A review on stochastic approach for dynamic power management in wireless sensor networks
 Anuradha Pughat^{1}Email author and
 Vidushi Sharma†^{1}
https://doi.org/10.1186/s1367301500216
© Pughat and Sharma; licensee Springer. 2015
Received: 29 July 2014
Accepted: 26 January 2015
Published: 12 February 2015
Abstract
Wireless sensor networks (WSNs) demand low power and energy efficient hardware and software. Dynamic Power Management (DPM) technique reduces the maximum possible active states of a wireless sensor node by controlling the switching of the low power manageable components in power down or off states. During DPM, it is also required that the deadline of task execution and performance are not compromised. It is seen that operational level change can improve the energy efficiency of a system drastically (up to 90%). Hence, DPM policies have drawn considerable attention. This review paper classifies different dynamic power management techniques and focuses on stochastic modeling scheme which dynamically manage wireless sensor node operations in order to minimize its power consumption. This survey paper is expected to trigger ideas for future research projects in power aware wireless sensor network arenas.
Keywords
Wireless sensor networks Stochastic approach Dynamic power management Markov modelIntroduction
A wireless sensor network (WSN) consists of mostly tiny, resourceconstrained, selforganized, low power, low cost and simple sensor nodes which are organized in a cooperative manner. The sensor nodes can sense, communicate and control the surrounding environment. They can provide interaction between the users (human being), physical environment and embedded computers in order to perform some specific operation. They follow IEEE 802.15.4 as basis standard for lower layers (physical and medium access control) and other standards like ZigBee, ISA100.11a etc. as upper layer (application, routing) protocols. WSNs have wide application bandwidth emerging the areas of agricultural, medical, military, environmental, industrial control, monitoring, civil and mechanical, etc. Target tracking and continuous monitoring in WSNs are important energy hungry problems with a large spectrum of applications, such as surveillance [1], natural disaster relief [2], traffic monitoring [3] and pursuit evasion games, and so forth. A wide range of wireless sensor network applications helps in transforming human lives in various aspects of intelligent living technology. These attractive applications have generated a great interest amongst industrialists and researchers [4].
DPM is referred to as an operating systemlevel algorithm/technique which is used to control the power and performance parameters of a low power system, by increasing idle time slots of its devices and switching the devices to low power mode. Broadly, the ultralowpower components of the sensor node make the node energy efficient by implementing dynamic power management policies to achieve longer lifetime [5]. The total power dissipation of sensor node can be modelled with static and dynamic power dissipation. Static power consumption is the result of leakage current flow in ultralow power components of sensor node that can be reduced at design time by using static techniques. The static power can be reduced using synthesis and compilation at design time, whereas the dominate part such as dynamic power is the result of switching power consumption that can be reduced by selectively switching or shutting down hardware components on a sensor node. The switching or dynamic power consumption decreases quadratically with supply voltage (i.e. power gating) and linearly with the reduction in the working frequency (i.e. clock gating). Further, more the power modes of a component more is the saving of energy in a sensor node. To maximize the lifetime of the battery, the power consumption of sensor node components should reduce. Hence, the power management problem minimizes switching power or the power consumption of components. Switching power is defined as the power required for the component to change over from low power mode to high power mode and vice versa. The stochastic modelling is used for studying DPM in a wireless sensor network for power management [6,7]. Emphasis on the system model for power management shows the basic requirements for sensor node components and demands for power management.
The rest of this paper is organized as follows. Next section illustrates the abstract system model for dynamic power management and the system component requirements are identified. The section 3 classifies the major policies such as greedy schemes, timeout schemes, predictive schemes, stochastic schemes, dynamic scaling schemes, switching and scheduling schemes with their pros and cons. A brief discussion on other state of the art on discrete time and continuous time techniques is also presented. In section 4, the power consumption issues in continuous time Markov model and semi Markov model have been analyzed in detailed case studies 1 & 2 respectively. It also provides some background about existing stochastic models for dynamic power management as described in the literature, aiming at their stiff and weak points in wireless sensor network applications [8]. Apart from this, it highlights the important key areas, challenges and lacuna in managing the power dynamically using power aware stochastic modelling techniques, which gives future direction for research in the WSN area. Finally, section 5 concludes the entire paper and states about the Author’s future interest and investigation.
