# An Energy Consumption Analytic Model for A Wireless Sensor MAC Protocol

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3 sleep period during a complete listen-sleep cycle. The sleep time T S and the idle listening time T I during period t can be expressed as: T S = p succ [ λ Ti λ R )t)t data + +[t (,j=1,i =j λ Rij λ T )t)t data ] λ Ti λ R )t)t data +,j=1,i =j λ Rij λ T )t)t data +N T (t RT S + t data + t CS + t BO + t SL +t CTS + t ACK +3t SIFS + t DIFS ) +N R (t RT S + t data + t CTS + t ACK +3t SIFS + t DIFS )) ɛ] ( T sleep ) (6) T I = [t p succ λ Ti λ R )t)t data +,j=1,i =j λ Rij λ T )t)t data ) +N T (t RT S + t data + t CS + t BO + t SL +t CTS + t ACK +3t SIFS + t DIFS ) +N R (t RT S + t data + t CTS + t ACK +3t SIFS + t DIFS )) ɛ] ( T listen )+ɛ (7) The p succ is related to the probability that a transmission is successful and the probability that the node is listening or not. The probability of successful transmission can be obtained as in [8]. In S-MAC, the sleep schedule for a node will be synchronized with all its neighbors, so we can assume that RTS/CTS control packets will be sent by the neighbors of the node only when the node wakes up. The assumption is quite reasonable just as described in []. By applying the probability of successful transmission, and assuming that each of the n stations contending on the same channel with transmission probability τ, we can derive p succ by the following formula: p succ = nτ(1 τ)n 1 1 (1 τ) n (8) The symbol ɛ represents the total extra idle period when a node change its mode back to periodic listen and sleep schedule. Such extra idle period occurs when a node finishes a packet transmitting or receiving. Because the finishing time of transmitting or receiving packet is not always fit to scheduled listen and sleep time, the node must keep idle for such extra idle period until the scheduled listen or sleep time arrives. If the node plays a role as a router in the network, the node just forwards the packets immediately, and the extra idle occurs only when the node finishes forwarding packets. Similar to Fig. 1. Fig.. The chain-hop topology used in validating our analytic model Another topology used in validating our analytic model sleep delay, since the packet transmission may also finish with equal probability within a frame, the extra idle period can be calculated as.letn I be the number of times that the extra idle period occurs, the total extra idle time is: ɛ = N I (9) By deriving the unknowns in (1) using ()(3)(4)(5)(6)(7)(8) (9), we can evaluate the energy consumption of a node in analytic method. V. ANALYTIC RESULT In this section, we will compare the simulation and analytic results to show the accuracy of our proposed model. We also shows how the model can be used to help sensor application design. Finally, we present some observations of S-MAC based on the proposed model. A. Model Validation We validate the analytic model of S-MAC by comparing the analytic results with simulation results. The simulation was done by using ns- network simulator. The MAC layer protocol used is S-MAC with overhearing avoidance and periodic sleep scheme. We also assume that all nodes adopt the same sleep schedule when making our analytic model, and Fig. 3. The energy consumption of node 0 in Fig. 1 evaluated by analytic 4535

4 Fig. 6. A grid topology used in analysis S-MAC based sensor network design Fig. 4. The energy consumption of node in Fig. 1 evaluated by analytic Fig. 7. Relative energy consumption, relative latency, and relative energy*delay of total network with duty cycle varying from 0.1 to duty cycle is the base Fig. 5. The energy consumption of node in Fig. evaluated by analytic the P Tx is 4.75mW, P Rx and P I are 13.5mW, and P S is 15 uw, just as the values used in []. The bandwidth is set to be 40kbps. The messages are generated from the source node to the destination node, and each message is 400 Bytes in size. The parameters described above are also used in the following experiments presented in this section. We set up two experiments to validate our model using topologies shown in Fig. 1 and Fig.. The message interarrival period is varying from 1s to 10s, and the duration is the time that 10 messages have been transmitted to the sink. The duty cycle ( T listen ) is set to 0%. In the topology of Fig. 1, each node i can receive radio only from its immediate neighbor (i 1 and i +1). In the topology of Fig., node 0, 1, 3, and 4 can only receive radio only from node. In the topology of Fig. 1, node 0 and node are selected to compare our analytic and simulation results. Node 0 is the source node, which generates the traffic, and node 0 can hear RTS when node 1 transmitting to node. Node is an intermediate node which can hear RTS when node 3 transmitting to node 4 and CTS when node 0 transmitting to node 1. As shown in Fig. 3 and Fig. 4, the results generated by proposed model are quite approaching to the simulation results. In the topology of Fig., node plays as a router, which receives packets from source node 0 (source 0) and node 1 (source 1) and forwards these packets to node 3 (sink 1) and node 4 (sink 0). Unlike any other nodes in Fig. 1 and Fig., node involves in every transmissions, that is, node sleeps only during scheduled sleep time. The analytic and simulation results of node in Fig. are shown in Fig. 5, and results generated by proposed model are also quite approaching to the simulation results. B. Energy Efficiency of S-MAC In many sensor network applications, energy consumption is not the only important design issue. For example, in the environment surveillance system, the latency for an event transmitted from source to data sink would be very important, so that the system can take appropriate actions as soon as possible. Sometimes, energy and latency would be a tradeoff. To find out the balance between energy and latency, some researchers adopt energy*delay product as the metric to evaluate the design trade-off [7] [13]. Periodic sleep scheme in S-MAC saves energy while nodes are idle, but this scheme also introduces additional delay for waiting the receiver back to listening from sleeping. Duty cycle is the parameter standing for the portion of time a node is listening in a frame. Therefore, duty cycle is the factor that influences the effect of energy saving in idle listening. However, short duty cycle would result in longer sleep delay, 4536

