Optimally Scheduling Admission of N Customers from Low–Price Buffer to High-Price Queue, Part I: Asymptotic Rate

This paper introduces the problem of optimally admitting a finite number of customers from an auxiliary buffer with a low holding cost into a single–server queue with a high holding cost without observing the status of the single-server queue. This paper formulates a static (off-line) optimization of the admission schedule for a finite number of customers, assuming that the single–server queue is initially empty. It is proven that the overall admission rate under the optimal schedule converges to the service rate of the main system as the number of customers increases. Part II (the sequel) of this paper will present numerical solutions and prove more asymptotic properties of the sequence of optimal schedules indexed by the number of customers.