--- a/src/wifi/model/ap-wifi-mac.cc	Wed Aug 21 15:27:21 2013 -0700
+++ a/src/wifi/model/ap-wifi-mac.cc	Wed Aug 21 21:17:38 2013 -0400
@@ -648,7 +648,9 @@ 
   m_beaconEvent.Cancel ();
   if (m_enableBeaconGeneration)
     {
-      m_beaconEvent = Simulator::ScheduleNow (&ApWifiMac::SendOneBeacon, this);
+      m_beaconOffset = CreateObject<UniformRandomVariable> ();
+      Time offset = MicroSeconds (m_beaconOffset->GetValue (1, m_beaconInterval.GetMicroSeconds ()));
+      m_beaconEvent = Simulator::Schedule (offset, &ApWifiMac::SendOneBeacon, this);
     }
   RegularWifiMac::DoInitialize ();
 }
--- a/src/wifi/model/ap-wifi-mac.h	Wed Aug 21 15:27:21 2013 -0700
+++ a/src/wifi/model/ap-wifi-mac.h	Wed Aug 21 21:17:38 2013 -0400
@@ -26,6 +26,7 @@ 
 #include "ht-capabilities.h"
 #include "amsdu-subframe-header.h"
 #include "supported-rates.h"
+#include "ns3/random-variable-stream.h"
 
 namespace ns3 {
 
@@ -128,6 +129,7 @@ 
   Time m_beaconInterval;
   bool m_enableBeaconGeneration;
   EventId m_beaconEvent;
+  Ptr<UniformRandomVariable> m_beaconOffset;
 };
 
 } // namespace ns3