Is it possible for server A to access a private queue from server B?
There is little functional difference between a public and private queue, except that MSMQ publishes information about public queues in Active Directory (AD).
I've never done this myself, but it appears that if you know the full path to the private queue, you can access it from another server:
Private queues
Private queues are queues that are not published in Active Directory and are displayed only on the local computer that contains them. Private queues have the following features:
Message Queuing registers private queues locally by storing a description of the queue in the LQS (local queue storage) directory on the local computer. In MSMQ 2.0, and Message Queuing 3.0, the default location is %windir%\system32\msmq\storage\lqs. Note that a description of each public queue created on the local computer is also stored locally in a separate file in the LQS folder.
Private queues are registered on the local computer, not in the directory service, and typically cannot be located by other Message Queuing applications.
Private queues are accessible only by Message Queuing applications that know the full path name, the direct format name, or the private format name of the queue, as follows:
Path name:ComputerName\private$\QueueName.
Path name on local computer: \private$\QueueName.
Direct format name:: DIRECT=ComputerAddress\PRIVATE$\PrivateQueueName.
Private format name: PRIVATE=ComputerGUID\QueueNumber.
For more information on path names and format names, see Queue names.
Private queues have the advantage of no directory service overhead, making them quicker to create, no latency in accessing them, and no replication overhead.
Private queues are not dependent on the directory service, and thus can be created and deleted when the directory service is not working. This is useful for offline operation.
One way that private queues can be exposed to other applications is by setting a message property. To distribute the location of a private queue, an application can send a format name of the private queue as the response queue property of a message.
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