Joint Sleep Scheduling and Mode Assignment in Wireless Cyber-Physical Systems

Transcription

1 Joint Sleep Scheduling and Mode ssignment in Wireless Cyber-Physical Systems Chun Jason Xue, Guoliang Xing, Zhaohui Yuan, Zili Shao and Edwin Sha City University of Hong Kong, jasonxue, Michigan State University, Polytechnical University of Hong Kong, University of Texas at Dallas, bstract Designing cyber-physical systems with high efficiency, adaptability, autonomy, reliability and usability is a challenging task In this paper, we focus on minimizing networkwide energy consumption for real-time applications in wireless cyber-physical systems While a lot of work has been done to manage energy consumption on single processor real-time systems, little work has been done in network-wide energy consumption management for real-time applications Existing work on network-wide energy minimization assumes that the underlying network is always connected, which is not consistent with the practice in which wireless nodes often turn off their network interfaces in a sleep schedule to reduce energy consumption This paper jointly consider the radio sleep scheduling of wireless nodes and the execution modes of processors ased on different wireless network topologies, different schemes are proposed to minimize energy consumption while guaranteeing the timing constraint and precedence constraint When the precedence graph is a tree, optimal result on energy management is achieved The experiments show that our approach significantly reduces total energy consumption compared with the previous work Introduction Cyber-Physical Systems (CPS) are integrations of computation with physical processes, eg, automated traffic control, robotic surgery, autonomous collision avoidance, and zeronet energy buildings These systems are often comprised of computation nodes connected wirelessly and collaborating in finishing a set of real-time tasks Designing cyber-physical systems with high efficiency, adaptability, autonomy, reliability and usability is a challenging task In this paper, we focus on minimizing network-wide energy consumption for real-time applications in wireless cyber-physical systems Reducing energy consumption for stand alone systems has been extensively studied y reducing processor supply voltage and clock frequency, we can reduce energy consumption at the cost of performance Various embedded processors such as Intel XScale processor [], and MD s mobile processor with MD PowerNow! technology [2] are all able to effectively reduce dynamic power consumption by supply voltage scaling To reduce CPU energy consumption on single processor architecture with independent tasks, dynamic voltage scaling (DVS) solutions are first proposed in [3], [4] Supply voltage and clock frequency are typically scaled down to achieve energy reduction with performance trade off For networked embedded systems, it is important to consider energy reduction for all the nodes in the network Some work has been done in this area to consider CPU energy for each nodes In [], slack distribution schemes are introduced for scheduling distributed real-time embedded systems while considering admission control and service demands In [6], static slack is assigned based on the degree of parallelism in the schedule While the above work consider CPUs in the network embedded systems, little work has been done to consider network-wide energy minimization in wireless embedded systems esides CPU, radio is another major source of power expenditure in wireless cyber-physical systems n effective approach to conserve radio power is to schedule radios to be turned off when not in use number of sleep scheduling schemes have been implemented in practice [7], [8], [9] Sleep scheduling introduces new challenges for networked embedded applications For example, it is not suitable to simply assume that the underlying network is always ready The execution of distributed real-time tasks thus must be jointly scheduled with the radio activity of nodes in the network When a computation node finishes execution, the wireless radio of the next node in the task execution chain may still be in sleep mode Communication can only take place when both nodes wireless radios wake up Scheduling real-time tasks incognizant of radio status may lead to not only more energy consumption but also deadline misses t the same time, most of the current sleep scheduling schemes are unaware of the computation status and often lead to unnecessary wakeups which waste energy In [0], network-wide energy consumption was studied with the consideration of both CPUs and wireless radios, where a general network topology was given an sleep scheduling was fixed and given as input In this paper, we propose solutions to minimize network-wide energy consumption for real-time tasks with precedence constraints executing on wireless embedded systems ased on different

