diff --git a/store/src/test/java/org/apache/rocketmq/store/MessageStoreStateMachineTest.java b/store/src/test/java/org/apache/rocketmq/store/MessageStoreStateMachineTest.java
index d00074dbcbc..333e419681a 100644
--- a/store/src/test/java/org/apache/rocketmq/store/MessageStoreStateMachineTest.java
+++ b/store/src/test/java/org/apache/rocketmq/store/MessageStoreStateMachineTest.java
@@ -19,7 +19,6 @@
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
 import static org.junit.jupiter.api.Assertions.assertThrows;
-import static org.junit.jupiter.api.Assertions.assertTrue;
 import static org.mockito.ArgumentMatchers.anyString;
 import static org.mockito.ArgumentMatchers.eq;
 import static org.mockito.Mockito.anyLong;
@@ -107,41 +106,4 @@ public void testGetCurrentState() {
         // Verify the current state
         assertEquals(MessageStoreState.INIT, stateMachine.getCurrentState());
     }
-
-    /**
-     * Test getTotalRunningTimeMs method.
-     */
-    @Test
-    public void testGetTotalRunningTimeMs() {
-        // Sleep for a short duration to simulate elapsed time
-        try {
-            Thread.sleep(100);
-        } catch (InterruptedException e) {
-            Thread.currentThread().interrupt();
-        }
-
-        // Verify the total running time is approximately correct
-        long totalTime = stateMachine.getTotalRunningTimeMs();
-        assertTrue(totalTime >= 100 && totalTime < 200);
-    }
-
-    /**
-     * Test getCurrentStateRunningTimeMs method.
-     */
-    @Test
-    public void testGetCurrentStateRunningTimeMs() {
-        // Perform a state transition
-        stateMachine.transitTo(MessageStoreState.LOAD_COMMITLOG_OK);
-
-        // Sleep for a short duration to simulate elapsed time
-        try {
-            Thread.sleep(100);
-        } catch (InterruptedException e) {
-            Thread.currentThread().interrupt();
-        }
-
-        // Verify the current state running time is approximately correct
-        long currentStateTime = stateMachine.getCurrentStateRunningTimeMs();
-        assertTrue(currentStateTime >= 100 && currentStateTime < 200);
-    }
 }
diff --git a/tieredstore/src/main/java/org/apache/rocketmq/tieredstore/TieredMessageStore.java b/tieredstore/src/main/java/org/apache/rocketmq/tieredstore/TieredMessageStore.java
index f1c935d00b7..19b587fa327 100644
--- a/tieredstore/src/main/java/org/apache/rocketmq/tieredstore/TieredMessageStore.java
+++ b/tieredstore/src/main/java/org/apache/rocketmq/tieredstore/TieredMessageStore.java
@@ -370,11 +370,11 @@ public long getOffsetInQueueByTime(String topic, int queueId, long timestamp, Bo
                 .build();
             TieredStoreMetricsManager.apiLatency.record(stopwatch.elapsed(TimeUnit.MILLISECONDS), latencyAttributes);
             if (offsetInTieredStore == -1L && !isForce) {
-                return next.getOffsetInQueueByTime(topic, queueId, timestamp);
+                return next.getOffsetInQueueByTime(topic, queueId, timestamp, boundaryType);
             }
             return offsetInTieredStore;
         }
-        return next.getOffsetInQueueByTime(topic, queueId, timestamp);
+        return next.getOffsetInQueueByTime(topic, queueId, timestamp, boundaryType);
     }
 
     @Override
diff --git a/tieredstore/src/test/java/org/apache/rocketmq/tieredstore/TieredMessageStoreTest.java b/tieredstore/src/test/java/org/apache/rocketmq/tieredstore/TieredMessageStoreTest.java
index bb259ae811a..1a0240681c0 100644
--- a/tieredstore/src/test/java/org/apache/rocketmq/tieredstore/TieredMessageStoreTest.java
+++ b/tieredstore/src/test/java/org/apache/rocketmq/tieredstore/TieredMessageStoreTest.java
@@ -62,7 +62,6 @@
 import static org.mockito.ArgumentMatchers.anyInt;
 import static org.mockito.ArgumentMatchers.anyLong;
 import static org.mockito.ArgumentMatchers.anyString;
-import static org.mockito.ArgumentMatchers.eq;
 import static org.mockito.Mockito.when;
 
 public class TieredMessageStoreTest {
@@ -275,19 +274,43 @@ public void testGetMessageStoreTimeStampAsync() {
 