Basic power management system model
The switching between different power modes increases latency and degrades performance, which results the power and latency tradeoffs. The authors presented the basic idea behind dynamic power management and the resulting power and performance tradeoff space in wireless sensor network.
Ideally, a power manageable component with more than two power down states and its switching to deep sleep state can reduce more power consumption. Moreover, switching from power down to power up states and vice versa, require finite transition time and overhead of storing processor state before turning the device into low power mode or off. Deeper sleep state requires larger waking up time and which in turn increases the latency. Hence, there is a great need of an optimized DPM scheme that can reduce power consumption with performance constraints and gain performance with power constraints for power source limited applications in wireless sensor networks.
Dynamic power management
Static approach has a priori knowledge of different power manageable component states and stationary workload. Adaptive approach accounts for nonstationary nature of the workloads and uses policy precharacterization, parameter learning and policy interpolation in taking the determination for power down states of parts [19]. Adaptive Markov Control Process for nonstationary workloads are online adaptation DPM schemes for nonstationary workloads or reallife systems [20].
In discrete time Markov decision policy (DTMDP), the power manager takes the decision for next state at discrete time intervals regardless of the input nature. A discrete time, finite state Markov decision model for powermanaged systems are proposed for giving the exact solution using linear optimization problem in polynomial time [21]. This discrete time Markov model takes decision for the next state at every defined discrete interval of time. Therefore, it is not suitable for continuous monitoring or event driven processes. In discrete finite horizon Markov decision process (MDP), the sensor’s battery discharge process as an MDP is modelled stochastically and characterized the optimal transmission strategy [22]. The scheme can be generalized for the decentralized case with the stochastic game theory technique. Generally, network lifetime analysis models in the literature assume average node power consumption. A discrete time Markov model for a node with a Bernoulli distribution of arrival process and phasetype distribution of service time has been validated for single and multihop network [23]. Observations tell that, these schemes have limitations in terms of architectural modification.
A continuous time Markov decision policy (CTMDP) is event driven and the decision taken can change only at event occurrence. A wrong decision can increase energy overhead than energy saving. The continuous time Markov models [11] need all the stochastic processes as exponential processes. These models overcome the problems in discrete time methods. Continuous time modelling is complex and does not give good results for real time systems. Therefore, semiMarkov model reduces the need of strict exponential distribution. Time indexed semi Markov Decision Process (TISMDP) combines the advantages of event driven Semi Markov Decision process model with discrete time Markov decision process (DTMDP) model, but limited to nonexponential arrival distribution coupled with nonuniform transition distribution [24]. The multiple nonexponential processes require a more flexible model and the Timeindexed semiMarkov models can be one of its solution. A model with multiple nonexponential processes increases the model as well as system complexity. Nevertheless, the nonstationary nature of work loads can save more power because of its adaptive nature scheme [9]. The Npolicy gives accumulation of N events and then processing to make the system more energy efficient.
