diff --git a/tests/src/test/scala/com/nvidia/spark/rapids/ResourceBoundedExecutorSuite.scala b/tests/src/test/scala/com/nvidia/spark/rapids/ResourceBoundedExecutorSuite.scala
index b289d77de5f..d1da3e2a7f0 100644
--- a/tests/src/test/scala/com/nvidia/spark/rapids/ResourceBoundedExecutorSuite.scala
+++ b/tests/src/test/scala/com/nvidia/spark/rapids/ResourceBoundedExecutorSuite.scala
@@ -17,6 +17,7 @@
 package com.nvidia.spark.rapids
 
 import java.util.concurrent.{Future => JFuture}
+import java.util.concurrent.locks.{Lock, ReentrantLock}
 
 import scala.collection.mutable
 
@@ -39,12 +40,18 @@ class ResourceBoundedExecutorSuite extends AnyFunSuite with RmmSparkRetrySuiteBa
    * Builds a dummy function that simulates the CPU task, which returns the timestamp of the
    * completion of the task.
    */
-  private def buildDummyFn(sleepMs: Long = 5L): () => Long = {
+  private def buildDummyFn(startBlk: Lock): () => Long = {
     () => {
-      // Make sure the task execution slower than the task submission, so that the execution
-      // order will be determined by the task priority.
-      Thread.sleep(sleepMs)
-      System.nanoTime()
+      // Block the start of task execution until the lock is released.
+      startBlk.lock()
+      try {
+        // Make sure the task execution slower than the task submission, so that the execution
+        // order will be determined by the task priority.
+        Thread.sleep(5L)
+        System.nanoTime()
+      } finally {
+        startBlk.unlock()
+      }
     }
   }
 
@@ -52,20 +59,22 @@ class ResourceBoundedExecutorSuite extends AnyFunSuite with RmmSparkRetrySuiteBa
   // different priorities and memory requirements, then verifying the actual execution sequence
   // matches the expected priority-based task scheduling behavior.
   test("AsyncCpuTask task priority") {
+    // Lock to control the start of task execution.
+    val lck = new ReentrantLock()
     // Create a single-threaded bounded executor to control the execution order of tasks.
     val executor = createSingleThreadedBoundedExecutor(maxThreadNumber = 1)
     // Test the task scheduling based on priority:
     // Tasks with higher priority should be executed first even if they are submitted later.
     // Execution order: 4, 2, 3, 5, 1
     val executionPriority = Seq(2, 4, 3, 1, 5)
-    executor.submit(AsyncRunner.newCpuTask(buildDummyFn(),1 << 20, priority = 1))
-    // Guarantee the first task is executed first to avoid uncertain execution order.
-    Thread.sleep(1)
-    var results = executionPriority.map { p =>
-      p -> executor.submit(AsyncRunner.newCpuTask(buildDummyFn(), 1 << 20, priority = p))
-    }.sortBy(_._1).map {
-      case (_, future) => future.get().data
-    }
+    lck.lock() // Block tasks from starting execution.
+    executor.submit(AsyncRunner.newUnboundedTask(buildDummyFn(lck)))
+    Thread.sleep(1L)
+    var sortedFut = executionPriority.map { p =>
+      p -> executor.submit(AsyncRunner.newCpuTask(buildDummyFn(lck), 1 << 20, priority = p))
+    }.sortBy(_._1).map(_._2)
+    lck.unlock() // Allow tasks to start executing.
+    var results = sortedFut.map(_.get().data)
     (0 until results.length - 1).foreach { i =>
       require(results(i) > results(i + 1), s"Unexpected order of wallTime: ${results.toList}")
     }
@@ -73,49 +82,52 @@ class ResourceBoundedExecutorSuite extends AnyFunSuite with RmmSparkRetrySuiteBa
     // Test priority penalty by memory usage:
     // Tasks requiring less resource should be executed first even if they are submitted later.
     // Execution order: 1, 2, 3, 4, 5
-    results = (1 to 5).map { i =>
-      executor.submit(AsyncRunner.newCpuTask(buildDummyFn(), memoryBytes = i << 20))
-    }.map {
-      future => future.get().data
+    lck.lock() // Block tasks from starting execution.
+    executor.submit(AsyncRunner.newUnboundedTask(buildDummyFn(lck)))
+    Thread.sleep(1L)
+    sortedFut = (1 to 5).map { i =>
+      executor.submit(AsyncRunner.newCpuTask(buildDummyFn(lck), memoryBytes = i << 20))
     }
+    lck.unlock() // Allow tasks to start executing.
+    results = sortedFut.map(_.get().data)
     (0 until results.length - 1).foreach { i =>
       require(results(i) < results(i + 1), s"Unexpected order of wallTime: ${results.toList}")
     }
-    // Execution order: 1, 5, 4, 3, 2
-    executor.submit(AsyncRunner.newCpuTask(buildDummyFn(), memoryBytes = 5 << 20))
-    // Guarantee the first task is executed first to avoid uncertain execution order.
-    Thread.sleep(1)
-    results = (4 to 1 by -1).map { i =>
-      executor.submit(AsyncRunner.newCpuTask(buildDummyFn(), memoryBytes = i << 20))
-    }.map {
-      future => future.get().data
+    // Execution order: 4, 3, 2, 1
+    lck.lock() // Block tasks from starting execution.
+    executor.submit(AsyncRunner.newUnboundedTask(buildDummyFn(lck)))
+    Thread.sleep(1L)
+    sortedFut = (4 to 1 by -1).map { i =>
+      executor.submit(AsyncRunner.newCpuTask(buildDummyFn(lck), memoryBytes = i << 20))
     }
+    lck.unlock() // Allow tasks to start executing.
+    results = sortedFut.map(_.get().data)
     (0 until results.length - 1).foreach { i =>
       require(results(i) > results(i + 1), s"Unexpected order of wallTime: ${results.toList}")
     }
 
