Efficient online computation of core speeds to maximize the throughput of thermally constrained multi-core processors

Abstract

Abstract-We address the problem of efficient online computation of the speeds of different cores of a multi-core processor to maximize the throughput (which is expressed as a weighted sum of the speeds), subject to an upper bound on the core temperatures. We first compute the solution for steady-state thermal conditions by solving a linear program. We then present two approaches to computing the transient speed curves for each core: (i) a local solution, which involves solving a linear program every time step (of about 10 ms), and (ii) a global solution, which computes the optimal speed curve over a large time window (of about 100 s) by solving a non-linear program. We showed that the local solution is insensitive to the weights assigned in the performance objective (hence the need for the global solution). This is because a reduction in the speed of a core can only reduce the temperature of the other cores over much larger time periods (of the order of several seconds). The local solution is then completely determined by the temperature constraint equations. We show that the constraint matrix exhibits a special property -it can be expressed as the sum of a diagonal matrix and a matrix with identical rows. This allows us to solve the multi-core thermal constraint equations analytically to determine the (temporally) local optimum speeds. Further, we showed that due to this property, the steady-state speed solution selects a set of threads to operate at maximum temperature, and turns off all unused cores. Hence, to ensure that all available threads are scheduled, we impose a "fairness" constraint. Finally, we show how the open-loop speed control methods proposed above could be used together with a feedback controller to achieve robustness to model uncertainty.

Runtime temperature-based power estimation for optimizing throughput of thermal-constrained multi-core processors

“…Leakage power consumption is considered in this formula which is proportional to the temperature but the output of this optimization is to maximize total dynamic power consumption. We decide to use the result of this optimization formula instead of dynamic convex optimization methods proposed in [6][7] [8]. The mina difference between ours and previous is that we can have an absolute value of dynamic power consumption available in real time.…”

“…Although the computational cost of dynamic runtime convex optimization can be minimized using various approximation methods, the size of the resistance matrix grows in the order of N 2 ,where N is the number of cores on a die. In [8] the proposed method requires average power consumption of each core within each sampling interval for throughput optimization. However, the runtime estimation of average power consumption during a discrete sampling interval is not trivial, particularly with a limited number of thermal sensors.…”

“…To minimize the degradation of the throughput, various dynamic thermal management techniques such as voltage and frequency scaling and instruction throttling have been proposed. Since both voltage and frequency scaling as well as instruction fetch throttling impact the throughput of multi-core processors directly, various convex optimization methods were proposed to maximize the throughput of multi-core processors [6][7] [8]; a few efficient ways to reach a global and local throughput optimal point only with a temperature constraint. Although the computational cost of dynamic runtime convex optimization can be minimized using various approximation methods, the size of the resistance matrix grows in the order of N 2 ,where N is the number of cores on a die.…”

“…Some researchers have already explored various methods to maximize the throughput of thermal-constrained multi-core processors using convex optimization methods [6], [7], [8]. They assign optimal voltage and frequency to each core through dynamic convex optimization to minimize the degradation of the throughput.…”

Minimizing the power consumption of a Chip Multiprocessor under an average throughput constraint

“…The real-time power management techniques include local responses at the core-level [2] [7] [8] or global task scheduling heuristics [6] [9]- [11]. Typically, the problem formulations target performance optimization under a power/energy budget [1] [3] or a thermal constraint [7] [12]- [14], or attempt to minimize a composite cost function in the form of energy per throughput [5] [12]. Minimization of the total power consumption of a general-purpose CMP system while meeting a total throughput constraint [4] [15] is an equally interesting problem, which is the focus of the present paper.…”