Other techniques such as dynamic scaling [13], decreases the power consumption of the system components by operating them at different low voltage and frequency levels during active phase. The switching and scheduling schemes help in power saving by controlling idle periods of the system [25]. The sleep state policy also improves energy efficiency to the greatest extent [26]. The anticipated workload of the different subsystems and the estimation of the task arrival rate at the scheduler are crucial preconditions for a DPM technique. Various cases of filters as estimation techniques are investigated [27,28]. These filters are predicting based which trace the past N number of tasks at scheduler and define the work load of the microcontroller for the next observation point. In a more precise estimation process, the workload of every hardware component is first observed and then the future load on the sensor node can be determined. This is particularly useful for selective switching. The scheduler can give the appropriate workload information regarding input events and event counter counts frequency and timeperiod of hardware employed by each task [29]. A stochastic sleep scheduling (SSS) with and without adaptive listening scheme is proposed and proved better in terms of energy consumption and delay reduction at the network level for SMAC. This scheme is applicable for high node scalability and stochastic sensor sleep period [30]. The energy efficiency can be improved in the routing layer to enhance the network lifetime. Several energy efficient routing algorithms for wireless sensor network are discussed which assume arrival of the input as a stochastic process [31]. The authors have shown improvement in wireless sensor network lifetime introducing dynamic power management policy in broadband routing [32], target tracking [33] and other applications [3437]. It is remarked that instead of energy efficiency improvement in routing protocols, power management can also improve energy efficiency. An OSdirected, event based, predictive power management technique [38] is proposed for single node energy efficiency improvement. PowerTOSSIM [39], mTOSSIM [40] and eSENSE [41] are easily available platform for sensor node life estimation.
Stochastic optimal control approach
Stochastic schemes are based on Markov decision policies which a power manager uses to direct the power manageable devices about the state change. Established in the memoryless property of Markov decision policy, power manager considers only present state of the devices for taking next state decisions. Here, the term “State” is the power mode of the device. The main function of stochastic approaches is the development and analysis of a system model to direct the system components for suitable operating mode to achieve the maximum power savings. The wireless sensor nodes observe the presence of the random interarrival of events on their input. Therefore, the input pattern follows any one of the exponential distribution, Pareto distribution, uniform distribution, normal distribution, Bernoulli distribution and Poisson distributions for modelling [42]. A paper on controllable Markov decision model provides heuristic and stochastic policies with linear programming optimization [43]. This work gives the importance to workload statistics for two, three and four state system model. It establishes that the delay in attending an event decreases with increase in timeout duration but the power consumption increases.
The advanced Partially Observable Markov Decision Process (POMDP) enabled the Hidden Markov model and event arrival distribution by causing modifications in the likelihood of the observed input sequence and optimizing it [44]. The paper focused on the Hidden Markov model (HMM) modelling of the service requester and the rest of the system (including service provider and service queue) is modelled in DTMDP. The authors compared the achieved results for HMM with other models and found 65.4% higher than earlier. In accumulation and fire (A&F) policy based model, the power manager can be entirely shut down when the service provider (SP) is activated. However, the A&F policy does not involve updating tasks [45,46]. This reduces average power dissipation. The PM latency is extremely small. A finite state Markov model for the server that minimizes the workload demand during energy minimization at the cost of reliability in hosting clusters is presented [47]. Thus, the hierarchical approaches are required to scale down the large systems consisting of a number of servers.
It is found through literature review that the power manager (PM) is the component which dissipates negligible power. Therefore, there is a need of policy that can consider power consumption of power manager along with the other component power on the system. Markov model based policies are not proven globally optimum for stationary Markovian workload. The accuracy of Markov models for nonstationary workload increases by incorporating a number of power states in the Markov chain. Different techniques of dynamic power management have their different implementation approach depending on the application requirement. The power consumption depends on the workload pattern and the states of the different components on the sensor node. The nongeometric transition times of the states and their complex cost functions can also be improved adding more states into a Markov chain of power managed system. However, this can increase the complexity of the system. Finally, constrained by the coarsegrain power management policy, one can search for a refined policy for the states inside each sensor node component dynamically.
Case study 1