5 more time in sending packets to wait for the receiver back to listening mode, and this wastes energy of sender nodes. The results also points out that while the network traffic is heavy, shorter duty cycle may not always result in better energy saving. Fig. 8. Relative energy consumption of total network of 0 chain-hops. The duty cycle varies from 0.1 to duty cycle is the base because the packets may arrive when receiver is sleeping with a higher probability. That is, choosing a shorter duty cycle would decrease the idle listening time, but increase the latency. With our analytic model, we can estimate the energy consumption under different duty cycles for sensor nodes and evaluate the design trade-offs easily. Fig. 6 shows a portion of an exemplary sensor network topology where node 0 is the data source, and the data are transmitted along the path of node 1, node 4, and node 7 to the destination data sink node 8. The nodes in Fig. 6 can transmit or receive packets to or from the neighbor nodes which connected by hidden lines or arrows in the figure. The packets are generated from data source every 10 seconds, and each message is sized in 400 Bytes. Fig. 7 shows the relative energy consumption, relative latency, and relative energy*delay of total network with duty cycle varying from 0.1 to 1, and 0.1 duty cycle is chosen as the base. As shown in Fig. 7, we can see that the longer the duty cycle is, the more energy consumes since shorter duty cycle saves more energy from idle listening. In contrast, the latency becomes shorter when duty cycle is longer. The best energy*delay balance appears at the point where duty cycle is 0.4. According to formula (1), the energy consumption of S- MAC based sensor nodes can be divided into four parts: sending packets, receiving packets, idle listening, and sleeping. In order to explore the performance of S-MAC under heavy traffic, we also set up and analyze another scenario. The scenario forms like Fig. 1, but the number of hops is increased to 0 hops. Fig. 8 shows the relative total energy consumption of the 0-hop-chain sensor network, and energy consumption of each duty cycle is divided into four parts corresponding to the energy consumption in sending packets, receiving packets, idle listening, and sleeping. Each message is sized in 400 Bytes, and the interarrival period of messages is set to 5 seconds, which the traffic is heavier than 10 seconds in the above cases. The lowest energy consumption holds when duty cycle is 0., not 0.1, which saves the most idle listening energy. Due to much longer sleep delay, the nodes must spend VI. CONCLUSIONS AND FUTURE WORK S-MAC have received considerable attention due to its energy saving schemes designed for sensor network. This paper introduces an analytical model to estimate the energy consumption of S-MAC. Our model shows its accuracy by comparing with NS- simulation results. With the help of our model, sensor network application designers can evaluate the energy efficiency of their S-MAC based sensor network under different parameters, such as duty cycles, interarrival periods, and etc. S-MAC saves energy, but sacrifices latency. To achieve better energy efficiency than S-MAC, the future work includes the improvement of energy consumption and the reduction of packet latency of S-MAC. ACKNOWLEDGMENT This work was supported by the MediaTek Inc. under the project Wireless Communication Systems. REFERENCES [1] M. Stemm and R. H. Katz, Measuring and reducing energy consumption of network interfaces in hand-held devices, IEICE Transactions on Communications, vol. E80-B, no. 8, pp , [] W. Ye, J. Heidemann, and D. Estrin, An energy-efficient MAC protocol for wireless sensor networks, in Proceedings of IEEE INFOCOM, June 00, pp [3] S. Singh and C. Raghavendra, PAMAS: Power aware multi-access protocol with signalling for ad hoc networks, ACM Computer Communication Review, vol. 8, no. 3, pp. 5 6, July [4] C. Schurgers, V. Tsiatsis, S. Ganeriwal, and M. Srivastava, Optimizing sensor networks in the energy-latency-density design space, IEEE Transactions on Mobile Computing, vol. 1, pp , January 00. [5] University of california, berkeley, mica schematics, March 003. [Online]. Available: design/orcad FILES/MICA/ ACLEAN.pdf [6] An adaptive energy efficient MAC protocol for wireless sensor networks, in Proceedings of the First ACM Conference on Embedded Networked Sensor Systems, November 003, pp [7] An adaptive energy-efficient and low-latency MAC for data gathering in sensor networks, in Proceedings of 18th International Parallel and Distributed Processing Symposium, April 004, pp [8] G. Bianchi, Performance analysis of the IEEE distributed coordination function, IEEE Journal of Selected Areas in Communication, vol. 18, no. 3, pp , March 000. [9] L. Chandran-Wadia, S. Mahajan, and S. Iyer, Redefining internet in the context of pervasive computing, in Proceedings of the 15th international conference on Computer communication, 00, pp [10] Y. Xiao and J. Rosdahl, Performance analysis and enhancement for the current and future IEEE MAC protocols, ACM SIGMOBILE Mobile Computing and Communications Review, vol. 7, pp. 6 19, 003. [11] H. Wu, Y. Peng, K. Long, S. Cheng, and J. Ma, Performance of reliable transport protocol over IEEE wireless LAN: Analysis and enhancement, in Proceedings of IEEE INFOCOM, vol. 1, no. 1, June 00, pp [1] Queueing analysis and delay mitigation in IEEE random access MAC based wireless networks, in proceedings of IEEE INFOCOM, March 004. 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