Flexible Load Balancing with Multi-dimensional State-space Collapse

Abstract

Heavy traffic delay analysis for load balancing policies has relied heavily on a condition called state-space collapse onto a single-dimensional line. In this paper, via Lyapunov driftbased method, we rigorously prove that even under a multidimensional state-space collapse, steady-state heavy-traffic delay optimality can still be achieved for a general load balancing system. This result directly implies that achieving steady-state heavy-traffic delay optimality simply requires that no server is kept idling while others are busy at heavy loads, thus complementing and extending the result obtained by diffusion approximations. Further, we explore the greater flexibility provided by allowing a multidimensional state-space collapse in designing new load balancing policies that are both throughput optimal and heavytraffic delay optimal in steady state.