2 network topology, we propose static energy management schemes to minimize energy consumption while guaranteeing the timing constraint and precedence constraint Optimal solutions are proposed in this paper for static energy management when the given task precedence graph is a tree Sleep scheduling was conducted together with mode assignments The experiments show that our approach reduces total energy consumption significantly compared with the previous work The remainder of this paper is organized as follows Section 2 introduces basic concepts and definitions Theorems and algorithms are proposed in Section 3 Experimental results and concluding remarks are provided in Section 4 and, respectively 2 Models 2 Task model In this paper, we consider a set of tasks with precedence constraints and sharing a common period The precedence constraints and communication cost between tasks within an application are represented by a directed acyclic graph (DG),, where vertexes represent tasks and edges represent dependencies between tasks n example task graph is shown in Figure C D (a) Frequency 400 MHz 300 MHz 200 MHz (b) Power 4 mw 283 mw 7 mw Figure (a) n example task graph (b) Xscale PX2 power spec 22 CPU Power model We assume each node supports discrete operating modes Each operating mode has different energy consumptions and different execution times Each mode can have a different frequency level For example, Intel Xscale PX2 processor can operate in 3 different frequency levels, 200MHz, 300MHz, and 400MHz s shown in Figure (b), when operating in different frequency levels, PX2 has different power requirements We use operating mode instead of frequency because it is more general For example, each mode can also have its own body bias setting to manage leakage power 23 Network model In this paper, we consider a single-hop networked embedded system with nodes, which are connected by a wireless network esides CPU, another major source of power dissipation of networked embedded systems is wireless radio ccording to several empirical studies [], wireless radios working in idle listening state consume similar amount of power as in transmitting state Therefore, an effective radio power conservation approach is to schedule radios to sleep when they are not actively transmitting In this paper, we assume the radios of all the nodes in the wireless network operate according to their sleep schedules The sleep schedule of the radio of each node will be determined jointly with the mode assignment in our proposed techniques to minimize network-wide energy consumption In our network model, two nodes can communicate only when both radios are on simultaneously In this paper, we assume that every time a radio wakes up, it wakes up for a small fixed time radio may wake up one or several times during a period Fig 2 illustrates the sleep schedules of three nodes In this scheduling scheme, the sender and receiver of a communication task always wake up at the same time We note that there also exists a class of ondemand sleep scheduling schemes [2] in which the sender and receiver wake up at different times and synchronize before the communication Compared with such a sleeping scheme, the synchronous sleeping scheme is more suitable for wireless real-time systems [3] In particular, by staging the on time of different nodes, communication collisions in the synchronous sleeping schedule can be largely avoided This is critical for real-time systems that require guarantees on communication delay R R2 R3 α Communicate Period p Communicate Figure 2 The sleep schedules of three nodes We note that the sleep scheduling model assumed in this paper is very general This model is consistent with several synchronous sleep scheduling schemes such as the ones used by S-MC [8] and 802 Power Saving Mode (PSM) [7] 24 Problem Formulation We formulate the network-wide energy minimization problem as follows:

3 4 K? h U Input: task graph, where is the task set and is the set of dependencies between tasks; Operating mode for each node, where is the number of modes, is the execution time for mode and is the energy consumption for mode ; Radio wakeup time ; time constraint, which is the deadline of completion of all the tasks Output: The sleep schedule of each node s radio and the mode assignment of each node so that the network-wide energy is minimized while the deadline is met For each node parts:, the energy consumed is composed of two where is the energy of CPU execution of node and is the energy consumed by node s radio The objective then is to minimize:! "#! $ %' In this paper, we assume the energy consumed by a node s radio is proportional to the radio wake up time We also assume that task mapping to computation nodes and task scheduling have been performed previously with a feasible schedule The main focus of this paper is to jointly assign operating modes and wireless network sleep time to reduce the total energy consumption of the input schedule without violating the deadline and precedence constraints We note that the power consumption of CPU and radio are comparable in several wireless embedded system platforms, which poses the need to jointly minimize the total energy as a whole For example, on the sensor network platform Mic2 motes [4], TMEL