diff --git a/metrosim/models/pt_network.py b/metrosim/models/pt_network.py
index b6adfb4..114e408 100644
--- a/metrosim/models/pt_network.py
+++ b/metrosim/models/pt_network.py
@@ -13,6 +13,8 @@ from collections import defaultdict
 
 import networkx as nx
 
+from metrosim.exceptions import MetroInputError
+
 
 class PTNetwork(nx.MultiDiGraph):
     """Class representing a public-transit network.
@@ -113,10 +115,10 @@ class PTNetwork(nx.MultiDiGraph):
             print('Warning: Discarded {} stop-times with invalid pickup or '
                   'dropoff'.format(invalid_stop_types))
 
+        null_travel_times = 0
         for trip_id, stop_times in legs_dict.items():
             # Sort stop_times by increasing stop_sequence.
-            stop_times = sorted(
-                stop_times, key=lambda x: int(x['stop_sequence']))
+            stop_times = sorted(stop_times, key=lambda x: x['departure_time'])
             first_departure = _parse_time(stop_times[0]['departure_time'])
             last_arrival = _parse_time(stop_times[-1]['arrival_time'])
             if first_departure > to_time or last_arrival < from_time:
@@ -125,6 +127,13 @@ class PTNetwork(nx.MultiDiGraph):
             for prev_stop, next_stop in zip(stop_times[:-1], stop_times[1:]):
                 dep_time = _parse_time(prev_stop['departure_time'])
                 arr_time = _parse_time(next_stop['arrival_time'])
+                if dep_time == arr_time:
+                    null_travel_times += 1
+                    arr_time += timedelta(seconds=1)
+                if dep_time > arr_time:
+                    msg = (
+                        'Invalid trip (non-positive travel-time): {}')
+                    raise MetroInputError(msg.format(trip_id))
                 route_id = self.trips[trip_id]['route_id']
                 self.add_edge(
                     prev_stop['stop_id'],
@@ -137,6 +146,10 @@ class PTNetwork(nx.MultiDiGraph):
                     type=self.routes[route_id]['type'],
                 )
 
+        if null_travel_times:
+            print('Warning: Increased the travel-time of {} stop-times with '
+                  'null travel-time'.format(null_travel_times))
+
     def _add_valid_routes(self, reader, routes):
         """Add route data to the PT network.