Optimally Scheduling Admission of N Customers from Low–Price Buffer to High-Price Queue, Part II: Edge Effect

This paper continues to study the problem of optimally admitting a finite number 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, which was introduced in Part I. This paper first proves a few asymptotic properties of the sequence of optimal schedules indexed by the number of customers. In particular, it is proven that the first inter-admission time converges to 0 as the number of customers increases. Then, a number of optimal schedules were numerically computed for different cost ratio and the number of customers. On the basis of the numerical results and queueing theoretic intuition, it is conjectured that in each optimal schedule the inter-admission times are monotonically non-decreasing if arranged in chronological order.