Optimal Content Placement and Multicast Delivery Under Cost and Storage Constraints

Abstract

Content placement can substantially reduce peaktime network load by creating coded multicast opportunities, but classical formulations typically assume that placement is free. Under the placement-cost model $c_{r}=\rho r^{\alpha}$ with the nonew-peak constraint, the optimal scheme is known in closed form when user storage is unlimited. This paper solves the practically dominant case in which each user has a cache of only $M \leq N$ files, so that the placement budget and the storage budget may bind simultaneously. Formulating joint content placement and multicast delivery as a linear program, we first derive an exact (necessary and sufficient) partition of the parameter space into three operating scenarios via a single concavity argument, sharpening - and in one case correcting -previously reported partial characterizations. Our main result is a complete, self-contained solution of the intersection scenario as a feasibility-ordered trichotomy: the optimum is the placement-limited solution when it fits the storage budget, the generalized memory-sharing solution when it fits the placement budget, and otherwise a new closed-form vertex on two adjacent caching types at which both constraints are tight - a regime with no unlimitedmemory counterpart. The optimal scheme always uses at most two adjacent caching types, and the Maddah-Ali-Niesen scheme is recovered at $\rho=0$. Numerical results at both small and large scale $(N=1000, K=100)$ map the operating regimes and show that the joint design reduces the realized peak network load by up to $3.4\times$ relative to cost-blind coded placement, which itself violates the no-new-peak constraint by more than an order of magnitude at moderate placement cost.