Energy-aware task mapping onto heterogeneous platforms using DVFS and sleep states

Abstract

Heterogeneous multicore platforms are becoming an interesting alternative for embedded computing systems with limited power supply as they can execute specific tasks in an efficient manner. Nonetheless, one of the main challenges of such platforms consists of optimising the energy consumption in the presence of temporal constraints. This paper addresses the problem of task-to-core allocation onto heterogeneous multicore platforms such that the overall energy consumption of the system is minimised. To this end, we propose a two-phase approach that considers both dynamic and leakage energy consumption: (i) the first phase allocates tasks to the cores such that the dynamic energy consumption is reduced; (ii) the second phase refines the allocation performed in the first phase in order to achieve better sleep states by trading off the dynamic energy consumption with the reduction in leakage energy consumption. This hybrid approach considers core frequency set-points, tasks energy consumption and sleep states of the cores to reduce the energy consumption of the system. Major value has been placed on a realistic power model which increases the practical relevance of the proposed approach. Finally, extensive simulations have been carried out to demonstrate the effectiveness of the proposed algorithm. In the best-case, savings up to $18\,\%$ of energy are reached over the first fit algorithm, which has shown, in previous works, to perform better than other bin-packing heuristics for the target heterogeneous multicore platform.

Appendix: List of symbols

Description	Symbols	Description	Symbols
Heterogeneous multicore platform	$\pi$	Average energy consumption at specific frequency	$E^m_{i,j}$
Number of core types	M	Individual utilisation of a task on a core type $\pi ^m$ at frequency $f^m_j$	$U_{i,j}^m$
core index	m	Utilisation of a core type at frequency $f^m_j$	$U_j^m$
core type m	$\pi ^m$	Set of frequency combinations	$\mathscr {A}$
Active power of a core	$P_A^m$	Frequency combination	$\Lambda _k$
Idle power of a core	$P_I^m$	A core $\pi ^m$ running on a frequency $f_v^m$	$\pi _v^m$
Sleep index	n	Energy density of a task on $\pi _v^m$	$ED_{i,v}^m$

Frequency index	v	Density difference of a task on $\pi _v^m$	$DD_{i,v}^m$
Vector of frequencies	$\mathop {f_v^m}\limits ^{\rightarrow }$	Energy density of a task on its favourite core	$ED_i^{min}$
Vector of sleep states	$\mathop {S_n^m}\limits ^{\rightarrow }$	Energy density of a task on its least preferred core	$ED_i^{max}$
Frequency of a core	$f_v^m$	Current density difference of a task	$CDD_i$
Sleep state of a core	$S_n^m$	Set of $CDD_i$	CDD
Critical speed	$f_{cric}^m$	Expected energy consumption of $\pi _v^m$	$EEC_v^m$
Power of a sleep state	$P_j^m$	Maximum feasible threshold	$th^m$
Transition delay	$tr_j^m$	Energy consumption of a sleep state	$\mathscr {E}$
Energy overhead of a sleep state	$Es_j^m$	Procrastination interval	$Z_i$
Break-even-time of a sleep state	$bet_j^m$	Accumulative utilisation of all tasks on all cores	$U_{sum}^j$
Power dissipation at a frequency $f_v^m$	$P_{f_v^m}^m$	Set of threshold value	$\rho _v^m$
Task-set	$\tau$	i th group of tasks to enable specific sleep state on $\pi ^m$	$G_i^m$
Task	$\tau _i$	Sporadic delay limit	$\Upsilon$
Task-set size	$\ell$	Task-set distribution	$\xi$
Relative deadline	$D_i$	Best-case execution time limit	$C^b$
Minimum inter-arrival time	$T_i$	Characteristics factor to model task’s behaviour	$\beta$
Vector of execution profiles of $\tau _{i}$ on different core types	$\mathop {C_i}\limits ^{\Rightarrow }$	Average speed up factor of $\pi ^m$	$\eta ^m$
Vector of WCET of a task on a specific core type at different frequencies	$\mathop {C_i^m}\limits ^{\rightarrow }$	Average capacity of the heterogeneous platform	$U_a$
WCET at specific frequency	$C_{i,j}^m$	Latency hiding low limit frequency	$F_{LH}$
Vector of average energy consumption profiles of $\tau _{i}$ on different core types	$\mathop {E_i}\limits ^{\Rightarrow }$	Latency hiding saturation frequency	$F_{Sat}$
Vector of average energy consumption of a task on a specific core type at different frequencies	$\mathop {E^m_i}\limits ^{\rightarrow }$	Default core type	$\pi ^D$