diff --git a/vllm/config.py b/vllm/config.py
index ddd63dfd6ee1..aa0973b1588c 100644
--- a/vllm/config.py
+++ b/vllm/config.py
@@ -459,6 +459,8 @@ class SchedulerConfig:
         max_paddings: Maximum number of paddings to be added to a batch.
         policy: Policy of sequence scheduling(`fcfs` or `reorder`).
         reorder_window: Allowed reorder window size(in sec) for `reorder` policy.
+        swap_tolerance: Maximum acceptable number of swapped sequences to start
+            a new waiting request. 0 means to process SWAP first.
     """
 
     def __init__(
@@ -469,6 +471,7 @@ def __init__(
         max_paddings: int,
         policy: str = 'fcfs',
         reorder_window: float = 0,
+        swap_tolerance: int = 0,
     ) -> None:
         if max_num_batched_tokens is not None:
             self.max_num_batched_tokens = max_num_batched_tokens
@@ -481,6 +484,7 @@ def __init__(
         self.max_paddings = max_paddings
         self.policy = policy
         self.reorder_window = reorder_window
+        self.swap_tolerance = swap_tolerance
         self._verify_args()
 
     def _verify_args(self) -> None:
@@ -504,6 +508,7 @@ def _verify_args(self) -> None:
             raise ValueError(
                 f"fcfs policy doesn't support reorder_window ({self.reorder_window})."
             )
+        assert self.swap_tolerance >= 0
 
 
 class DeviceConfig:
diff --git a/vllm/core/scheduler.py b/vllm/core/scheduler.py
index 1b3fc4d0e974..a6245955da9b 100644
--- a/vllm/core/scheduler.py
+++ b/vllm/core/scheduler.py
@@ -150,7 +150,7 @@ def _schedule(self) -> SchedulerOutputs:
         blocks_to_copy: Dict[int, List[int]] = {}
 
         # Join waiting sequences if possible.
-        if not self.swapped:
+        if len(self.swapped) <= self.scheduler_config.swap_tolerance:
             ignored_seq_groups: List[SequenceGroup] = []
             scheduled: List[SequenceGroup] = []
             # The total number of sequences on the fly, including the
diff --git a/vllm/engine/arg_utils.py b/vllm/engine/arg_utils.py
index 7995c0f2ea36..af8cd7184cbf 100644
--- a/vllm/engine/arg_utils.py
+++ b/vllm/engine/arg_utils.py
@@ -34,6 +34,7 @@ class EngineArgs:
     max_logprobs: int = 5  # OpenAI default value
     scheduler_policy: str = 'fcfs'
     scheduler_reorder_window: float = 0
+    scheduler_swap_tolerance: int = 0
     disable_log_stats: bool = False
     revision: Optional[str] = None
     code_revision: Optional[str] = None
@@ -230,6 +231,12 @@ def add_cli_args(
                             type=float,
                             default=EngineArgs.scheduler_reorder_window,
                             help='allowed sequences reorder window(in sec)')
+        parser.add_argument(
+            '--scheduler-swap-tolerance',
+            type=int,
+            default=EngineArgs.scheduler_swap_tolerance,
+            help='Maximum acceptable number of swapped sequences to start a '
+            'new waiting request')
         parser.add_argument('--disable-log-stats',
                             action='store_true',
                             help='disable logging statistics')
@@ -331,12 +338,11 @@ def create_engine_configs(
                                          self.max_parallel_loading_workers,
                                          self.disable_custom_all_reduce,
                                          self.ray_workers_use_nsight)
-        scheduler_config = SchedulerConfig(self.max_num_batched_tokens,
-                                           self.max_num_seqs,
-                                           model_config.max_model_len,
-                                           self.max_paddings,
-                                           self.scheduler_policy,
-                                           self.scheduler_reorder_window)
+        scheduler_config = SchedulerConfig(
+            self.max_num_batched_tokens, self.max_num_seqs,
+            model_config.max_model_len, self.max_paddings,
+            self.scheduler_policy, self.scheduler_reorder_window,
+            self.scheduler_swap_tolerance)
         lora_config = LoRAConfig(
             max_lora_rank=self.max_lora_rank,
             max_loras=self.max_loras,