diff --git a/src/Logging/Logging.AzureAppServices/src/Internal/BatchingLoggerProvider.cs b/src/Logging/Logging.AzureAppServices/src/Internal/BatchingLoggerProvider.cs
index c507b6e671..626412e504 100644
--- a/src/Logging/Logging.AzureAppServices/src/Internal/BatchingLoggerProvider.cs
+++ b/src/Logging/Logging.AzureAppServices/src/Internal/BatchingLoggerProvider.cs
@@ -18,6 +18,8 @@ namespace Microsoft.Extensions.Logging.AzureAppServices.Internal
         private readonly int? _batchSize;
         private readonly IDisposable _optionsChangeToken;
 
+        private int _messagesDropped;
+
         private BlockingCollection<LogMessage> _messageQueue;
         private Task _outputTask;
         private CancellationTokenSource _cancellationTokenSource;
@@ -85,6 +87,16 @@ namespace Microsoft.Extensions.Logging.AzureAppServices.Internal
                     limit--;
                 }
 
+                var messagesDropped = Interlocked.Exchange(ref _messagesDropped, 0);
+                if (messagesDropped != 0)
+                {
+                    _currentBatch.Add(new LogMessage()
+                    {
+                        Message = $"{messagesDropped} message(s) dropped because of queue size limit. Increase the queue size or decrease logging verbosity to avoid this.{Environment.NewLine}",
+                        Timestamp = DateTimeOffset.Now
+                    });
+                }
+
                 if (_currentBatch.Count > 0)
                 {
                     try
@@ -98,8 +110,10 @@ namespace Microsoft.Extensions.Logging.AzureAppServices.Internal
 
                     _currentBatch.Clear();
                 }
-
-                await IntervalAsync(_interval, _cancellationTokenSource.Token);
+                else
+                {
+                    await IntervalAsync(_interval, _cancellationTokenSource.Token);
+                }
             }
         }
 
@@ -114,7 +128,10 @@ namespace Microsoft.Extensions.Logging.AzureAppServices.Internal
             {
                 try
                 {
-                    _messageQueue.Add(new LogMessage { Message = message, Timestamp = timestamp }, _cancellationTokenSource.Token);
+                    if (!_messageQueue.TryAdd(new LogMessage { Message = message, Timestamp = timestamp }, millisecondsTimeout: 0, cancellationToken: _cancellationTokenSource.Token))
+                    {
+                        Interlocked.Increment(ref _messagesDropped);
+                    }
                 }
                 catch
                 {
@@ -172,4 +189,4 @@ namespace Microsoft.Extensions.Logging.AzureAppServices.Internal
             _scopeProvider = scopeProvider;
         }
     }
-}
\ No newline at end of file
+}
diff --git a/src/Logging/Logging.AzureAppServices/test/BatchingLoggerProviderTests.cs b/src/Logging/Logging.AzureAppServices/test/BatchingLoggerProviderTests.cs
index 0d4e1b85e0..9c9a42b966 100644
--- a/src/Logging/Logging.AzureAppServices/test/BatchingLoggerProviderTests.cs
+++ b/src/Logging/Logging.AzureAppServices/test/BatchingLoggerProviderTests.cs
@@ -1,4 +1,4 @@
-// Copyright (c) .NET Foundation. All rights reserved.
+// Copyright (c) .NET Foundation. All rights reserved.
 // Licensed under the Apache License, Version 2.0. See License.txt in the project root for license information.
 
 using System;
@@ -77,21 +77,16 @@ namespace Microsoft.Extensions.Logging.AzureAppServices.Test
             provider.IntervalControl.Resume();
             await provider.IntervalControl.Pause;
 
-            Assert.Single(provider.Batches);
+            Assert.Equal(2, provider.Batches.Count);
             Assert.Single(provider.Batches[0]);
             Assert.Equal("2016-05-04 03:02:01.000 +00:00 [Information] Cat: Info message" + _nl, provider.Batches[0][0].Message);
 
-            provider.IntervalControl.Resume();
-            await provider.IntervalControl.Pause;
-
-            Assert.Equal(2, provider.Batches.Count);
             Assert.Single(provider.Batches[1]);
-
             Assert.Equal("2016-05-04 04:02:01.000 +00:00 [Error] Cat: Error message" + _nl, provider.Batches[1][0].Message);
         }
 
         [Fact]
-        public async Task BlocksWhenReachingMaxQueue()
+        public async Task DropsMessagesWhenReachingMaxQueue()
         {
             var provider = new TestBatchingLoggingProvider(maxQueueSize: 1);
             var logger = (BatchingLogger)provider.CreateLogger("Cat");
@@ -99,14 +94,14 @@ namespace Microsoft.Extensions.Logging.AzureAppServices.Test
             await provider.IntervalControl.Pause;
 
             logger.Log(_timestampOne, LogLevel.Information, 0, "Info message", null, (state, ex) => state);
-            var task = Task.Run(() => logger.Log(_timestampOne.AddHours(1), LogLevel.Error, 0, "Error message", null, (state, ex) => state));
-
-            Assert.False(task.Wait(1000));
+            logger.Log(_timestampOne.AddHours(1), LogLevel.Error, 0, "Error message", null, (state, ex) => state);
 
             provider.IntervalControl.Resume();
             await provider.IntervalControl.Pause;
 
-            Assert.True(task.Wait(1000));
+            Assert.Equal(2, provider.Batches[0].Length);
+            Assert.Equal("2016-05-04 03:02:01.000 +00:00 [Information] Cat: Info message" + _nl, provider.Batches[0][0].Message);
+            Assert.Equal("1 message(s) dropped because of queue size limit. Increase the queue size or decrease logging verbosity to avoid this." + _nl, provider.Batches[0][1].Message);
         }
 
         private class TestBatchingLoggingProvider: BatchingLoggerProvider