diff --git a/lib/classes/task/scheduled_task.php b/lib/classes/task/scheduled_task.php
index ed2fc03144c..9c525e5860d 100644
--- a/lib/classes/task/scheduled_task.php
+++ b/lib/classes/task/scheduled_task.php
@@ -31,6 +31,15 @@ namespace core\task;
  */
 abstract class scheduled_task extends task_base {
 
+    /** Minimum minute value. */
+    const MINUTEMIN = 0;
+    /** Maximum minute value. */
+    const MINUTEMAX = 59;
+    /** Minimum hour value. */
+    const HOURMIN = 0;
+    /** Maximum hour value. */
+    const HOURMAX = 23;
+
     /** @var string $hour - Pattern to work out the valid hours */
     private $hour = '*';
 
@@ -88,10 +97,14 @@ abstract class scheduled_task extends task_base {
     }
 
     /**
-     * Setter for $minute.
+     * Setter for $minute. Accepts a special 'R' value
+     * which will be translated to a random minute.
      * @param string $minute
      */
     public function set_minute($minute) {
+        if ($minute === 'R') {
+            $minute = mt_rand(self::HOURMIN, self::HOURMAX);
+        }
         $this->minute = $minute;
     }
 
@@ -104,10 +117,14 @@ abstract class scheduled_task extends task_base {
     }
 
     /**
-     * Setter for $hour.
+     * Setter for $hour. Accepts a special 'R' value
+     * which will be translated to a random hour.
      * @param string $hour
      */
     public function set_hour($hour) {
+        if ($hour === 'R') {
+            $hour = mt_rand(self::HOURMIN, self::HOURMAX);
+        }
         $this->hour = $hour;
     }
 
@@ -302,8 +319,8 @@ abstract class scheduled_task extends task_base {
     public function get_next_scheduled_time() {
         global $CFG;
 
-        $validminutes = $this->eval_cron_field($this->minute, 0, 59);
-        $validhours = $this->eval_cron_field($this->hour, 0, 23);
+        $validminutes = $this->eval_cron_field($this->minute, self::MINUTEMIN, self::MINUTEMAX);
+        $validhours = $this->eval_cron_field($this->hour, self::HOURMIN, self::HOURMAX);
 
         // We need to change to the server timezone before using php date() functions.
         $origtz = date_default_timezone_get();
diff --git a/lib/tests/scheduled_task_test.php b/lib/tests/scheduled_task_test.php
index bb81535d0a4..599c5010082 100644
--- a/lib/tests/scheduled_task_test.php
+++ b/lib/tests/scheduled_task_test.php
@@ -242,4 +242,35 @@ class core_scheduled_task_testcase extends advanced_testcase {
         $this->assertDebuggingCalled();
         $this->assertNull($task);
     }
+
+    /**
+     * Tests the use of 'R' syntax in time fields of tasks to get
+     * tasks be configured with a non-uniform time.
+     */
+    public function test_random_time_specification() {
+
+        // Testing non-deterministic things in a unit test is not really
+        // wise, so we just test the values have changed within allowed bounds.
+        $testclass = new \core\task\scheduled_test_task();
+
+        // The test task defaults to '*'.
+        $this->assertInternalType('string', $testclass->get_minute());
+        $this->assertInternalType('string', $testclass->get_hour());
+
+        // Set a random value.
+        $testclass->set_minute('R');
+        $testclass->set_hour('R');
+
+        // Verify the minute has changed within allowed bounds.
+        $minute = $testclass->get_minute();
+        $this->assertInternalType('int', $minute);
+        $this->assertGreaterThanOrEqual(0, $minute);
+        $this->assertLessThanOrEqual(59, $minute);
+
+        // Verify the hour has changed within allowed bounds.
+        $hour = $testclass->get_hour();
+        $this->assertInternalType('int', $hour);
+        $this->assertGreaterThanOrEqual(0, $hour);
+        $this->assertLessThanOrEqual(23, $hour);
+    }
 }
diff --git a/lib/upgrade.txt b/lib/upgrade.txt
index acf6e019cdc..339eebe13f6 100644
--- a/lib/upgrade.txt
+++ b/lib/upgrade.txt
@@ -13,6 +13,9 @@ information provided here is intended especially for developers.
 * New function cm_info::create($cm) can be used when you need a cm_info
   object, but have a $cm which might only be a standard database record.
 * $CFG->enablegroupmembersonly no longer exists.
+* Scheduled tasks have gained support for syntax to introduce variability when a
+  task will run across installs. When a when hour or minute are defined as 'R'
+  they will be installed with a random hour/minute value.
 
 DEPRECATIONS:
 * completion_info->get_incomplete_criteria() is deprecated and will be removed in Moodle 3.0.