Tmega28L CPU s average power is 8m, and CC000 radio s idle power is 0m Hence, it is important to jointly consider CPU and radio s power consumption 3 Joint Sleep Scheduling and Mode ssignment In this section, we propose two joint sleep scheduling and mode assignment algorithms based on different wireless network topologies When the given task dependency graph is a tree, an algorithm is presented to give the optimal solution This algorithm is efficient in practice though rigorously speaking it is pseudo polynomial To solve the general problem, a generic algorithm is proposed for general DG task graph 3 n Efficient lgorithm for Trees n efficient algorithm, (*) +,--0/ +32, is proposed in this section It gives optimal solution when the given task graph is a tree We call a root node to be a node without any parent and a leaf node to be a node without any child post-ordering for a tree is a linear ordering of all its nodes such that if there is an edge 467 in the tree, then 4 appears before in the ordering For example, in Figure (a), both,,c,d and,,c,d are post-ordering for the given tree The pseudo polynomial algorithm for trees, (*) +,--8/ +32, is shown in lgorithm 3 Following the post-ordering in Step, we can get +9 ;: <4 for each node 4 by setting the minimum execution time for each node and computing the longest path from any leaf node to 4 In Step 2, basically, we select the minimum energy cost from all possible energy costs caused by adding 4 into the subtree In the following, we prove lgorithm (+) +,-=-0/ +32= gives the optimal solution when the given task graph is a tree Theorem (EDFGDH ) obtained by lgorithm (*) +,--8/ +32 is the minimum system cost of the subtree ended on 4 with total execution time D Proof: y induction asic Step: When I, because the computation of? J follows the post-ordering, 4 must have no parent node Thus, K?C ML ON?C ML and +9 ;: < ML, so?j QPORS =T VU if, where DWXD Thus, When Q, Theorem 3 is true Induction Step: We need to show that for, if?c is the minimum system cost of the subtree ended on 4, then ;Y'J?C is the minimum system cost of the subtree ended on 4 Y' ccording to the post-ordering, the computation of? C for each parent node of 4 ;YZ has been finished before computing ;YZ? J From Step 3, \[ Y'] K?J gets the summation of the minimum system cost of all parent nodes of 4 ;Y' because they can be allocated and executed simultaneously within time The minimum system cost is selected from all possible system costs caused by adding 4 Y' into the subtree ended on 4 Y' So ;Y'?J is the minimum system cost of the subtree ended on 4 ;Y' Therefore, Theorem 3 is true for any ( ED^D_H ) K?J WL if 4 ;K? From C Step 4, has no parent node and a`b? C if 4 has only one parent node 4 c` Thus, we do not really need to compute ;K? C in these cases Using these simplified methods, an example is shown in Figure 3 for the given tree in Figure (a) ssume that there are 2 different modes, d and fe The post-ordering node set of the given tree and the corresponding execution times and execution costs are shown in Figure 3(a) and Figure 3(b) respectively The computation procedure using lgorithm (*) +,--0/ +g2 is shown in Figure 3(c) when the timing constraint is h time units In?C Figure 3(c), the mode assignments are recorded below Node 4ji has two parent nodes, 4 and 4jk, so a pseudo node 4ji is added and Vi K? C l?c mk?c When computing?c, all possible system costs caused by adding considering network wake up time are computed and the minimum cost is selected The minimum cost mn o and

4 ? h! U u u u2 u3 u4 m T E m2 T2 E2 2 2 u3 u4 (a) 4 4 u2 3 3 X [j] 2 m j= X [j] r3 2 2 X4[j] (b) m2 m2 m2 m2 m2 m m m m m2 m2 m2 m2 X [j] r,r2 X 3[j] r3 r4 m m m2 m m 0 9 (c) m m m Figure 3 n example for a tree with 2 operating modes and I the assignment is dq4 n The assignment for the tree is V 4 V 4 k ef 4 i and d 4 n, which is obtained by tracing how to reach Vn Z The complexity of lgorithm (*) +,--0/ +32 is given time constraint, and, where is the number of nodes, is the is the number of modes When equals ( is a constant) which is the general case in practice, lgorithm (*) +,--0/ +32 is polynomial 32 n Efficient lgorithm for DGs n efficient algorithm, (*) +,--0/ V,, is proposed in this section It is a greedy heuristic solution when the given task graph is a generic DG Details of (*) +,--8/ V, algorithm are shown in lgorithm 32 Each execution node is initialized with the slowest running mode, which gives the longest execution time and the least energy consumption Radio of each node is woken up as soon as the computation of the node finishes The corresponding node will wake up its radio to receive the message at the same time If the deadline is met, then the sleep scheduling and mode assignment are completed While the deadline is not met, we choose one node to increment its energy consumption mode by one level to reduce the total execution time How to judiciously choose a node during each step is the key of (*) +,--0/ V, algorithm We define a variable, where, for each node, is the energy difference for node s incremental mode