This paper considers a reader-writer queue with alternating exhaustive priorities. The system can process an unlimited number of readers simultaneously. However, writers have to be processed one at a time. Both readers and writers arrive according to Poisson processes. Writer and reader service times are general iid random variables. There is infinite waiting room for both. The alternating exhaustive priority policy operates as follows. Assume the system is initially idle. The first arriving customer initiates service for the class (readers or writers) to which it belongs. Once processing begins for a given class of customers, this class is served exhaustively, i.e. until no members of that class are left in the system. At this point, if customers of the other class are in the queue, priority switches to this class, and it is served exhaustively. This system is analyzed to produce a stability condition and Laplace-Stieltjes transforms (LSTs) for the steady state queueing times of readers and writers. An example is also given.
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