17 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 Β© Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ Effect of Switching Energy in Different Low Power Modes in Duty Cycling Sensor Network Bilge Kartal Γ‡etin* Ege University Email: bilge.kartal@ege.edu.tr Abstract Duty cycling is one of the most efficient power saving mechanisms to prolong sensor network lifetime. In the existing duty cycling networks, low latency and high network connectivity are achieved by shortening the duty cycling parameter that means increasing the frequency of switching between sleep-awake states. However, switching energy is generally not considered in energy efficiency analyses of sensor network. In this paper, the energy cost for switching and different sleeping modes are investigated for sensor network lifetime. To this end, we present a linear programming (LP) formulation which allow to analyze the energy consumption of the sensor network while guarantying the optimum load distribution for maximum lifetime. Proposed mathematical programming model can be applied any synchronized duty cycling mechanism with a fixed duty cycling periods. Analytical results reveal that the switching energy is not negligible effect on network lifetime. Keywords: Duty cycling; sensor network; network lifetime; switching energy. 1. Introduction Duty cycling is one of the most important way of saving energy in wireless sensor networks (WSNs). Currently, none of the existing duty-cycling medium access control (MAC) schemes [1,2,3,7,8] investigated the effect of specific value of duty-cycling parameter and switching frequency. Instead they focused on minimizing latency and data loss due to sleeping nodes. However, low latency and low data loss is generally achieved by increasing the switching frequency by lowering duty cycling parameter [8]. ------------------------------------------------------------------------ * Corresponding author. http://asrjetsjournal.org/ American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 36, No 1, pp 17-23 18 In this paper, the effect of switching energy consumption on network lifetime are investigated for different duty cycling parameters. Authors in [4] studied the switching energy for assessment of MAC protocols in a simulation environment with 3 node network scenario. Then, they introduced an adaptive radio low power sleep modes based on current traffic condition for selecting optimal MAC protocol by using an energy model that considers the switching energy in [6]. However, both of the studies are independent from the routing and network lifetime. In this study, we investigate the duty cycling for a more complicated network scenario where packet routing exists with the aim of maximum network lifetime. To this end, we developed a linear programming (LP) model for the problem of routing the packets for the maximum network lifetime in a duty cycling sensor network. Then, we use the model to analysis of the network lifetime for different low power modes and investigate the effect of switching energy on the network lifetime. 2. Mathematical Model Each node 𝑛𝑛 in the sensor network has an initial energy 𝐸𝐸𝑛𝑛𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (joule) and they generate data with a predefined rate 𝑔𝑔𝑛𝑛 (packet/second). The problem is to determine the optimum total amount of flow (fL) on each link 𝐿𝐿 and to find the total switching number of each node in the allocated load for the maximum lifetime. The network lifetime 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 is defined as the time span in which all nodes of the network are alive, i.e., all individual node lifetimes, 𝑇𝑇𝑛𝑛 , are at least equal to 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 or greater than 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 . Sensor network is modeled as a directed graph 𝐺𝐺(𝑁𝑁, 𝐿𝐿�) where 𝑁𝑁 is the set of all nodes, and 𝐿𝐿� is the set of the links between them. If two nodes 𝑖𝑖 and 𝑗𝑗 are connected by a link, they can communicate with each other. Let variables fL On and fL In are the total amount of flow (fl) during the network lifetime on the outgoing (On) and incoming (In) links of a node 𝑛𝑛, respectively, and depicted as fL On = βˆ‘ fll∈On , fL In = βˆ‘ fll∈In 𝑛𝑛 ∈ 𝑁𝑁,𝐿𝐿 ∈ 𝐿𝐿� (1) Lifetime 𝑇𝑇𝑛𝑛 of the individual node 𝑛𝑛 is formulated as being the sum of the time spent in transmission, reception, idle listening, sleeping, channel access, and switching and shown as follow; 𝑇𝑇𝑛𝑛 = fL On . ttx + fL On . tcca + fL In . π‘‘π‘‘π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ + fL In . tcca + 𝑑𝑑𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠𝑛𝑛 + 𝑑𝑑𝑖𝑖𝑖𝑖𝑠𝑠𝑛𝑛𝑛𝑛 +kn. tswc (2) 𝑇𝑇𝑛𝑛 β‰₯ 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 (3) where ttx and π‘‘π‘‘π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ are constants and represent the transmission time and the reception time of a data packet, respectively, tcaa is a constant and represents the time for clear channel assessment mechanism in the IEEE 802.15.4 technical standard. In the Equation 2, 𝑑𝑑𝑖𝑖𝑖𝑖𝑠𝑠𝑛𝑛𝑛𝑛 and 𝑑𝑑𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠𝑛𝑛 are variables that represent the total idle and sleep time of the node during its lifetime, respectively. Note that the variable 𝑑𝑑𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠𝑛𝑛 represents the total sleep time of the node n while the rest of the terms in the right hand side of the Equation 2 represents the total active time of the node n during its lifetime. The objective function of the optimization model is defined as the network lifetime, 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 , and all individual American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 36, No 1, pp 17-23 19 lifetimes has to be longer or equal to the network lifetime (Equation 3). Equation 4 represents the conservation of the data during the lifetime of the network (i.e total flow out of a node is equal to the sum of the total generated data at the node and the total flow into the node. fL On = 𝑔𝑔𝑛𝑛 .𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 + fL In 𝑛𝑛 ∈ 𝑁𝑁 . (4) The total energy consumption of a node throughout the network lifetime is the sum of the energy consumption in each operation mode and cannot exceed its initial energy. It is formulated with the help of the flow variables and unit energy consumptions as follow; etx. fL On . ttx + etx. fL On . tcca + erx . fL In . π‘‘π‘‘π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ + erx. fL In . tcca + 𝑒𝑒𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠 . 𝑑𝑑𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠𝑛𝑛 + 𝑒𝑒𝑖𝑖𝑖𝑖𝑠𝑠𝑛𝑛 . 𝑑𝑑𝑖𝑖𝑖𝑖𝑠𝑠𝑛𝑛𝑛𝑛 + kn. 𝑒𝑒𝑠𝑠𝑠𝑠𝑠𝑠 ≀ 𝐸𝐸𝑛𝑛𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (5) where etx, erx , 𝑒𝑒𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠, 𝑒𝑒𝑖𝑖𝑖𝑖𝑠𝑠𝑛𝑛 (joule/second) are constants and represent the energy consumed per unit time when radio is in transmission, reception, sleeping, and idle mode, respectively. The constant parameter 𝑒𝑒𝑠𝑠𝑠𝑠𝑠𝑠 (joule) is energy consumption for switching and its value depends on the preference of low power mode.The model can represent any synchronized duty cycling mechanism with a fixed duty cycling periods such as SMAC [1]. Individual lifetime for a node 𝑛𝑛 consist of π‘˜π‘˜π‘›π‘› number of constant duty cycling period 𝑑𝑑𝑠𝑠𝑐𝑐𝑠𝑠𝑠𝑠𝑛𝑛as shown in Fig. 1. The relationships between active time and sleep time are determined by a constant duty-cycling parameter 𝑑𝑑𝑑𝑑, and depicted as 𝑇𝑇𝑛𝑛 βˆ’ 𝑑𝑑𝑑𝑑.𝑇𝑇𝑛𝑛 = 𝑑𝑑𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠𝑛𝑛 (5) 𝑇𝑇𝑛𝑛 = π‘˜π‘˜π‘›π‘›. 𝑑𝑑𝑠𝑠𝑐𝑐𝑠𝑠𝑠𝑠𝑛𝑛 (6) Figure 1: Duty cycling mechanishm for a node in the sensor network The problem of maximizing the network lifetime, given the data generation rate 𝑔𝑔𝑛𝑛, is formulated as a linear programming problem as follows max 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 subject to 𝑇𝑇𝑛𝑛 = fL On . ttx + fL On . tcca + fL In . π‘‘π‘‘π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ + fL In . tcca + 𝑑𝑑𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠𝑛𝑛 + 𝑑𝑑𝑖𝑖𝑖𝑖𝑠𝑠𝑛𝑛𝑛𝑛 +kn. tswc American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 36, No 1, pp 17-23 20 𝑇𝑇𝑛𝑛 β‰₯ 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 fL On = 𝑔𝑔𝑛𝑛 .𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 + fL In 𝑛𝑛 ∈ 𝑁𝑁 . etx. fL On . ttx + etx. fL On . tcca + erx . fL In . π‘‘π‘‘π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ + erx. fL In . tcca + 𝑒𝑒𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠 . 𝑑𝑑𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠𝑛𝑛 + 𝑒𝑒𝑖𝑖𝑖𝑖𝑠𝑠𝑛𝑛 . 𝑑𝑑𝑖𝑖𝑖𝑖𝑠𝑠𝑛𝑛𝑛𝑛 + kn. 𝑒𝑒𝑠𝑠𝑠𝑠𝑠𝑠 ≀ 𝐸𝐸𝑛𝑛𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑇𝑇𝑛𝑛 βˆ’ 𝑑𝑑𝑑𝑑.𝑇𝑇𝑛𝑛 = 𝑑𝑑𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑠𝑠𝑛𝑛 𝑇𝑇𝑛𝑛 = π‘˜π‘˜π‘›π‘›. 𝑑𝑑𝑠𝑠𝑐𝑐𝑠𝑠𝑠𝑠𝑛𝑛 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 ,𝑇𝑇𝑛𝑛, fL On , fL In , kn β‰₯ 0 3. Numerical Study In this section, the switching energy and effect of sleeping modes on the network lifetime is investigated in an example network. The most of radios for sensor network support multiple low power modes for sleeping. For example, CC2420 radio has three low power modes (LPM). LPM1 saves energy by turning off the radio frequency synthesizer which control the channel selection and up/down RF conversion. In addition to the frequency synthesizer, LPM2 also turns off the crystal oscillator which provides the timing reference for the entire radio chip. LPM3 is power off mode and turning off the voltage regulator which powers the radio chip. Transition to active mode from LPM1 is the fastest but the most energy expensive while transition from LPM3 is less energy expensive but has longest delay. Therefore preference of the low power mode is important as much as choosing the optimum duty cycling parameter. We explore the effect of switching energy on network lifetime for different low power modes in a network which consist of 10 nodes located in a 50m-by-50m area in a random manner. Transmission range is chosen as 35 m. The sink node lies at the one corner of the area. All nodes have 1.8V AA batteries with 2200 mAh current capacity. They have CC2420 radio and data transmission rate is 250kbps. Packet size is 100 bytes (π‘‘π‘‘π‘›π‘›π‘Ÿπ‘Ÿ and π‘‘π‘‘π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿare 3.2ms).Each node has the same packet generation rate (sense every 3s). The time for clear channel assessment mechanism is taken as 0.128 ms for default 4 bytes preamble length at 250 kbps. Table 1 shows the energy consumption characteristics and switching time for the CC2420 radio [5]. Table 1: CC2420 Energy and Switching Characteristics. Mode of operation Power Switching Time Switching Energy Tx@0 dBm etx=31.32 mW Rx erx=33.84 mW Idle Listening 𝑒𝑒𝑖𝑖𝑖𝑖𝑠𝑠𝑛𝑛 =33.84 mW LPM 1 𝑒𝑒𝐿𝐿𝐿𝐿𝐿𝐿1 =0.7668mW 0.03 ms 1.035 Β΅J LPM 2 𝑒𝑒𝐿𝐿𝐿𝐿𝐿𝐿2 =0.036 mW 1.2 ms 42.3 Β΅J LPM 3 (max) 𝑒𝑒𝐿𝐿𝐿𝐿𝐿𝐿3 =1.8 Β΅ W 2.4 ms 85.7 Β΅J American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 36, No 1, pp 17-23 21 In Figure 2, network lifetime difference in percentage is shown for different sleeping modes preferences. Figure 3 shows the difference in percentage when LPM3 is chosen instead of LPM2 and it is seen that the difference on network lifetime has maximum value of 11% at 1% duty cycle and minimum value of 1% at 10% duty cycle. Figure3 shows the difference when LPM2 (max 200%-min20%) or LPM3 (max 230% -min 22%) is chosen instead of LPM1. For instance, for %10 duty cycling, choosing LMP2 or LPM3 instead of LPM1 results in 20% increase on network lifetime. It has been observed that the effect of sleep mode preference on network life is reduced by high duty cycles due to short sleeping durations Figure 2: Difference of network lifetime between preferences of two low power modes LPM2 and LPM3 In Figure 3, the graph shows the percentage decrease on network lifetime when switching energy is considered for three sleeping modes. In the Figure 3., it is seen that the switching energy consumption of LPM1 does not affect the network lifetime. It takes maximum value of 0.009%. However, in LPM3 mode the switching energy causes higher decrease on network lifetime compared to LMP2. Figure 3: Difference of network lifetime preference of LPM1 or other two modes. 