Microsoft throttles ingestion into Office 365 mailboxes and Personal Archives which can lead to slow migration rates with Mailbox Shuttle. This article explains the parameters that should be relaxed by Microsoft.
For customers with over 1000 accounts, the customer can create a ticket with Microsoft Support to make the following changes to the throttling policy:

PowerShellMaxConcurrency 20 PowerShellMaxBurst 900000 PowerShellRechargeRate 2520000 PowerShellCutoffBalance 3000000 PowerShellMaxTenantConcurrency 100 PowerShellMaxOperations 400 PowerShellMaxCmdletsTimePeriod 5 ExchangeMaxCmdlets 200 PowerShellMaxCmdletQueueDepth 100 PowerShellMaxDestructiveCmdlets 120 PowerShellMaxDestructiveCmdletsTimePeriod 60 PowerShellMaxCmdlets 400 PowerShellMaxRunspaces 20 PowerShellMaxTenantRunspaces 200 PowerShellMaxRunspacesTimePeriod 60
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