diff --git a/lzero/entry/train_alphazero.py b/lzero/entry/train_alphazero.py
index 9cd79aaf9..6744ef871 100644
--- a/lzero/entry/train_alphazero.py
+++ b/lzero/entry/train_alphazero.py
@@ -4,14 +4,15 @@
 from typing import Optional, Tuple
 
 import torch
-from tensorboardX import SummaryWriter
-
 from ding.config import compile_config
 from ding.envs import create_env_manager
 from ding.envs import get_vec_env_setting
 from ding.policy import create_policy
 from ding.utils import set_pkg_seed
 from ding.worker import BaseLearner, create_buffer
+from tensorboardX import SummaryWriter
+
+from lzero.entry.utils import log_buffer_memory_usage
 from lzero.policy import visit_count_temperature
 from lzero.worker import AlphaZeroCollector, AlphaZeroEvaluator
 
@@ -93,6 +94,7 @@ def train_alphazero(
     # Learner's before_run hook.
     learner.call_hook('before_run')
     while True:
+        log_buffer_memory_usage(learner.train_iter, replay_buffer, tb_logger)
         collect_kwargs = {}
         # set temperature for visit count distributions according to the train_iter,
         # please refer to Appendix D in MuZero paper for details.
diff --git a/lzero/entry/train_muzero.py b/lzero/entry/train_muzero.py
index c4e3fd0fa..5f1dc649c 100644
--- a/lzero/entry/train_muzero.py
+++ b/lzero/entry/train_muzero.py
@@ -4,14 +4,15 @@
 from typing import Optional, Tuple
 
 import torch
-from tensorboardX import SummaryWriter
-
 from ding.config import compile_config
 from ding.envs import create_env_manager
 from ding.envs import get_vec_env_setting
 from ding.policy import create_policy
 from ding.utils import set_pkg_seed
 from ding.worker import BaseLearner
+from tensorboardX import SummaryWriter
+
+from lzero.entry.utils import log_buffer_memory_usage
 from lzero.policy import visit_count_temperature
 from lzero.worker import MuZeroCollector, MuZeroEvaluator
 
@@ -109,6 +110,7 @@ def train_muzero(
     # Learner's before_run hook.
     learner.call_hook('before_run')
     while True:
+        log_buffer_memory_usage(learner.train_iter, replay_buffer, tb_logger)
         collect_kwargs = {}
         # set temperature for visit count distributions according to the train_iter,
         # please refer to Appendix D in MuZero paper for details.
diff --git a/lzero/entry/utils.py b/lzero/entry/utils.py
new file mode 100644
index 000000000..2da99f3fa
--- /dev/null
+++ b/lzero/entry/utils.py
@@ -0,0 +1,40 @@
+import os
+
+import psutil
+from pympler.asizeof import asizeof
+from tensorboardX import SummaryWriter
+
+
+def log_buffer_memory_usage(train_iter: int, buffer: "GameBuffer", writer: SummaryWriter) -> None:
+    """
+    Overview:
+        Log the memory usage of the buffer and the current process to TensorBoard.
+    Arguments:
+        - train_iter (:obj:`int`): The current training iteration.
+        - buffer (:obj:`GameBuffer`): The game buffer.
+        - writer (:obj:`SummaryWriter`): The TensorBoard writer.
+    """
+    writer.add_scalar('Buffer/num_of_all_collected_episodes', buffer.num_of_collected_episodes, train_iter)
+    writer.add_scalar('Buffer/num_of_game_segments', len(buffer.game_segment_buffer), train_iter)
+    writer.add_scalar('Buffer/num_of_transitions', len(buffer.game_segment_game_pos_look_up), train_iter)
+
+    game_segment_buffer = buffer.game_segment_buffer
+
+    # Calculate the amount of memory occupied by self.game_segment_buffer (in bytes).
+    buffer_memory_usage = asizeof(game_segment_buffer)
+
+    # Convert buffer_memory_usage to megabytes (MB).
+    buffer_memory_usage_mb = buffer_memory_usage / (1024 * 1024)
+
+    # Record the memory usage of self.game_segment_buffer to TensorBoard.
+    writer.add_scalar('Buffer/memory_usage/game_segment_buffer', buffer_memory_usage_mb, train_iter)
+
+    # Get the amount of memory currently used by the process (in bytes).
+    process = psutil.Process(os.getpid())
+    process_memory_usage = process.memory_info().rss
+
+    # Convert process_memory_usage to megabytes (MB).
+    process_memory_usage_mb = process_memory_usage / (1024 * 1024)
+
+    # Record the memory usage of the process to TensorBoard.
+    writer.add_scalar('Buffer/memory_usage/process', process_memory_usage_mb, train_iter)
diff --git a/lzero/mcts/buffer/game_buffer.py b/lzero/mcts/buffer/game_buffer.py
index 385bd5ab3..4d025b564 100644
--- a/lzero/mcts/buffer/game_buffer.py
+++ b/lzero/mcts/buffer/game_buffer.py
@@ -358,6 +358,7 @@ def remove_oldest_data_to_fit(self) -> None:
         Overview:
             remove some oldest data if the replay buffer is full.
         """
+        assert self.replay_buffer_size > self._cfg.batch_size, "replay buffer size should be larger than batch size"
         nums_of_game_segments = self.get_num_of_game_segments()
         total_transition = self.get_num_of_transitions()
         if total_transition > self.replay_buffer_size:
@@ -397,7 +398,7 @@ def get_num_of_game_segments(self) -> int:
 
     def get_num_of_transitions(self) -> int:
         # total number of transitions
-        return len(self.game_pos_priorities)
+        return len(self.game_segment_game_pos_look_up)
 
     def __repr__(self):
-        return f'current buffer statistics is: num_of_episodes: {self.num_of_collected_episodes}, num of game segments: {len(self.game_segment_buffer)}, number of transitions: {len(self.game_pos_priorities)}'
+        return f'current buffer statistics is: num_of_all_collected_episodes: {self.num_of_collected_episodes}, num of game segments: {len(self.game_segment_buffer)}, number of transitions: {len(self.game_segment_game_pos_look_up)}'