change, and is the total execution time lgorithm 3 lgorithm for Tree (JointssignTree) Require: H nodes with executing modes, a tree, and the timing constraint Ensure: n optimal assignment for the tree Post-order and let =4 4 k ; 4 4 Y' be the post-ordering node set For each node 4 let <4 k ; execution time of node 4 and 4 T, where is the for executing mode ; T k where T is the for executing mode? to each node 4 energy cost of node 4 2 ssociate an array and let? C store the minimum energy cost of the subtree ended on 4 with total execution time D For D D, N?C _L 3 For I to H? C, compute?c +9 ;: " # \ ;K? < %$ < H )$j(' -*)+< -=),+ 4 ) ) -=2/g -= ; by: T < <4 where: T is the energy cost for node 4 under mode, is the execution time for node 4 under mode, is the radio wakeup time, D D ; j9 : 4 is the minimum time needed to process subtree ended on 4 except 4 ; 40 is a pseudo node ssume that 4 4 k 4 2 are all the parent nodes of node 4 and 3 is the number of parent nodes of node 4, then ;K? C e ; is calculated as: K? C ! " # L if R=0 c`b? 2D? J 6+8('7$ )8$d - 2=9 ) +;: ) * T - *+=< if R= if R E ^-4 )8$d -E *=2/7: )8$F'7+=+Z - T -b *+G<C2 is the minimum system cost and the assign- 4 YZ? ment can be obtained by tracing how to reach Y'? saved is calculated for each node, and is chosen to increase its energy consumption mode by one level For nodes with the same values, priority is given to the node that has the t each step, H the node with the maximum longest path to leaf nodes and is closest to root nodes In this way, after (*) +,--0/ V, algorithm stops, we either have a mode assignment that gives near optimal result in low energy consumption, or no feasible solution can be achieved with the given deadline The complexity of lgorithm (*) +,--0/ V, is

5 lgorithm 32 lgorithm for DG (JointssignDG) Require: Nodes with executing modes, a DG, and timing constraint Ensure: n assignment for the DG Initialize: Set the execution mode for each node with the least energy consumption; while Total execution time E and not all the nodes are running in the fastest execution mode do for each node ; Calculate H Select node with the largest ; Update mode for node ; Get the new Total execution time; end while 7, where is the number of nodes, and is the number of modes lgorithm (+) +,-=-0/ V, is polynomial The actual execution time for each task is often less than the worst case estimate (WCET) used in the offline static scheduling However, radio sleep scheduling has already been determined in offline static scheduling To utilize the dynamic slack generated at run-time, we would need to update the radio sleep schedule of the child nodes which requires the radios to wake up periodically to check to sleep scheduling updates Extra energy and computation time are needed and the savings could easily be out-weighted by the expense In this paper, we propose to leave radio sleep scheduling fixed and do not attempt to utilize the dynamic slacks generated at run-time This is on the contrary of previous techniques and the experiment results show our scheme do save more energy globally compare with previous techniques with dynamic slack allocations 4 Experiments This section presents the simulation results to validate the effectiveness of the proposed algorithms Simulation is used for the evaluations The simulations are performed on sixteen wireless embedded systems represented by task precedence graph sets 3 m to 3 ll the task graphs are based on real world examples like automotive, consumer, or DSP applications When the input task precedence graph is a tree, we compare the normalized energy cost of algorithms =4 2,,--0/ +g2, :,--0/ +g2, and (*) +,--0/ +32 lgorithm (*) +,--0/ +g2 is presented in Section 3 lgorithm =4 2,,--0/ +g2, and :,--0/ +32 do not schedule wireless radio sleep time and a simple prefixed sleep scheduling is used In this simple sleep scheduling, each radio wakes up periodically based on a prefixed schedule These three algorithms differ in the mode assignment only lgorithm =4 2 is a generic greedy heuristic solution that does slack allocation similar to most and V,O to V, of the previous work [6] asically, =4 2 first sets the mode of each node to be the fastest possible, thus we can finish execution as quick as possible with the highest energy consumption Then, =4 2 does slack allocation based on which node will give the maximum energy saving locally if step down one level =4 2 stops slack allocation when the timing constraint deadline is reached or when all the nodes are executing in the lowest energy mode lgorithm,--0/ +32 does static mode assignment similar to lgorithm (*) +,--0/ +32 It also considers the wireless radio up time However, it does not do joint radio sleep scheduling with mode assignment Each radio simply wakes up periodically based on a pre-fixed schedule lgorithm :,--8/ +32 is the combination of running static assignment using,-=-0/ +32= and running dynamic assignment updates t run time, upon receiving message from its parent, each node will pick a mode that consumes the least energy and starts execution Heu_pre ssigntree