diff --git a/examples/analytical_apps/pagerank/pagerank_directed.h b/examples/analytical_apps/pagerank/pagerank_directed.h
index 3abc2a78..9815af8b 100644
--- a/examples/analytical_apps/pagerank/pagerank_directed.h
+++ b/examples/analytical_apps/pagerank/pagerank_directed.h
@@ -112,6 +112,9 @@ class PageRankDirected
 
       for (fid_t i = 2; i < frag.fnum(); ++i) {
         fid_t src_fid = messages.UpdatePartialOuterVertices();
+        if (src_fid == kInvalidFid) {
+          continue;
+        }
         ForEach(inner_vertices, [src_fid, &frag, &ctx](int tid, vertex_t u) {
           double cur = ctx.next_result[u];
           auto es = frag.GetIncomingAdjList(u, src_fid);
@@ -123,22 +126,24 @@ class PageRankDirected
       }
 
       fid_t src_fid = messages.UpdatePartialOuterVertices();
-      ForEach(inner_vertices, [src_fid, &frag, &ctx, base, &dangling_sums](
-                                  int tid, vertex_t u) {
-        double cur = ctx.next_result[u];
-        auto es = frag.GetIncomingAdjList(u, src_fid);
-        for (auto& e : es) {
-          cur += ctx.result[e.get_neighbor()];
-        }
-        int en = frag.GetLocalOutDegree(u);
-        cur = ctx.delta * cur + base;
-        if (en == 0) {
-          dangling_sums[tid] += cur;
-          ctx.next_result[u] = cur;
-        } else {
-          ctx.next_result[u] = cur / en;
-        }
-      });
+      if (src_fid != kInvalidFid) {
+        ForEach(inner_vertices, [src_fid, &frag, &ctx, base, &dangling_sums](
+                                    int tid, vertex_t u) {
+          double cur = ctx.next_result[u];
+          auto es = frag.GetIncomingAdjList(u, src_fid);
+          for (auto& e : es) {
+            cur += ctx.result[e.get_neighbor()];
+          }
+          int en = frag.GetLocalOutDegree(u);
+          cur = ctx.delta * cur + base;
+          if (en == 0) {
+            dangling_sums[tid] += cur;
+            ctx.next_result[u] = cur;
+          } else {
+            ctx.next_result[u] = cur / en;
+          }
+        });
+      }
     } else {
       // If the fragment is sparse or there is only one fragment, one round of
       // iterating inner vertices is prefered.
diff --git a/examples/analytical_apps/pagerank/pagerank_local.h b/examples/analytical_apps/pagerank/pagerank_local.h
index 3838a4a4..29675a59 100644
--- a/examples/analytical_apps/pagerank/pagerank_local.h
+++ b/examples/analytical_apps/pagerank/pagerank_local.h
@@ -112,14 +112,16 @@ class PageRankLocal
         ctx.preprocess_time += GetCurrentTime();
         ctx.exec_time -= GetCurrentTime();
 #endif
-        ForEach(inner_vertices, [src_fid, &frag, &ctx](int tid, vertex_t u) {
-          double cur = ctx.next_result[u];
-          auto es = frag.GetOutgoingAdjList(u, src_fid);
-          for (auto& e : es) {
-            cur += ctx.result[e.get_neighbor()];
-          }
-          ctx.next_result[u] = cur;
-        });
+        if (src_fid != kInvalidFid) {
+          ForEach(inner_vertices, [src_fid, &frag, &ctx](int tid, vertex_t u) {
+            double cur = ctx.next_result[u];
+            auto es = frag.GetOutgoingAdjList(u, src_fid);
+            for (auto& e : es) {
+              cur += ctx.result[e.get_neighbor()];
+            }
+            ctx.next_result[u] = cur;
+          });
+        }
 #ifdef PROFILING
         ctx.exec_time += GetCurrentTime();
 #endif
@@ -133,27 +135,31 @@ class PageRankLocal
         ctx.preprocess_time += GetCurrentTime();
         ctx.exec_time -= GetCurrentTime();
 #endif
-        if (last_step) {
-          ForEach(inner_vertices, [src_fid, &frag, &ctx](int tid, vertex_t u) {
-            double cur = ctx.next_result[u];
-            auto es = frag.GetOutgoingAdjList(u, src_fid);
-            for (auto& e : es) {
-              cur += ctx.result[e.get_neighbor()];
-            }
-            ctx.next_result[u] = 1 - ctx.delta + ctx.delta * cur;
-          });
-        } else {
-          ForEach(inner_vertices, [src_fid, &frag, &ctx](int tid, vertex_t u) {
-            double cur = ctx.next_result[u];
-            auto es = frag.GetOutgoingAdjList(u, src_fid);
-            for (auto& e : es) {
-              cur += ctx.result[e.get_neighbor()];
-            }
-            ctx.next_result[u] = 1 - ctx.delta + ctx.delta * cur;
-            int en = frag.GetLocalOutDegree(u);
-            ctx.next_result[u] =
-                en > 0 ? ctx.next_result[u] / en : ctx.next_result[u];
-          });
+        if (src_fid != kInvalidFid) {
+          if (last_step) {
+            ForEach(inner_vertices,
+                    [src_fid, &frag, &ctx](int tid, vertex_t u) {
+                      double cur = ctx.next_result[u];
+                      auto es = frag.GetOutgoingAdjList(u, src_fid);
+                      for (auto& e : es) {
+                        cur += ctx.result[e.get_neighbor()];
+                      }
+                      ctx.next_result[u] = 1 - ctx.delta + ctx.delta * cur;
+                    });
+          } else {
+            ForEach(inner_vertices,
+                    [src_fid, &frag, &ctx](int tid, vertex_t u) {
+                      double cur = ctx.next_result[u];
+                      auto es = frag.GetOutgoingAdjList(u, src_fid);
+                      for (auto& e : es) {
+                        cur += ctx.result[e.get_neighbor()];
+                      }
+                      ctx.next_result[u] = 1 - ctx.delta + ctx.delta * cur;
