Ordering Build Queue
TeamCity Build Queue when adding builds; however, it is possible to manage the queue builds manually.
Manually Reordering Builds in Queue
To reorder builds in the Build Queue, you can simply drag them to the desired position. To move a build configuration to the top position, click the arrow button next to the build sequence number 
.
Managing Build Priorities
In TeamCity you can control build priorities by creating Priority Classes. A priority class is a set of build configurations with a specified priority (the higher the number, the higher the priority. For example, priority=2 is higher than priority=1). The higher priority a configuration has, the higher place it gets when added to the Build Queue. To access these settings, on the Build Queue tab, click the Configure Build Priorities link in the upper right corner of the page.
By default, there are two predefined priority classes: Personal and Default, both with priority=0.
All personal builds (Remote Run or Pre-Tested (Delayed) Commit) are assigned to the Personal priority class once they are added to the build queue. Note that you can change the priority for personal builds here.
The Default class includes all the builds not associated with any other class. This allows to create a class with priority lower than default and place some builds to the bottom of the queue.
To create a new priority class:
Click Create new priority class.
Specify its name, priority (in the range
-100..100) and additional description. Click Create.Click the Add configurations link to specify which build configurations should have priority defined in this class.
Removing Builds From Build Queue
To remove build(s) from the Queue, check the configurations using Del box, then select Remove selected builds from the queue from the Actions menu. If a build to be removed from the Queue is a part of a build chain, TeamCity shows the following message below comment field: "This build is a part of a build chain". Refer to the Build Chain description for details.
Also you can remove all your personal builds from the queue at once from the Actions menu.
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Limiting Maximum Size of Build Queue
Since TeamCity 8.1.2, it is possible to limit the maximum number of builds in the queue. By default, the limit is set to 3000 builds. The default value can be changed using the teamcity.buildTriggersChecker.queueSizeLimit Configuring TeamCity Server Startup Properties.
When the queue size reaches the limit, TeamCity will pause Configuring Build Triggers. Automatic build triggering will be re-enabled once the queue size gets below limit. While triggering is paused, a warning message is shown to all of the users.
While automatic triggering is paused, it is still possible to add builds to the queue Triggering a Custom Build.