diff --git a/benchmarks/benchmark/tools/profile-generator/container/benchmark_serving.py b/benchmarks/benchmark/tools/profile-generator/container/benchmark_serving.py
index 9ebb26ad5..e0cab7a27 100644
--- a/benchmarks/benchmark/tools/profile-generator/container/benchmark_serving.py
+++ b/benchmarks/benchmark/tools/profile-generator/container/benchmark_serving.py
@@ -21,6 +21,8 @@
 
 import aiohttp
 import numpy as np
+from sympy import symbols
+from sympy.parsing.sympy_parser import parse_expr
 from transformers import AutoTokenizer
 from transformers import PreTrainedTokenizerBase
 
@@ -30,6 +32,8 @@
 CLIENT_TIMEOUT_SEC = 3 * 60 * 60
 NEW_TEXT_KEY = "\nOutput:\n"
 PROMETHEUS_PORT = 9090
+NS_IN_SEC = 1_000_000_000
+
 
 # Prometheus Metrics
 prompt_length_metric = Histogram("LatencyProfileGenerator:prompt_length", "Input prompt length", buckets=[2**i for i in range(1, 16)])
@@ -38,6 +42,7 @@
 tpot_metric = Histogram('LatencyProfileGenerator:time_per_output_token', 'Time per output token per request (excluding first token)')
 ttft_metric = Histogram('LatencyProfileGenerator:time_to_first_token', 'Time to first token per request')
 active_requests_metric = Gauge('LatencyProfileGenerator:active_requests', 'How many requests actively being processed')
+request_rate_metric = Gauge('LatencyProfileGenerator:request_rate', "The current request rate in seconds")
 
 # Add trace config for monitoring in flight requests
 async def on_request_start(session, trace_config_ctx, params):
@@ -110,18 +115,26 @@ def get_filtered_dataset(
 
 async def generate_next_request(
     input_requests: List[Tuple[str, int, int]],
-    request_rate: float,
+    request_rate_expr: float,
+    start_time: float,
 ) -> AsyncGenerator[Tuple[str, int, int], None]:
   """Gets request async."""
   while True:
     request = random.choice(input_requests)
     yield request
 
-    if request_rate == float("inf"):
+    if request_rate_expr == "oo":
       # If the request rate is infinity, then we don't need to wait.
       continue
+
+    # Evaluate the request rate at this point in time
+    t = symbols('t')
+    expr_parsed = parse_expr(request_rate_expr, transformations="all", local_dict={"t": t})
+    request_rate_at_t = expr_parsed.subs(t, ((time.time_ns() - start_time) / NS_IN_SEC))
+    request_rate_metric.set(request_rate_at_t)
+
     # Sample the request interval from the exponential distribution.
-    interval = np.random.exponential(1.0 / request_rate)
+    interval = np.random.exponential(1.0 / request_rate_at_t)
     # The next request will be sent after the interval.
     await asyncio.sleep(interval)
 
@@ -408,7 +421,7 @@ async def benchmark(
   benchmark_start_time = time.time()
   tasks: List[asyncio.Task] = []
   prompts_sent: int = 0
-  async for request in generate_next_request(input_requests, args.request_rate):
+  async for request in generate_next_request(input_requests, args.request_rate, time.time_ns()):
     if args.num_prompts <= prompts_sent:
       break
     prompt, prompt_len, output_len = request
@@ -548,7 +561,7 @@ def save_json_results(args: argparse.Namespace, benchmark_result, server_metrics
   # Save to file
   model_without_slash = model.replace("/","-")
   file_name = (
-      f"{args.file_prefix}-{args.backend}-{args.request_rate}qps-{args.start_datetime.strftime('%Y%m%d-%H%M%S')}-{model_without_slash}.json"
+      f"{args.file_prefix}-{args.backend}-{args.start_datetime.strftime('%Y%m%d-%H%M%S')}-{model_without_slash}.json"
   )
   with open(file_name, "w", encoding="utf-8") as outfile:
     json.dump(final_json, outfile)
@@ -876,16 +889,32 @@ async def main(args: argparse.Namespace):
           " LLaMA2 models."
       ),
   )
+  # Input assertions
+  def is_expression_of_t(input_str):
+    if input_str == "inf":
+      return "oo"
+    # Check if expression uses variables other than 't' by attempting to evaluate with only 't' defined
+    try:
+      t = symbols('t')
+      expr_parsed = parse_expr(input_str, transformations="all", local_dict={"t": t})
+      expr_parsed.subs(t, 1)
+      return input_str
+    except Exception:
+      raise ValueError(f"Request rate {input_str}, must be numeric or an expression of `t`")
+    
   parser.add_argument(
       "--request-rate",
-      type=float,
-      default=float("inf"),
+      type=is_expression_of_t,
+      default="inf",
       help=(
-          "Number of requests per second. If this is inf, "
-          "then all the requests are sent at time 0. "
-          "Otherwise, we use Poisson process to synthesize "
-          "the request arrival times."
-      ),
+          "Specifies the request rate as a function of time, f(t)."
+          " Example format: '1+1.05*t', where 't' represents seconds from"
+          " start. If set to 'inf', all requests are sent at time 0."
+          " Otherwise, the function is interpreted to generate a Poisson"
+          " process for request arrival times based on the provided rate"
+          " expression. Current value emitted as the following prometheus"
+          " metric: 'LatencyProfileGenerator:request_rate'"
+    ),
   )
   parser.add_argument("--seed", type=int, default=int(time.time()))
   parser.add_argument(
diff --git a/benchmarks/benchmark/tools/profile-generator/container/requirements.txt b/benchmarks/benchmark/tools/profile-generator/container/requirements.txt
index c3bfdaca3..6ab15ecec 100644
--- a/benchmarks/benchmark/tools/profile-generator/container/requirements.txt
+++ b/benchmarks/benchmark/tools/profile-generator/container/requirements.txt
@@ -36,4 +36,5 @@ accelerate
 aiohttp
 google-auth
 google-cloud-storage >= 2.18.2
-prometheus_client >= 0.21.0
\ No newline at end of file
+prometheus_client >= 0.21.0
+sympy >= 1.13
\ No newline at end of file