+                      int en = frag.GetLocalOutDegree(u);
+                      ctx.next_result[u] =
+                          en > 0 ? ctx.next_result[u] / en : ctx.next_result[u];
+                    });
+          }
         }
 #ifdef PROFILING
         ctx.exec_time += GetCurrentTime();
@@ -183,14 +189,16 @@ class PageRankLocal
         ctx.preprocess_time += GetCurrentTime();
         ctx.exec_time -= GetCurrentTime();
 #endif
-        ForEach(frag.OuterVertices(src_fid),
-                [&frag, &ctx](int tid, vertex_t u) {
-                  double cur = ctx.result[u] * ctx.delta;
-                  auto es = frag.GetIncomingAdjList(u);
-                  for (auto& e : es) {
-                    atomic_add(ctx.next_result[e.get_neighbor()], cur);
-                  }
-                });
+        if (src_fid != kInvalidFid) {
+          ForEach(frag.OuterVertices(src_fid),
+                  [&frag, &ctx](int tid, vertex_t u) {
+                    double cur = ctx.result[u] * ctx.delta;
+                    auto es = frag.GetIncomingAdjList(u);
+                    for (auto& e : es) {
+                      atomic_add(ctx.next_result[e.get_neighbor()], cur);
+                    }
+                  });
+        }
 #ifdef PROFILING
         ctx.exec_time += GetCurrentTime();
 #endif
diff --git a/examples/analytical_apps/pagerank/pagerank_opt.h b/examples/analytical_apps/pagerank/pagerank_opt.h
index 2857c21a..9920adeb 100644
--- a/examples/analytical_apps/pagerank/pagerank_opt.h
+++ b/examples/analytical_apps/pagerank/pagerank_opt.h
@@ -134,14 +134,16 @@ class PageRankOpt : public BatchShuffleAppBase<FRAG_T, PageRankContext<FRAG_T>>,
         ctx.preprocess_time += GetCurrentTime();
         ctx.exec_time -= GetCurrentTime();
 #endif
-        ForEach(inner_vertices, [src_fid, &frag, &ctx](int tid, vertex_t u) {
-          double cur = ctx.next_result[u];
-          auto es = frag.GetOutgoingAdjList(u, src_fid);
-          for (auto& e : es) {
-            cur += ctx.result[e.get_neighbor()];
-          }
-          ctx.next_result[u] = cur;
-        });
+        if (src_fid != kInvalidFid) {
+          ForEach(inner_vertices, [src_fid, &frag, &ctx](int tid, vertex_t u) {
+            double cur = ctx.next_result[u];
+            auto es = frag.GetOutgoingAdjList(u, src_fid);
+            for (auto& e : es) {
+              cur += ctx.result[e.get_neighbor()];
+            }
+            ctx.next_result[u] = cur;
+          });
+        }
 #ifdef PROFILING
         ctx.exec_time += GetCurrentTime();
 #endif
@@ -155,31 +157,33 @@ class PageRankOpt : public BatchShuffleAppBase<FRAG_T, PageRankContext<FRAG_T>>,
       ctx.preprocess_time += GetCurrentTime();
       ctx.exec_time -= GetCurrentTime();
 #endif
-      if (ctx.step != ctx.max_round) {
-        ForEach(inner_vertices,
-                [src_fid, &frag, &ctx, base](int tid, vertex_t u) {
-                  double cur = ctx.next_result[u];
-                  auto es = frag.GetOutgoingAdjList(u, src_fid);
-                  for (auto& e : es) {
-                    cur += ctx.result[e.get_neighbor()];
-                  }
-                  int en = frag.GetLocalOutDegree(u);
-                  ctx.result[u] = en > 0 ? (ctx.delta * cur + base) / en : base;
-                });
-
-        messages.SyncInnerVertices<fragment_t, double>(frag, ctx.result,
-                                                       thread_num());
-      } else {
-        ForEach(inner_vertices,
-                [src_fid, &frag, &ctx, base](int tid, vertex_t u) {
-                  double cur = ctx.next_result[u];
-                  auto es = frag.GetOutgoingAdjList(u, src_fid);
-                  for (auto& e : es) {
-                    cur += ctx.result[e.get_neighbor()];
-                  }
-                  int en = frag.GetLocalOutDegree(u);
-                  ctx.result[u] = en > 0 ? (ctx.delta * cur + base) : base;
-                });
+      if (src_fid != kInvalidFid) {
+        if (ctx.step != ctx.max_round) {
+          ForEach(inner_vertices, [src_fid, &frag, &ctx, base](int tid,
+                                                               vertex_t u) {
+            double cur = ctx.next_result[u];
+            auto es = frag.GetOutgoingAdjList(u, src_fid);
+            for (auto& e : es) {
+              cur += ctx.result[e.get_neighbor()];
+            }
+            int en = frag.GetLocalOutDegree(u);
+            ctx.result[u] = en > 0 ? (ctx.delta * cur + base) / en : base;
+          });
+
+          messages.SyncInnerVertices<fragment_t, double>(frag, ctx.result,
+                                                         thread_num());
+        } else {
+          ForEach(inner_vertices,
+                  [src_fid, &frag, &ctx, base](int tid, vertex_t u) {
+                    double cur = ctx.next_result[u];
+                    auto es = frag.GetOutgoingAdjList(u, src_fid);
+                    for (auto& e : es) {
+                      cur += ctx.result[e.get_neighbor()];
+                    }
+                    int en = frag.GetLocalOutDegree(u);
+                    ctx.result[u] = en > 0 ? (ctx.delta * cur + base) : base;
+                  });
+        }
       }
 #ifdef PROFILING
       ctx.exec_time += GetCurrentTime();
diff --git a/grape/config.h b/grape/config.h
index aa33dbcb..7f60cfe8 100644
--- a/grape/config.h
+++ b/grape/config.h
@@ -38,6 +38,7 @@ namespace gflags = google;
 
