor/executor2/op_task.cc
+++ b/dali/pipeline/executor/executor2/op_task.cc
@@ -22,6 +22,7 @@
 #include "dali/core/nvtx.h"
 #include "dali/pipeline/operator/operator.h"
 #include "dali/pipeline/operator/checkpointing/checkpoint.h"
+#include "dali/core/call_at_exit.h"
 
 namespace dali {
 namespace exec2 {
@@ -39,6 +40,11 @@ tasking::SharedTask OpTask::CreateTask(ExecNode *node, CachedWorkspace ws) {
 }
 
 OpTask::OpTaskOutputs OpTask::Run() {
+  auto c = ++node_->actual_concurrency;
+  AtScopeExit([&]() { --node_->actual_concurrency; });
+  if (node_->concurrency) {
+    assert(c <= node_->concurrency->MaxCount());
+  }
   SetWorkspaceInputs();
   SetupOp();
   RunOp();
diff --git a/include/dali/core/exec/tasking/sync.h b/include/dali/core/exec/tasking/sync.h
index 90158e1a3dc..16c04d0ee8a 100644
--- a/include/dali/core/exec/tasking/sync.h
+++ b/include/dali/core/exec/tasking/sync.h
@@ -158,6 +158,8 @@ class Semaphore : public Releasable {
   explicit Semaphore(int max_count) : Semaphore(max_count, max_count) {}
   Semaphore(int max_count, int initial_count) : count(initial_count), max_count(max_count) {}
 
+  constexpr int MaxCount() const { return max_count; }
+
  protected:
   mutable spinlock lock_;