Inactive mode power consumption0 W

Inactive mode startup energy4.75 J

Transition time from inactive to active5 Sec

Active mode power consumption1.9 W

Active mode startup energy0 W

Transition time from active to inactive0 W

Accumulation limit (k) 4

Task execution rate (greedy policy) 100,1000

Task execution rate (A&F policy) 100
Case Study 2

Event arrival rate range:150.000/hr.  12960000.000/hr.

Average number of jobs per event:1.666667e + 000/event

Event duration:1 Sec

Duty cycle range:0.010  0.900

Duty period:5 Sec
Power consumption and lifetime between Mica2 and Telos motes
ᅟ  Mica2 mote  Telos mote 

Power states  Power consumption (mW)  
S_{0} (sleep)  8.309  0.007 
S_{1} (processing)  68.00  15.927 
S_{2} (communication)  93.50  50.926 
S_{3} (idle)  17.60  0.104 
S_{4} (listening)  53.00  40.705 
Detection probability  Lifetime (days)  ᅟ 
Detection probability = 1  0.837  14.986 
Detection probability = 0.210  2.124  107.130 
Comparison of power breakdown for mica2 and Telos motes
Power Breakdown (mW)  

Mica2 mote  Telos mote  
Duty cycle=  Duty cycle=  Duty cycle=  Duty cycle=  Duty cycle=  Duty cycle=  
0. 01  0. 455  0. 9  0. 01  0. 455  0. 9  
Active state  0.472  1.597  3.312  0.111  0.374  0.776 
Sleep state  8.164  4.871  1.104  0.007  0.004  0.001 
Idle state  0.157  6.773  14.204  0.001  0.040  0.084 
Transmission state  0.145  0.491  1.018  0.079  0.267  0.554 
Reception state  0.004  0.013  0.027  0.003  0.010  0.021 
Modeling requirement for stochastic processes
Process name  Application  Event arrival distribution  Service time distribution  Transition time distribution  Processor  Model states 

DTMDP [21]  Laptop, desktop computer  Exponential  Geometric  Bellshaped  ARM SA1100  Two 
DTMDP [50]  Security, health care    Geometric    ATmega12  Four 
DTMDP [51]  Tracking        MSP430  Eight 
CTMDP [43]    Exponential, Pareto, uniform, normal  Exponential, uniform  Exponential    Four 
CTMDP [11]  Portable devices  Poisson  Exponential  Exponential    Three 
CTMDP [52]    Gaussian  Exponential  Gaussian    Three 
Portable systems  Exponential  Erlang  Poisson    Four  
DTMDP, CTMDP [53]    Deterministic, exponential, Erlang, uniform, Pareto  Uniform  Exponential    Five 
SMDP [54]  Camera node platform  Poisson  Arbitrary  Arbitrary  MSP430 and MS360LP  Five 
TISMDP [55]  Telnet, web browser  Exponential, Pareto  Exponential  Nonexponential, uniform    Three 
TISMDP [24]  Laptop, smart Badge  Pareto  Exponential  Uniform    Three 
Observations and challenges

The continuous time (event driven) model does not need synchronization pulse at each interval of time, as in case of discrete time system model.

The mission critical applications require the immediate service (high priority) queue and regular service (lower priority) queue.

Stochastic modelling outperforms over other dynamic power management techniques, but the solution of modelling becomes complex with the increase in the number of parameters used.

Pareto distribution is more suited for modelling event arrival when idle periods are long [10].

A stochastic modelling for dynamic power management along with dynamic voltage and frequency scaling will be the effective way of power consumption reduction in wireless sensor networks.

Consider the parameters such as delay in servicing an event, the number of waiting tasks, clock frequency, power manager delay, state transition time, detection probability and task execution deadline etc. as performance measure parameters.

Stochastic modelling for nonstationary service request needs improvement and directs toward future research area.

The knowledge gained from literature review is useful in the development of dynamic power management technique/algorithm for power hungry applications, e.g. continuous monitoring and detection of critical and emergency applications.

The cost of power manager needs to be evaluated for actual power consumption measurement in complete system.

