Load balancing and speed scaling interaction in processor-sharing systems with exponential power functions

摘要

Speed scaling has been widely adopted in energy-efficient operation of communication and computer systems. An important related issue is the interaction of speed scaling with other resource allocation mechanisms such as load balancing. This paper studies the interaction between load balancing and speed scaling in processor-sharing systems with exponential power functions. We consider three different load balancing models - the delay-minmax, delay-optimal, and energy-optimal load balancing - under speed scaling, and characterize the efficiency loss of the load-balancing-speed-scaling equilibrium with the traditional delay-minmax model in delay as well as in energy consumption. As with systems with the polynomial power functions studied in our prior work, our results show that the efficiency loss in the system with the exponential power functions is mostly bounded by the heterogeneity of the system but does not scale with the size of the system. These results provide insights in understanding the interaction of load balancing with speed scaling and guiding new designs for communication systems where the power consumption is usually an exponential function of the link rate.