diff --git a/scripts/cache_aware_proxy.py b/scripts/cache_aware_proxy.py
index 497fa69..89e0591 100644
--- a/scripts/cache_aware_proxy.py
+++ b/scripts/cache_aware_proxy.py
@@ -50,6 +50,8 @@ class Settings:
     overload_factor: float = 2.0
     max_offload_inflight: int = 4
     cache_gate_ratio: float = 0.0
+    decode_iteration_s: float = 0.05      # per-request decode iteration cost (H20)
+    migration_discount_cap: int = 5       # max turns to discount
 
 
 SETTINGS = Settings()
@@ -531,15 +533,20 @@ async def _handle_combined(api, req_data, token_ids, input_length, session_id, h
     def _instance_cost(i: int) -> tuple[float, bool]:
         """Expected latency if this request goes to instance i."""
         inst = combined_instances[i]
-        queue = (inst.pending_prefill_tokens + inst.ongoing_decode_tokens) / throughput
+        contention = inst.num_requests * SETTINGS.decode_iteration_s
+        prefill_queue = inst.pending_prefill_tokens / throughput
         local_hit = cache_hits[i]
         local_new = max(0, input_length - local_hit)
-        local_cost = queue + local_new / throughput
+        local_cost = contention + prefill_queue + local_new / throughput
 
         if (offload_enabled and best_cache_hit > 0 and _push_allowed(best_cache_hit)
                 and i != best_cache_idx and local_hit < best_cache_hit):
             push_new = max(0, input_length - best_cache_hit)
-            push_cost = queue + push_new / throughput + SETTINGS.rdma_overhead_s
+            target_contention = inst.num_requests * SETTINGS.decode_iteration_s
+            push_cost = target_contention + push_new / throughput + SETTINGS.rdma_overhead_s
+            if session_id and session_id in session_affinity_combined:
+                turn_discount = min(SETTINGS.migration_discount_cap, 3) * SETTINGS.decode_iteration_s
+                push_cost -= turn_discount
             if push_cost < local_cost:
                 return push_cost, True
         return local_cost, False
@@ -948,6 +955,8 @@ def parse_args():
     p.add_argument("--cache-gate-ratio", type=float, default=0.0,
                    help="Min cache_hit/input ratio to allow offload "
                         "(0.0 disables gate, 1.0 disables offload entirely)")
+    p.add_argument("--decode-iteration-s", type=float, default=0.05,
+                   help="Estimated per-request decode iteration time in seconds")
     args = p.parse_args()
 
     args.prefill = []
@@ -969,6 +978,7 @@ if __name__ == "__main__":
     SETTINGS.overload_factor = global_args.overload_factor
     SETTINGS.max_offload_inflight = global_args.max_offload_inflight
     SETTINGS.cache_gate_ratio = global_args.cache_gate_ratio
+    SETTINGS.decode_iteration_s = getattr(global_args, 'decode_iteration_s', 0.05)
     print("SETTINGS: throughput=%.0f rdma_overhead=%.2f offload=%s" % (
         SETTINGS.prefill_throughput, SETTINGS.rdma_overhead_s,
         getattr(global_args, 'offload', False)))