The components other than processor should be working on scale down the voltage and frequency for achieving the more flexibility in modeling.
Conclusion
After in depth survey of power management techniques during the last two decades, this paper gives a brief review of papers which can be helpful in making decision for power management policy selection for wireless sensor network. The stochastic schemes as the Markov decision model helps in reducing the power consumption in wireless sensor network and thus, increases the sensor node life. The implementation and execution of dynamic power management policies are possible at operating system/software level. Thus, the energy efficiency of a sensor node can increase without requiring any specific power management hardware. This paper provides a brief study of Markov models. The work on specific stochastic modelling techniques for power and performance tradeoffs in wireless sensor network will be investigated and upgraded in our future report. The need of power management tends towards a quest to design simpler, energy efficient, optimized and flexible modelling techniques which itself are less power consuming and need less memory to fulfil the requirement of wireless sensor network environment.
Notes
Declarations
Acknowledgement
The author’s would like to thank Gautam Buddha University for providing workplace, support and resources.
Authors’ Affiliations
References
 Valera M, Velastin SA (2005) Intelligent distributed surveillance systems: a review. In: IEE Proceedings of Vision, Image, and Signal Processing, Institution of Engineering and Technology (IET). 152(2):192–204, doi:10.1049/ipvis:20041147Google Scholar
 Wang Z, Li H, Shen X, Sun X, Wang Z (2008) Tracking and Predicting Moving Targets in Hierarchical Sensor Networks. In: IEEE International Conference on Networking, Sensing and Control. Sanya, IEEE, 11691173. Available: http://dx.doi.org/10.1109/icnsc.2008.4525393
 Li X, Shu W, Li M, Huang HY, Luo PE, Wu MY (2009) Performance evaluation of vehiclebased mobile sensor networks for traffic monitoring. IEEE Trans Vehicle Tech 58:1647–1653View ArticleGoogle Scholar
 Song AJ, Lv JT (2014) Remote Medical Monitoring Based on Wireless Sensor Network. Applied Mechanics and Materials. Trans Tech Publ 556–562:3327–30Google Scholar
 Otis B, Rabaey J (2007) Wireless Sensor Networks. UltraLow Power Wireless Technologies for Sensor Networks. Springer, US, 10.1007/9780387493138_1Google Scholar
 Chandrakasan A, Sinha A (2004) Dynamic Power Management in Sensor Networks. Handbook of Sensor Networks. CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 28 Jul 2004. doi:10.1201/9780203489635.sec7Google Scholar
 Fallahi A, Hossain E (2007) QoS provisioning in wireless video sensor networks: a dynamic power management framework. IEEE Wirel Commun 14(6):40–9View ArticleGoogle Scholar
 PowerAware Wireless Sensor Networks (2003) Wireless Sensor Network Designs. John Wiley & Sons, Ltd, pp 63–100. doi:10.1002/0470867388.ch3Google Scholar
 Simunic T, Benini L, De Micheli G (2001) Energyefficient design of batterypowered embedded systems. IEEE Transactions on Very Large Scale Integration (VLSI) Systems 9(1):15–28View ArticleGoogle Scholar
 Wang X (2007) Dynamic power optimization with target prediction for measurement in wireless sensor networks. Chinese J Mechanical Engineer 43(08):26View ArticleGoogle Scholar
 Qiu Q, Pedram M (1999) Dynamic power management based on continuoustime Markov decision processes. In: Proceedings of the 36th ACM/IEEE conference on Design automation conference–DAC, ACM Press, New Orleans, Louisiana, United StatesGoogle Scholar