1 2 3 4 5 6 7 8 9 100 2 4 6 8 10 12 Duty Cycling % % R at io % Ratio of Network Lifetime Difference LPM2 and LPM3 1 2 3 4 5 6 7 8 9 100 2 4 6 8 10 12 Duty Cycling % % R at io % Ratio of Network Lifetime Difference LPM2 and LPM3 1 2 3 4 5 6 7 8 9 100 50 100 150 200 250 Duty Cycling % % Ratio of Network Lifetime Difference % R at io LPM1 and LPM2 LPM1 and LPM3 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 36, No 1, pp 17-23 22 Figure 4: Effect of switching energy on network lifetime for different low power modes Figure 5 and Figure 6 show the comparison of switching and sleeping energies at different duty cycles. In the Figure 5, it is showed that for LPM2 the switching energy consumption is less than the sleeping energy and it corresponds to 1% of total energy consumption of the network. In Figure 6, it is seen that for LPM3 compare to the sleeping energy the switching energy consumption accounts for higher percentage of total energy consumption. Figure 5: Ratio of sleeping and switching energy to the total energy consumption when LPM2 is chosen. (Average of ten randomly generated network with 10 nodes.) Figure 6: Ratio of sleeping and switching energy to the total energy consumption when LPM3 is chosen. (Average of ten randomly generated network with 10 nodes.) 1 2 3 4 5 6 7 8 9 100 0.5 1 1.5 2 2.5 3 Duty Cycling % % D ec re as e on N et w or k Li fe tim e % Effect of Switching Energy on Network Lifetime LPM3 LPM2 LPM1 1 2 3 4 5 6 7 8 9 100 2 4 6 8 10 12 Duty Cycling % % o f t he T ot al E ne rg y C on su m pt io n % of the Total Energy Consumption for network with 10 nodes for LPM2 Sleeping Energy Switching Energy 1 2 3 4 5 6 7 8 9 100 0.5 1 1.5 2 2.5 3 Duty Cycling % % o f t he T ot al E ne rg y C on su m pt io n % of the Total Energy Consumption for network with 10 nodes for LPM3 Sleeping Energy Switching Energy American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 36, No 1, pp 17-23 23 4. Conclusion In this paper, the energy cost of switching in duty cycling sensor networks was investigated. Firstly, using a linear programming the optimum total amount of flow was determined for each link to be assigned by a routing algorithm that leads the maximization of the network lifetime. Then, the effect of switching energy and different sleeping modes on network lifetime are evaluated with the proposed LP through a numerical example. As a conclusion, the switching energy has not negligible effect on network lifetime. Therefore neglecting the switching energy in energy consumption analysis misleads the performance assessment of different duty cycling schemes and sleeping modes. References [1] W. Ye, J. Heidemann, and D. Estrin, β€œAn energy-efficient MAC protocol for wireless sensor networks,” in Proc. INFOCOM 2002, pp. 1567-1576, [2] Michael Buettner, Gary V. Yee, Eric Anderson, and Richarh Han. X-mac:A short preamble mac protocol for duty-cycled wireless sensor networks. In proceeding of SenSys, pages 307-320, 2006 [3] Shu Du, A.K. Saha, and D.B. Johnson. Rmac: A routing-enhances duty-cycle mac protocol for wireless sensor networks. In INFOCOM 2007. 26th IEEE international Conference on Computer Communications.pages 1478-1486, may 2007. [4] A.G Ruzzelli, P. Cotan, G.M.P. O’Hare, R.Tynan, Protocol assessment issues in low duty cycle sensor networks: The switching energy, Proceedings of IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing (SUTC 2006). [5] Chipcon CC2420, Texas Instrument, Datasheet, SWRS041C, (rev date 2013-02-20) [6] R. Jurdak, A. G. Ruzzelli, G.M.P.O’Hare, Radio Sleep Mode Optimization in Wireless Sensor Networks, IEEE Trans. On Mobile Computing, Vol.9, No.7, July 2010. [7] C. Fischione, P. Park, S. Coleri Ergen, "Analysis and optimization of duty-cycle in preamble-based random access networks", Wireless Networks, vol. 19, pp. 1691, 2013, ISSN 1022-0038. [8] Nursen Aydin, Mehmet Karaca, Ozgur Ercetin, "Scheduling and Power Control for Energy-Optimality of Low Duty Cycled Sensor Networks", International Journal of Distributed Sensor Networks, vol. 2015, pp. 1, 2015, ISSN 1550-1329.