     // Comprehensive test for task priority and memory usage (including unbounded tasks):
-    // Execution order: 1, 4, 6, 2, 5, 3
+    // Execution order: 2(prior=4), 3(prior=2), 5(prior=-46), 1(prior=MAX), 4(prior=-3)
     val futures = mutable.ArrayBuffer[JFuture[AsyncResult[Long]]]()
+    lck.lock() // Block tasks from starting execution.
+    executor.submit(AsyncRunner.newUnboundedTask(buildDummyFn(lck)))
+    Thread.sleep(1L)
     // (1) priority = 5 - 1KB = 4
-    futures += executor.submit(AsyncRunner.newCpuTask(buildDummyFn(),
-      memoryBytes = 100 << 10, priority = 5L))
-    // Guarantee the first task is executed first to avoid uncertain execution order.
-    Thread.sleep(1)
+    futures += executor.submit(AsyncRunner.newCpuTask(buildDummyFn(lck),
+      memoryBytes = 1 << 10, priority = 5L))
     // (2) priority = 3 - 1KB = 2
-    futures += executor.submit(AsyncRunner.newCpuTask(buildDummyFn(),
+    futures += executor.submit(AsyncRunner.newCpuTask(buildDummyFn(lck),
       memoryBytes = 1 << 10, priority = 3L))
     // (3) priority = 4 - 50KB = -46
-    futures += executor.submit(AsyncRunner.newCpuTask(buildDummyFn(),
+    futures += executor.submit(AsyncRunner.newCpuTask(buildDummyFn(lck),
       memoryBytes = 50 << 10, priority = 4L))
     // (4) Unbounded task with the highest priority
-    futures += executor.submit(AsyncRunner.newUnboundedTask(buildDummyFn()))
+    futures += executor.submit(AsyncRunner.newUnboundedTask(buildDummyFn(lck)))
     // (5) priority = 7 - 10KB = -3
-    futures += executor.submit(AsyncRunner.newCpuTask(buildDummyFn(),
+    futures += executor.submit(AsyncRunner.newCpuTask(buildDummyFn(lck),
       memoryBytes = 10 << 10, priority = 7L))
-    // (6) Unbounded task with the highest priority
-    futures += executor.submit(AsyncRunner.newUnboundedTask(buildDummyFn()))
-    results = Array(1, 4, 6, 2, 5, 3).zip(futures).sortBy(_._1).map {
+    lck.unlock() // Allow tasks to start executing.
+    results = Seq(2, 3, 5, 1, 4).zip(futures).sortBy(_._1).map {
       case (_, fut) => fut.get().data
     }
     (0 until results.length - 1).foreach { i =>