 Ren Z, Krogh BH, Marculescu R (2005) Hierarchical Adaptive Dynamic Power Management. IEEE Trans Comput 54(4):409–20View ArticleGoogle Scholar
 Simunic T, Benini L, Acquaviva A, Glynn P, De Micheli G (2001) Dynamic voltage scaling and power management for portable systems. In: Proceedings of the 38th annual Design Automation Conference. ACM, New York, NY, USA, pp 524–529Google Scholar
 Estrin D, Heidemann J, Xu Y (2001) Geographyinformed energy conservation for Adhoc routing. In: Proceedings of the ACM/IEEE International Conference on Mobile Computing and Networking, ACM, New York, USA, pp 70–84, Jul 2001Google Scholar
 Zamora NH, Kao JC, Marculescu R (2007) Distributed PowerManagement Techniques for Wireless Network Video Systems. In: Design, Automation & Test in Europe Conference & Exhibition, Apr 2007. Nice Acropolis, France, IEEE. Available from: http://dx.doi.org/10.1109/date.2007.364653
 Srivastava MB, Chandrakasan AP, Brodersen RW (1996) Predictive system shutdown and other architectural techniques for energy efficient programmable computation. IEEE Transactions on Very Large Scale Integration (VLSI) Systems 4:42–55View ArticleGoogle Scholar
 Hwang CH, Wu ACH (1997) A predictive system shutdown method for energy saving of eventdriven computation. In: Proceedings of IEEE/ACM international conference on Computeraided design, Digest of Technical Papers (ICCAD ‘97). IEEE Computer Society Press, Washington, Brussels, Tokyo, pp 28–32, Nov 1997View ArticleGoogle Scholar
 Shen Y, Li X (2008) Wavelet Neural Network Approach for Dynamic Power Management in Wireless Sensor Networks. In: International Conference on Embedded Software and Systems. 2931 Jul 2008, Sichuan, IEEE, 376381. doi:10.1109/icess.2008.36Google Scholar
 Wu K, Liu Y, Zhang H, Qian D (2010) Adaptive power management with finegrained delay constraints. In: 3rd International Conference on Computer Science and Information Technology 911 Jul 2010, Chengdu, IEEE, 2:633637. doi:10.1109/iccsit.2010.5565140Google Scholar
 Chung EY, Benini L, Bogliolo A, Lu YH, Micheli GD (2002) Dynamic power management for nonstationary service requests. IEEE Trans Comput 51(11):1345–1361View ArticleMathSciNetGoogle Scholar
 Benini L, Bogliolo A, Paleologo GA, Micheli GD (1999) Policy optimization for dynamic power management. IEEE Transactions ComputerAided Design Integrated Circuits and Systems 18(6):813–833View ArticleGoogle Scholar
 Kobbane A, Koulali MA, Tembine H, Koutbi ME, Benothman J (2012) Dynamic power control with energy constraint for multimedia wireless sensor networks, IEEE ICC 2012  Adhoc and Sensor networking Symposium. 518522, 1015 Jun 2012, Ottawa, Canada, IEEE, doi:10.1109/ICC.2012.6363971Google Scholar
 Wang Y, Vuran MC, Goddard S (2010) Stochastic Analysis of Energy Consumption in Wireless Sensor Networks. In: Proceedings of 7th Annual IEEE Communications Society Conference on Sensor Mesh and Ad Hoc Communications and Networks (SECON), pp 1–9 Boston, MA, 2125 Jun 2010, IEEE, doi:10.1109/SECON.2010.5508259Google Scholar
 Simunic T, Benini L, Glynn P, Micheli GD (2000) Dynamic power management for portable systems. In: Proceedings of 6th International Conference on Mobile Computing and Networking, pp 1119, Boston, MA, ACM, 1 Aug 2000.Google Scholar
 Mei J, Li K, Hu J, Yin S, ᅟ HM, Sha E (2013) Energyaware preemptive scheduling algorithm for sporadic tasks on DVS platform. Microprocessors and Microsystems. Elsevier BV 37(1):99–112Google Scholar