     @Test
     public void testGetOffsetInQueueByTime() {
+        final long earliestMsgTime = 100L;
         Properties properties = new Properties();
         properties.setProperty("tieredStorageLevel", "FORCE");
         configuration.update(properties);
 
-        Mockito.when(fetcher.getOffsetInQueueByTime(anyString(), anyInt(), anyLong(), eq(BoundaryType.LOWER))).thenReturn(1L);
-        Mockito.when(defaultStore.getOffsetInQueueByTime(anyString(), anyInt(), anyLong())).thenReturn(2L);
-        Mockito.when(defaultStore.getEarliestMessageTime()).thenReturn(100L);
+        Mockito.when(fetcher.getOffsetInQueueByTime(anyString(), anyInt(), anyLong(), any(BoundaryType.class)))
+            .thenAnswer(ivk -> ivk.getArgument(3, BoundaryType.class) == BoundaryType.LOWER ? 1L : 2L);
+        Mockito.when(defaultStore.getOffsetInQueueByTime(anyString(), anyInt(), anyLong(), any(BoundaryType.class)))
+            .thenAnswer(ivk -> {
+                long time = ivk.getArgument(2, Long.class);
+                if (time < earliestMsgTime) {
+                    return -1L;
+                }
+                return ivk.getArgument(3, BoundaryType.class) == BoundaryType.LOWER ? 3L : 4L;
+            });
+        Mockito.when(defaultStore.getEarliestMessageTime()).thenReturn(earliestMsgTime);
+
+        // Message not in disk, but force, found in tired storage.
         Assert.assertEquals(1L, currentStore.getOffsetInQueueByTime(mq.getTopic(), mq.getQueueId(), 1000, BoundaryType.LOWER));
+        Assert.assertEquals(2L, currentStore.getOffsetInQueueByTime(mq.getTopic(), mq.getQueueId(), 1000, BoundaryType.UPPER));
+        // Message in disk, and force, found in tired storage.
         Assert.assertEquals(1L, currentStore.getOffsetInQueueByTime(mq.getTopic(), mq.getQueueId(), 0, BoundaryType.LOWER));
+        Assert.assertEquals(2L, currentStore.getOffsetInQueueByTime(mq.getTopic(), mq.getQueueId(), 0, BoundaryType.UPPER));
 
-        Mockito.when(fetcher.getOffsetInQueueByTime(anyString(), anyInt(), anyLong(), eq(BoundaryType.LOWER))).thenReturn(-1L);
+        // Message in disk, but force, and not found in tired storage.
+        Mockito.when(fetcher.getOffsetInQueueByTime(anyString(), anyInt(), anyLong(), any(BoundaryType.class))).thenReturn(-1L);
         Assert.assertEquals(-1L, currentStore.getOffsetInQueueByTime(mq.getTopic(), mq.getQueueId(), 0));
         Assert.assertEquals(-1L, currentStore.getOffsetInQueueByTime(mq.getTopic(), mq.getQueueId(), 0, BoundaryType.LOWER));
+
+        properties.setProperty("tieredStorageLevel", "NOT_IN_DISK");
+        configuration.update(properties);
+        // Message not in disk, and not found in tired storage.
+        Assert.assertEquals(-1L, currentStore.getOffsetInQueueByTime(mq.getTopic(), mq.getQueueId(), 0, BoundaryType.LOWER));
+        Assert.assertEquals(-1L, currentStore.getOffsetInQueueByTime(mq.getTopic(), mq.getQueueId(), 0, BoundaryType.UPPER));
+        // Message in disk, and found in disk.
+        Assert.assertEquals(3L, currentStore.getOffsetInQueueByTime(mq.getTopic(), mq.getQueueId(), 1000, BoundaryType.LOWER));
+        Assert.assertEquals(4L, currentStore.getOffsetInQueueByTime(mq.getTopic(), mq.getQueueId(), 1000, BoundaryType.UPPER));
     }
 
     @Test