There are settings in the rsreportserver.config file that might help with that...BOL mentions looking for this setting:
MaxActiveReqForOneUser
Specifies the maximum number of simultaneous and in-progress connections that a single user can open to the report server. Once the limit is reached, further connection requests from the user are denied. This configuration setting is intended to mitigate a denial of service attack. Valid values are 0 to a maximum integer. The default is 20.
Note that most requests process very quickly so it is unlikely that a single user will have more than 20 open connections at any given time. If users are opening more than 15 process-intensive reports at the same time, you might need to increase this value.
This setting is ignored for report servers that run in SharePoint integrated mode. For more information about server modes, see Deployment Modes for Reporting Services.
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Your lack of planning does not constitute an emergency on my part...unless you're my manager...or a director and above...or a really loud-spoken end-user..All right - what was my emergency again?