 // type alias
 using fid_t = unsigned;
+const fid_t kInvalidFid = std::numeric_limits<fid_t>::max();
 
 #ifdef USE_HUGEPAGES
 template <typename T>
diff --git a/grape/parallel/batch_shuffle_message_manager.h b/grape/parallel/batch_shuffle_message_manager.h
index b4eedbaf..3bfafec6 100644
--- a/grape/parallel/batch_shuffle_message_manager.h
+++ b/grape/parallel/batch_shuffle_message_manager.h
@@ -262,7 +262,9 @@ class BatchShuffleMessageManager : public MessageManagerBase {
    * is, messages from all other fragments are received.
    */
   void UpdateOuterVertices() {
-    MPI_Waitall(recv_reqs_.size(), &recv_reqs_[0], MPI_STATUSES_IGNORE);
+    if (!recv_reqs_.empty()) {
+      MPI_Waitall(recv_reqs_.size(), &recv_reqs_[0], MPI_STATUSES_IGNORE);
+    }
   }
 
   /**
@@ -272,6 +274,24 @@ class BatchShuffleMessageManager : public MessageManagerBase {
    * @return Source fragment id.
    */
   fid_t UpdatePartialOuterVertices() {
+    if (recv_reqs_.empty()) {
+      return kInvalidFid;
+    }
+
+    bool updateDone = true;
+    for (fid_t i = 0; i < fnum_; ++i) {
+      if (remaining_reqs_[i] > 0) {
+        updateDone = false;
+        break;
+      }
+    }
+    if (updateDone) {
+      remaining_frags_ = 0;
+      recv_reqs_.clear();
+      recv_from_.clear();
+      return kInvalidFid;
+    }
+
     int index;
     fid_t ret;
     while (true) {