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When running a VPN over the Internet, your VPN is subject to whatever the underlying Internet delays are. These might be seen by pinging, concurrently, "outside of" your VPN at the same time.
From what you described, since it appears volume related, to your own traffic, it might just be you're oversubscribing the available bandwidth. If so, the issue you're seeing would be expected. Also if so, stability and consistency might be improved by using QoS.
