Models and Problems of Dynamic Memory Allocation

Abstract

We construct and analyze some stochastic models for optimal allocation of memory in fragmented arenas. The arenas, as well as the item types they carry, are of various shapes: linear, cubic, pentagonal pie, S² (surface of sphere). Formulated as a Markov dynamic programming problem, the choice of optimal memory allocation closely resembles the choice of an optimal route for a telephone call. Much can be guessed about optimal operation from scrutiny of the partial ordering of the possible states reduced under symmetries; especially, in many specific examples, a natural relation B (read “better than ”) of preference can be defined among alternative allocations, and a topological fixed-point argument based on B given, to solve the allocation problem without resort to numerical solution of the Bellman equation.