 Lin C, He Y, Xiong N (2006) An EnergyEfficient Dynamic Power Management in Wireless Sensor Networks. In: Fifth International Symposium on Parallel and Distributed Computing, Jul 2006. pp. 148–154, Timisoara, Romania, IEEE doi:10.1109/ispdc.2006.8Google Scholar
 Sinha A, Chandrakasan A (2001) Dynamic power management in wireless sensor networks. IEEE Des Test 18(2):62–74View ArticleGoogle Scholar
 Zhang D, Miao Z, Wang X (2013) Saturated Power Control Scheme for Kalman Filtering via Wireless Sensor Networks. WSN Scie Res Publ Inc 05(10):203–207Google Scholar
 Isci C, Martonosi M (2003) Runtime power monitoring in highend processors: Methodology and empirical data. In: Proceedings of the 36th annual IEEE/ACM International Symposium on Microarchitecture MICRO 36. IEEE Computer Society Pub, Washington, DC, USA, p 93Google Scholar
 Zhao Y, Wu J (2010) Stochastic sleep scheduling for large scale wireless sensor networks. In: IEEE International Conference on Communications, ICC 2010, Cape Town, 23–27 May 2010, pp 15, IEEE, doi:10.1109/ICC.2010.5502306Google Scholar
 Haq U, Riaz, Norrozila, Sulaiman, Muhammad, Alam (2013) A Survey of Stochastic processes in Wireless Sensor Network: a Power Management Prospective In: Proceedings of 3rd International Conference on Software Engineering & Computer Systems (ICSECS  2013), Universiti Malaysia Pahang, Available from: http://umpir.ump.edu.my/5011/
 Sausen PS, Spohn MA, Perkusich A (2008) Broadcast routing in Wireless Sensor Networks with Dynamic Power Management. IEEE Symposium on Computers and Communications, 69 July 2008, pp 10901095, Marrakech, IEEE doi:10.1109/iscc.2008.4625620Google Scholar
 Li GJ, Zhou XN, Li J, Zhu JH (2013) Distributed Targets Tracking with Dynamic Power Optimization for Wireless Sensor Networks. Sensors Letter. Am Sci Publ 11(5):907–910Google Scholar
 Passos RM, Coelho CJN, Loureiro AAF, Mini RAF (2005) Dynamic Power Management in Wireless Sensor Networks: An ApplicationDriven Approach. Second Annual Conference on Wireless Ondemand Network Systems and Services. pp 109118, 1921 Jan 2005, IEEE doi:10.1109/wons.2005.13Google Scholar
 Halawani Y, Mohammad B, AlQutayri M, Saleh H (2013) Efficient power management in wireless sensor networks. IEEE 20th International Conference on Electronics, Circuits, and Systems (ICECS), Dec 2013. 811 Dec. 2013, pp 7273, Abu Dhabi, IEEE, doi:10.1109/icecs.2013.6815350Google Scholar
 Lee DH (2013) Yang WS (2013) The Npolicy of a discrete time Geo/G/1 queue with disasters and its application to wireless sensor networks. Appl Mathematical Modelling Elsevier BV 37(23):9722–9731View ArticleGoogle Scholar
 Zhang Y (2011) An EnergyBased Stochastic Model for Wireless Sensor Networks. WSN Sci Res Publ Inc 03(09):322–328Google Scholar
 Benini L, Bogliolo A, Micheli GD (2000) A survey of design techniques for systemlevel dynamic power management. IEEE Trans Very Large Scale Integr Syst 8(3):299–316View ArticleGoogle Scholar
 Perl E, Catháin AÓ, Carbajo RS, Huggard M, Mc Goldrick C (2008) PowerTOSSIM z. In: Proceedings of the 3rd ACM workshop on Performance monitoring and measurement of heterogeneous wireless and wired networks  PM2HW2N, ACM Press, pp 3542, ACM New York, NY, USA. doi:10.1145/1454630.1454636Google Scholar
 MoraMerchan JM, Larios DF, Barbancho J, Molina FJ, Sevillano JL, León C (2013) mTOSSIM: A simulator that estimates battery lifetime in wireless sensor networks, Simulation Modelling Practice and Theory. Elsevier BV 31:39–51Google Scholar
