Related works

de-termine APTM schemes at online adaption instants. Moreover, an offline algorithm is also given to search the key parameter of online adaption.

The rest of this chapter is organized as follows: The related work is briefly introduced in section 4.2. Section 4.3 describes our system mod-els and presents problem statement. A motivation example is presented in section 4.4. Section 4.5 presents backgrounds of our approach. Then, the real-time constraints are analyzed in section Section 4.6. The heuris-tic scheme is discussed in section 4.7 and section 4.8. Section 4.9 presents the evaluation of APTM. Section 4.10 concludes.

4.2 Related works

Pipelined multi-core architecture has been widely adopted for high per-formance. Several approaches can be found on thermal optimization of pipelined systems. Cox et al. proposed a fast thermal-aware ap-proach for streaming applications based on a 3D MPSoC model under the throughput constraints in [32]. The mapping of the multiple appli-cations is determined at design time such that the peak temperature is minimized under throughput constraints. This approach is based on task-mapping technology and assumes periodic task model. Cheng et al. presented an offline approach to minimize the peak temperature of pipelined systems under real-time constraints in [2]. The approach computes a PTM scheme for each stage to determine the switch on/off pattern during design phase. The above two approaches search the op-timal solution that minimizes the peak temperature in offline manner, considering the worst-case execution time and worst-case event arrivals, which rarely happen in real systems. Thus their results could be pes-simistic due to the runtime variability of event arrivals and execution time. There are also several approaches on this topic. However, they either don’t consider hard deadline constraints [3] or just reduce the deadline miss percentage into a low range [72]. Designed for hard real-time systems, our approach can guarantee the worst-case delay is no larger than the deadlines of the tasks.

Chen et al. explored how to apply dynamic power management in adap-tive manner to optimize leakage power consumption for pipelined multi-core systems under deadline constraints in [24]. As aforementioned, an effective power management may not be suitable for thermal manage-ment. In addition, the proposed approach has one major drawback.

At each adaption instant, the approach computes a set of time lengths for which the stages are allowed to sleep. After adaption, the stages sleep for the corresponding time length, and then stay active until next adaption instant. This simplifies the real-time analysis during online ex-ecution. However, this method demands a high adaption frequency, in other words, short adaption intervals. Otherwise, the results get worse very quickly since the stages could be active unnecessarily between two adaption instants. In our approach, the PTM schemes are adopted to the stages during adaption such that the results is much less influenced by the adaption period. Therefore, our approach can still offer acceptable results with large adaption periods.

There has been significant work on thermal management of multi-core architectures. The concept of Thermal-Resiliency is extended to multi-core systems by Pradeep et al. in [45]. Combining a control-theoretic framework, they proposed an approach which can maintain thermal con-straints and provide hard real-time guarantees. In [103], Wang et al. ad-dressed the problem of minimizing the peak temperature of a real-time application executed on multi-core platforms. Three computationally efficient algorithms are presented for deploying applications to individ-ual devices. Above two approaches both assumed simple task models, i.e., either periodic tasks or sporadic task model. The authors of [79] ad-dressed the DVS scheduling problem on multicore systems under both temperature and energy constraints. Since the problem is NP-hard, two algorithms, an accurate one and an approximated one, are proposed to give results in different levels of accuracy. A stochastic thermal control approach is proposed in [69] to reduce the chip-wide temperature gradi-ent of a multi-core processor handling multiple stochastic real-time task streams. The technique of job migration among active and passive cores of the stream is adopted to reduce the chip-wide temperature gradient.

While making great contributions to the field, the above two approaches cannot provide hard real-time guarantees.

To model general event arrivals, Real Time Calculus [96] are proposed to abstract task arrivals in time domain into arrival curve. In [78], Perathoner et al. presented an adaptive scheme for the scheduling of arbitrary event streams by combining optimistic and pessimistic DVFS scheduling. Adaptive online power managements have also been pro-posed in [49, 59] to adaptively reduce the power consumption of the processor by procrastinating the processing of arrived events as late as possible. The above approaches, unfortunately, are designed for single core processors and cannot be applied to multi-core architectures.

Au-4.3. system model thors of [58] introduced an online DVFS management scheme for

multi-core processors running hard real-time tasks. The technique in [59] is adopted to predict future event arrivals based on the arrival history.

Although aiming at minimizing the temperature, the online DVFS ap-proach doesn’t consider any temperature feedback or thermal property of the cores, which can help to reduce the temperature further. In con-trast, our approach implements Dynamic Power Management to man-age temperature utilizes the sampled temperature and the unique ther-mal properties of each core in determining PTM schemes to obtain lower peak temperature.

The related work is briefly introduced in this section. In next section, the definitions and notations that are used in this chapter are presented.

4.3 system model

Notation: In this chapter, matrices and vectors are represented by bold characters.

4.3.1 Hardware and Thermal Model

In this chapter, we consider the pipelined multi-core system adopted in Chapter 3. Therefore, we also have the following constraint due to mode-switching overhead.

t^{o f f} >t^{swo f f} (4.1)

In addition to the hardware model, the thermal and power models in Chapter 3 are also used to get the temperature evolution.

It is worth noting that the implementation our approach is not limited by such thermal and power models. In runtime, our approach only needs the temperature of the stages to make scheduling decisions. For proces-sors with physical thermal senproces-sors, the temperature can be obtained by reading the sensors. For processors without hardware thermal sensors on each core, soft thermal sensors [62] can be employed to estimate the temperature of a single core.

4.3.2 Adaptive Periodic Thermal Management

In this chapter, we study how to minimize the peak temperature for coarse-grained pipelined multi-core processors. An online approach

t P_a P_a

P_a P_a

Ps

P_a

t^on t^{of f} t^on

t^act t^slp

t^inv t^vld

t^swon t^{swof f} t^swon

Figure 4.1: The adaptive periodic thermal management schemes after two adaption instants.

named Adaptive Periodic Thermal Management is proposed to adap-tively switch the cores to ‘sleep’ in the run time.

At each adaption instant, an APTM scheme is applied to each core in the pipeline and is updated at the next adaption instant. The APTM scheme applied to the stage Pi is specified by a pair of parameters (t^on_i , t^{o f f}_i ). The period is calculated ast_i^prd =t^on_i +t^{o f f}_i . For brevity,t^onandt^off denote the vectors [t₁^on,t^on₂ ,· · · ^,tonn ] and [t₁^{o f f},t₂^{o f f},· · · ^{,to f f}n ], respectively.

Given an APTM scheme, whichever state it is currently at, stagePi first switches to ‘sleep’ state and stays for t_i^{o f f} time units. Then, it switches to ‘active’ or ‘idle’ state and keeps for t^on_i time units. This procedure repeats until the next adaption instant. An example of APTM scheme is demonstrated in Fig. 4.1. Note that due to the switching overhead, the valid/invalid time interval in each period for handling workload should be revised as:

t^vld = t^on−^{tswon (4.2)}

t^inv = t^{o f f} +t^swon (4.3)

In addition, we define the valid partition as:

K^vld =t^vld/t^prd (4.4)

4.3.3 Problem Statement

At each online adaption instant, our approach should offer an APTM (t^on_i , t^{o f f}_i ) scheme to each stage Pi in the pipelined system. The val-ues of t^on_i and t^{o f f}_i should be chosen prudently. First, it’s clear that the peak temperature can be reduced by increasing the sleep interval

4.4. Motivation of Our Work