Optimal admission to reader–writer systems with no queueing

We consider a reader–writer system with no queueing. An unlimited number of readers can be processed in parallel, whereas writers are processed one at a time. Both readers and writers arrive according to independent Poisson processes and request independent identically distributed service times. Every admitted customer generates a revenue and a holding cost. We derive optimal stationary admission policies that depend only on the number of readers and writers, to maximize the total expected discounted net profit, and the long-run net profit rate.