diff --git a/swh/scheduler/simulator/__init__.py b/swh/scheduler/simulator/__init__.py
--- a/swh/scheduler/simulator/__init__.py
+++ b/swh/scheduler/simulator/__init__.py
@@ -17,11 +17,10 @@
 from simpy import Event
 
 from swh.scheduler.interface import SchedulerInterface
-from swh.scheduler.model import ListedOrigin
 
 from . import origin_scheduler, task_scheduler
 from .common import Environment, Queue, SimulationReport, Task
-from .origins import load_task_process
+from .origins import generate_listed_origin, load_task_process
 
 logger = logging.getLogger(__name__)
 
@@ -111,15 +110,8 @@
     stored_lister = scheduler.get_or_create_lister(name="example")
     assert stored_lister.id is not None
 
-    origins = [
-        ListedOrigin(
-            lister_id=stored_lister.id,
-            url=f"https://example.com/{i:04d}.git",
-            visit_type="git",
-            last_update=datetime(2020, 6, 15, 16, 0, 0, i, tzinfo=timezone.utc),
-        )
-        for i in range(num_origins)
-    ]
+    # Generate 'num_origins' new origins
+    origins = [generate_listed_origin(stored_lister.id) for _ in range(num_origins)]
     scheduler.record_listed_origins(origins)
 
     scheduler.create_tasks(
diff --git a/swh/scheduler/simulator/origins.py b/swh/scheduler/simulator/origins.py
--- a/swh/scheduler/simulator/origins.py
+++ b/swh/scheduler/simulator/origins.py
@@ -6,23 +6,56 @@
 """This module implements a model of the frequency of updates of an origin
 and how long it takes to load it."""
 
-from datetime import timedelta
+from datetime import datetime, timedelta, timezone
 import hashlib
 import logging
 import os
 from typing import Iterator, Optional, Tuple
+import uuid
 
 import attr
 from simpy import Event
 
 from swh.model.model import OriginVisitStatus
-from swh.scheduler.model import OriginVisitStats
+from swh.scheduler.model import ListedOrigin, OriginVisitStats
 
 from .common import Environment, Queue, Task, TaskEvent
 
 logger = logging.getLogger(__name__)
 
 
+_nb_generated_origins = 0
+
+
+def generate_listed_origin(
+    lister_id: uuid.UUID, now: Optional[datetime] = None
+) -> ListedOrigin:
+    """Returns a globally unique new origin. Seed the `last_update` value
+    according to the OriginModel and the passed timestamp.
+
+    Arguments:
+      lister: instance of the lister that generated this origin
+      now: time of listing, to emulate last_update (defaults to :func:`datetime.now`)
+    """
+    global _nb_generated_origins
+    _nb_generated_origins += 1
+    assert _nb_generated_origins < 10 ** 6, "Too many origins!"
+
+    if now is None:
+        now = datetime.now(tz=timezone.utc)
+
+    url = f"https://example.com/{_nb_generated_origins:6d}.git"
+    visit_type = "git"
+    origin = OriginModel(visit_type, url)
+
+    return ListedOrigin(
+        lister_id=lister_id,
+        url=url,
+        visit_type=visit_type,
+        last_update=origin.get_last_update(now),
+    )
+
+
 class OriginModel:
     MIN_RUN_TIME = 0.5
     """Minimal run time for a visit (retrieved from production data)"""
@@ -33,6 +66,9 @@
     PER_COMMIT_RUN_TIME = 0.1
     """Run time per commit"""
 
+    EPOCH = datetime(2015, 9, 1, 0, 0, 0, tzinfo=timezone.utc)
+    """The origin of all origins (at least according to Software Heritage)"""
+
     def __init__(self, type: str, origin: str):
         self.type = type
         self.origin = origin
@@ -56,6 +92,19 @@
         return ten_y ** (bucket / num_buckets)
         # return 1 + (ten_y - 1) * (bucket / (num_buckets - 1))
 
+    def get_last_update(self, now: datetime):
+        """Get the last_update value for this origin.
+
+        We assume that the origin had its first commit at `EPOCH`, and that one
+        commit happened every `self.seconds_between_commits()`. This returns
+        the last commit date before or equal to `now`.
+        """
+        _, time_since_last_commit = divmod(
+            (now - self.EPOCH).total_seconds(), self.seconds_between_commits()
+        )
+
+        return now - timedelta(seconds=time_since_last_commit)
+
     def load_task_characteristics(
         self, env: Environment, stats: Optional[OriginVisitStats]
     ) -> Tuple[float, bool, str]: