diff --git a/kernel/sched/fair.c b/kernel/sched/fair.c
index ef5b66b110f8..cb6b7c83b74d 100644
--- a/kernel/sched/fair.c
+++ b/kernel/sched/fair.c
@@ -1892,7 +1892,7 @@ static void update_task_scan_period(struct task_struct *p,
 			unsigned long shared, unsigned long private)
 {
 	unsigned int period_slot;
-	int ratio;
+	int lr_ratio, ps_ratio;
 	int diff;
 
 	unsigned long remote = p->numa_faults_locality[0];
@@ -1922,25 +1922,36 @@ static void update_task_scan_period(struct task_struct *p,
 	 *	 >= NUMA_PERIOD_THRESHOLD scan period increases (scan slower)
 	 */
 	period_slot = DIV_ROUND_UP(p->numa_scan_period, NUMA_PERIOD_SLOTS);
-	ratio = (local * NUMA_PERIOD_SLOTS) / (local + remote);
-	if (ratio >= NUMA_PERIOD_THRESHOLD) {
-		int slot = ratio - NUMA_PERIOD_THRESHOLD;
+	lr_ratio = (local * NUMA_PERIOD_SLOTS) / (local + remote);
+	ps_ratio = (private * NUMA_PERIOD_SLOTS) / (private + shared);
+
+	if (ps_ratio >= NUMA_PERIOD_THRESHOLD) {
+		/*
+		 * Most memory accesses are local. There is no need to
+		 * do fast NUMA scanning, since memory is already local.
+		 */
+		int slot = ps_ratio - NUMA_PERIOD_THRESHOLD;
+		if (!slot)
+			slot = 1;
+		diff = slot * period_slot;
+	} else if (lr_ratio >= NUMA_PERIOD_THRESHOLD) {
+		/*
+		 * Most memory accesses are shared with other tasks.
+		 * There is no point in continuing fast NUMA scanning,
+		 * since other tasks may just move the memory elsewhere.
+		 */
+		int slot = lr_ratio - NUMA_PERIOD_THRESHOLD;
 		if (!slot)
 			slot = 1;
 		diff = slot * period_slot;
 	} else {
-		diff = -(NUMA_PERIOD_THRESHOLD - ratio) * period_slot;
-
 		/*
-		 * Scale scan rate increases based on sharing. There is an
-		 * inverse relationship between the degree of sharing and
-		 * the adjustment made to the scanning period. Broadly
-		 * speaking the intent is that there is little point
-		 * scanning faster if shared accesses dominate as it may
-		 * simply bounce migrations uselessly
+		 * Private memory faults exceed (SLOTS-THRESHOLD)/SLOTS,
+		 * yet they are not on the local NUMA node. Speed up
+		 * NUMA scanning to get the memory moved over.
 		 */
-		ratio = DIV_ROUND_UP(private * NUMA_PERIOD_SLOTS, (private + shared + 1));
-		diff = (diff * ratio) / NUMA_PERIOD_SLOTS;
+		int ratio = max(lr_ratio, ps_ratio);
+		diff = -(NUMA_PERIOD_THRESHOLD - ratio) * period_slot;
 	}
 
 	p->numa_scan_period = clamp(p->numa_scan_period + diff,