Errors “Cop: Total queue shared memory required 84025344” and subsequently “Cop: queue initialization failed – exiting” (4300448)

The following errors are observed in event_log when sp_cop dies shortly after it is invoked or started (the values shown below are from an actual failure at a site):

Notice 2015-12-17 20:22:15.036000 5228 6752 Cop: Total queue shared memory required 84025344; total for post queues 67108864 [module que]

Error 2015-12-17 20:22:15.052000 5228 6752 Cop: No support to convert queue version 0, in queue [module que]

Error 2015-12-17 20:22:16.114000 5228 6752 Cop: queue initialization failed - exiting [module cop]