 Liu H, Chandra A, Srivastava J (2006) eSENSE: energy efficient stochastic sensing framework for wireless sensor platforms. In: 5th International Conference on Information Processing in Sensor Networks. pp 235242, ACM New York, NY, USA, doi:10.1109/ipsn.2006.243752Google Scholar
 Heyman DP (1975) Queueing Systems, Volume 1: Theory by Leonard Kleinrock John Wiley & Sons, Inc. New York WileyBlackwell 6(2):189–190Google Scholar
 Qiu Q, Qu Q, Pedram M (2001) Stochastic modeling of a powermanaged systemconstruction and optimization. IEEE Transactions ComputAided Design Integrated Circuits Syst 20(10):1200–1217View ArticleGoogle Scholar
 Tan Y, Qiu Q (2008) A framework of stochastic power management using hidden Markov model. In: Proceedings of the conference on Design, automation and test in EuropeDATE’08, ACM Press. Date: August 2008 UK Performance Evaluation Workshop. pp 9297, ACM New York, NY, USA, doi:10.1145/1403375.1403402Google Scholar
 Chen Y, Xia F, Shang D, Yakovlev A (2008) Fine grain stochastic modelling and analysis of low power portable devices with dynamic power management. UK Performance Evaluation Workshop (UKPEW) Aug 2008, Imperial College London, DTR0809, pp 226236, http://ukpew.org/2008/papers/dynamicpowermanagement
 Chen Y, Xia F, Shang D, Yakovlev A (2009) Finegrain stochastic modelling of dynamic power management policies and analysis of their power–latency tradeoffs. IET Software. Inst Engineer Technol (IET) 3(6):458–469Google Scholar
 Guenter B, Jain N, Williams C (2011) Managing cost, performance, and reliability tradeoffs for energyaware server provisioning In: Proceedings of IEEE INFOCOM. 1015 Apr 2011, pp 3321340, Shanghai, IEEE. doi:10.1109/infcom.2011.5934917Google Scholar
 Ihler A, Hutchins J, Smyth P (2006) Adaptive event detection with timevarying Poisson processes. In: Proceedings of the 12th ACM SIGKDD International conference on knowledge discovery and data mining, ACM New York, NY, USA, pp 207–216Google Scholar
 Jung D, Teixeira T, Savvides A (2009) Sensor node lifetime analysis. TOSN. Assoc Comput Machinery (ACM) 5(1):1–33. doi:10.1145/1464420.1464423Google Scholar
 Munir A, GordonRoss A (2012) An MDPBased Dynamic Optimization Methodology for Wireless Sensor Networks. IEEE Transac Parallel Distributed Systems 23(4):616–625View ArticleGoogle Scholar
 Kang H, Li X, Moran PJ (2007) PowerAware Markov Chain Based Tracking Approach for Wireless Sensor Networks. In: Proceedings of the IEEE Wireless Communications and Networking Conference. Hong Kong, 11–15 Mar 2007, pp 4209–4214. doi:10.1109/wcnc.2007.769Google Scholar
 Xu D, Wang K (2014) Stochastic Modeling and Analysis with Energy Optimization for Wireless Sensor Networks. International Journal of Distributed Sensor Networks. Hindawi Publishing Corporation 2014:1–5Google Scholar
 Norman G, Parker D, Kwiatkowska M, Shukla S, Gupta R (2005) Using probabilistic model checking for dynamic power management. Springer Sci Business Media 17(2):160–176. doi:10.1007/s0016500500620MATHGoogle Scholar
 Jung D, Teixeira T, BartonSweeney A, Savvides A (2007) ModelBased Design Exploration of Wireless Sensor Node Lifetimes. In: Proceedings of the European Conference on Wireless Sensor Networks (EWSN), SpringerVerlag, Berlin Heidelberg, Aug 2006. pp 277–292. doi:10.1007/9783540698302_18Google Scholar
 Simunic T, Benini L, Glynn P, De Micheli G (2001) Eventdriven power management. IEEE Transactions ComputAided Design Integrated Circ Systems 20(7):840–857View ArticleGoogle Scholar
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