Dyn_ssignTree JointSchedule Tree Tree2 Tree3 Tree4 Tree Tree6 Tree7 Tree8 Figure 4 Comparison of energy cost when the input graphs are trees The comparison results of the four algorithms are shown in Figure 4 Y-axis of Figure 4 represents normalized energy consumption, where represents each node is set to run in highest-energy mode and radio wakes up based on a prefixed schedule From Figure 4, we can see that 4 2 is the most expensive in average in terms of energy consumption This is because most of previous slack allocation schemes like =4 2 do not take the underlaying wireless sleep scheduling into consideration With sleep scheduling applied in wireless network level, it is important to consider slack allocation together with each node s wireless radio s sleep and wakeup time On average, lgorithm,--0/ +g2 reduces energy consumption by 99% compared to lgorithm =4 2 Joint sleep scheduling and mode assignment achieves the best energy reduction out of the four algorithms On average, lgorithm (*) +,--0/ +32 reduces energy consumption by 369% compared to lgorithm =4 2, and lgorithm (*) +,--0/ +g2 reduces energy consumption by 2% compared to lgorithm,--0/ +g2 The main energy saving between lgorithm

6 ,--0/ +g2 and lgorithm (*) +,--0/ +32 is the radio energy In lgorithm (*) +,--0/ +32, the number of times that a radio needs to wakeup is significantly reduced compared to lgorithm,--0/ Heu_pre ssigndg Dyn_ssignDG JointssignDG DG DG2 DG3 DG4 DG DG6 DG7 DG8 Figure Comparison of energy cost when the input graphs are general DGs When the input task precedence graph is a general DG, We compare the normalized energy cost of algorithm 4 2,,-=-0/ V,, :,--0/,, and (*) +,--8/ V, lgorithm (+) +,-=-0/ V, is presented in Section 32 lgorithm =4 2 is the same as we presented above lgorithm,--8/ V, was proposed in [0] It does static mode assignment similar to lgorithm (*) +,--0/ V, It also considers the wireless radio up time However, it does not do joint radio,-=-0/ V, sleep scheduling with mode assignment Each radio simply wakes up periodically lgorithm : is the combination of running static assignment using,--0/, and running dynamic assignment update at run time The results are shown in Figure On average, lgorithm (*) +,--0/ V, reduces energy consumption by 26% compared to lgorithm =4 2, and lgorithm (*) +,--8/ V, reduces energy consumption by 97% compared to lgorithm,--8/ V, We can see that the improvement is not as significant as Figure 4 because lgorithm (*) +,--0/, is a heuristic solution instead of optimal solution like lgorithm,--8/ +32 Conclusion In this paper, we consider energy minimization for realtime wireless systems Specifically, network protocol is taken into account when assigning execution mode for each node Optimal joint sleep scheduling and mode assignment algorithm is given when the task graph is a tree Greedy heuristic algorithm is proposed for general graphs Experimental results showed significant improvement compared to solutions that did not consider the underlying network protocol cknowledgement This work is partially supported by a grand from City University of Hong Kong [Project No ] References [] [2] [3] F Yao, Demers, and S Shenker, scheduling model for reduced cpu energy, Proceedings of Symp Foundations of Computer Science, pp , Oct 99 [4] Manzak and C Chakrabarti, Variable voltage task scheduling algorithms for minimizing energy, Proceedings of Intl Symp Low Power Electronics and Design, ug 200 [] R Mahapatra and W Zhao, n energy-efficient slack distribution technique for multimode distributed real-time embedded systems, IEEE Transactions on Parallel and Distributed Systems, vol 7, no 7, Jul 200 [6] R Mishra, N Rastogi, D Zhu, D Mosse, and R Melhem, Energy aware scheduling for distributed real-time systems, Proceedings of the Intl Parallel and Distributed Processing Symposium, pr 2003 [7] IEEE, Wireless lan medium access control (mac) and physical layer (phy) specifications, IEEE Standard 802, 999 [8] W Ye, J Heidemann, and D Estrin, n energy-efficient mac protocol for wireless sensor networks, in INFOCOM, 2002 [9] I Rhee, Warrier, M ia, and J Min, Z-mac: a hybrid mac for wireless sensor networks, in Proceedings of the Third CM Conference on Embedded Networked Sensor Systems (SenSys), San Diego, California, US, 200 [0] C J Xue, G Xing, Z Yuan, Z Shao, and E Sha, Energyefficient operating mode assignment for real-time tasks in wireless embedded systems, Proceedings of the 4th IEEE International Conference on Embedded and Real-Time Computing Systems and pplications, 2008 [] Chen, K Jamieson, H alakrishnan, and R Morris, Span: n energy-efficient coordination algorithm for topology maintenance in ad hoc wireless networks, in MobiCom, 200 [2] J Polastre, J Hill, and D Culler, Versatile low power media access for wireless sensor networks, in SenSys, 2004 [3] Rowe, R Mangharam, and R Rajkumar, Rt-link: time-synchronized link protocol for energy constrained multihop wireless networks, Proceedings of the Third IEEE International Conference on Sensors, Mesh and d Hoc Communications and Networks (IEEE SECON), 2006 [4]