diff --git a/tests/system-traffic.at b/tests/system-traffic.at
index a6190ae8d..ad84de6fb 100644
--- a/tests/system-traffic.at
+++ b/tests/system-traffic.at
@@ -831,16 +831,27 @@ priority=100,in_port=2,icmp,ct_state=+trk+rel,ct_mark=1,action=1
 
 AT_CHECK([ovs-ofctl --bundle add-flows br0 flows.txt])
 
-dnl UDP packets from ns0->ns1 should solicit "destination unreachable" response.
-dnl We pass "-q 1" here to handle openbsd-style nc that can't quit immediately.
-NS_CHECK_EXEC([at_ns0], [bash -c "echo a | nc -q 1 -u 10.1.1.2 10000"])
+dnl If we simulate a UDP request to a port that isn't serving any real traffic,
+dnl then the destination responds with an ICMP "destination unreachable"
+dnl message, it should be marked as "related".
+AT_CHECK([ovs-ofctl -O OpenFlow13 packet-out br0 1 resubmit\(,0\) 'dnl
+0000 0000 0000 0000 0000 0000 0800 4500 dnl
+001e bb85 4000 4011 6945 0a01 0101 0a01 dnl
+0102 839c 1388 000a f1a6 610a'])
+
+AT_CHECK([ovs-ofctl -O OpenFlow13 packet-out br0 2 resubmit\(,0\) 'dnl
+0000 0000 0000 0000 0000 0000 0800 45c0 dnl
+003a 411e 0000 4001 22e1 0a01 0102 0a01 dnl
+0101 0303 131d 0000 0000 dnl
+4500 001e bb85 4000 4011 6945 0a01 0101 dnl
+0a01 0102 839c 1388 000a f1a6 610a'])
 
 AT_CHECK([ovs-appctl revalidator/purge], [0])
 AT_CHECK([ovs-ofctl dump-flows br0 | ofctl_strip | sort | grep -v drop], [0], [dnl
  n_packets=1, n_bytes=44, priority=100,udp,in_port=1 actions=ct(commit,exec(load:0x1->NXM_NX_CT_MARK[[]])),output:2
  n_packets=1, n_bytes=72, priority=100,ct_state=+rel+trk,ct_mark=0x1,icmp,in_port=2 actions=output:1
  n_packets=1, n_bytes=72, priority=100,ct_state=-trk,icmp,in_port=2 actions=ct(table=0)
- n_packets=2, n_bytes=84, priority=10,arp actions=NORMAL
+ priority=10,arp actions=NORMAL
 NXST_FLOW reply:
 ])