A Comprehensive Minimum Energy Routing Scheme for Wireless Ad hoc Networks

Transcription

1 A Comrehensive Minimum Energy Routing Scheme for Wireless Ad hoc Networks Jinhua Zhu, Chunming Qiao and Xin Wang Deartment of Comuter Science and Engineering State University of New York at Buffalo, Buffalo, NY 46 {jzhu, qiao, Abstract Current minimum energy routing schemes in wireless networks only consider energy consumtion for transmitting data ackets. However most wireless devices also transmit some control ackets such as RTS and CTS in 8. besides data ackets. Without considering the energy consumtion for control ackets, the existing minimum energy routing schemes tend to use more intermediate nodes, which results in more energy consumtion and less throughut. In this aer, we first roose more comrehensive energy consumtion models that consider the energy consumtion for data ackets as well as control ackets. Based on these models, we roose our minimum energy routing scheme. The simulation results verify that our scheme erforms better than the existing minimum energy routing schemes in terms of energy consumtion as well as throughut. I. INTRODUCTION A wireless ad hoc network usually consists of mobile devices with limited battery ower. Thus, energy-efficient communication techniques are very imortant. The most common technique is the ower control scheme, in which a node transmits data ackets to its neighbor at the minimum required ower level [7]. However, this scheme only minimizes the transmission ower within a node s neighborhood. Several energy-aware multi-ho routing rotocols have been roosed to minimize the total ower over all the nodes along the ath between a source and its destination [] [5]. In wireless networks, the ower of a transmitted signal is attenuated at the rate of /d n, where d is the distance between the sender and receiver and n is the ath loss exonent between and 6. Accordingly, transmitting data ackets directly to a node may consume more energy than going through some intermediate nodes. Based on this observation, most of the roosed energy-efficient routing rotocols have tried to find a ath that has many short-range hos in order to consume the least amount of total energy. These rotocols can be generally classified into the following three categories: Minimum Total Transmission Power MTTP rotocols: These rotocols set the link cost to the transmission ower and use a shortest ath algorithm to search for the minimum energy ath. PAMAS [] used the Dijkstra s shortest ath algorithm to search for the ath. The authors in [] modified DSR into a MTTP rotocol. PARO [5] erformed oweraware routing otimization across the MAC and Network layers. In this scheme, one or more intermediate nodes elect to forward ackets on behalf of the source-destination airs to reduce the transmission ower. Minimum Total TransCeiving Power MTTCP rotocols: As the intermediate nodes consume energy not only when forwarding ackets but also when receiving ackets, the rotocol in [] assigned the transmission ower as well as receiving ower to be the link cost metric, and used the Bellman-Ford shortest ath algorithm to find the minimum energy ath. Minimum Total Reliable Transmission Power rotocols: The authors in [4] claimed that a link cost should be a function of both the energy required for a single transmission attemt across the link and the link error rate, which determines the number of retransmission attemts needed for a successful transmission, and accordingly, roosed a minimum total reliable transmission ower rotocol. This rotocol aims to minimize the energy consumtion in transmitting data ackets from a source to a destination reliably. However, none of these rotocols considered the additional energy consumtion in sending control or signaling ackets at the Data Link layer. Therefore, the roosed energy consumtion models could not cature the actual energy consumtion in most wireless networks. For examle, in an 8. network, the energy consumtion by the RTS, CTS and ACK ackets accounts for a significant art of the total energy consumtion. Without considering such energy consumtion, these rotocols may tend to use a larger number of intermediate nodes, thus resulting in more energy consumtion, a lower throughut and/or a higher end-to-end acket error rate. To address the deficiency of the existing aroaches, in this aer, we first analyze the energy consumtion for three oular wireless ad hoc networks. After develoing these more accurate energy consumtion models, we roose new link costs for use by our minimum energy routing scheme. Our evaluation shows that the roosed minimum energy routing scheme erforms better in terms of the total energy consumtion as well as throughut than existing schemes. The rest of the aer is organized as follows. Section II contains our energy consumtion models for wireless networks. In Section III, our roosed minimum energy routing scheme is described and its imlementation issues are discussed. Simulation-based erformance evaluation is conducted in Section IV. Section V concludes the aer.

2 II. ENERGY CONSUMPTION MODELS In wireless ad hoc networks, there are two tyical reliable transmission modes [4]: End-to-End Retransmission EER and Ho-by-Ho Retransmission HHR. In the EER mode, intermediate nodes along a ath do not rovide any link-layer retransmission. The source node will retransmit the acket if it doesn t receive the acknowledgement acket ACK from the destination within some redefined eriod. In the HHR mode, the source node and all the intermediate nodes rovide link-layer retransmissions. Since neither the MTTP nor the MTTCP rotocols considers reliable transmissions, they don t distinguish the energy consumtion between these two modes. For examle, consider the scenario where there are M intermediate nodes between a source and a destination. Let the nodes along the ath from the source to the destination be numbered from to M in that order. Denote the acket error rate from node i to node j by i,j, the transmission ower from node i to node j by P i,j, and the receiving ower by P r. In addition, for a variable x, denote x by x, and the mean value of x by x. Then the total ower in transmitting data ackets to the destination calculated by a MTTP rotocol is M P i,i+. For a MTTCP rotocol, the total ower along the ath [] will be calculated as P i,i+ + P r. M On the other hand, the rotocol calculates the total ower differently for EER and HHR. For the EER mode, the total ower over the ath [4] is M P i,i+ M. i,i+ For the HHR mode, the total ower over the ath [4] is M P i,i+. i,i+ Note that, the energy consumtion models used by the MTTP, MTTCP and rotocols only consider the energy consumtion by data ackets. However, in most wireless ad hoc networks, control ackets, which also consume energy, need to be sent before and/or after the data ackets are sent. Therefore, the existing energy consumtion models underestimate the real energy consumtion, and as a result, alying an otimization technique based on such inaccurate energy consumtion models will lead to a subotimal solution only. To address the above roblem, we will develo more accurate energy consumtion models for three common wireless MAC rotocols: CSMA, MACA and 8.. The first two belong to the EER mode where end-to-end retransmission is rovided by the Transort layer using e.g.,tcp and may involve ACK ackets as control ackets. The third 8. belongs to the HHR mode, and may also contain ACK ackets as control ackets. Other MAC rotocols can be analyzed in a similar way. A. Energy Consumtion Models for the EER mode Carrier Sense Multile Access CSMA: In CSMA, a node transmits a data acket if the channel is sensed idle; otherwise, it will defer the transmission. If the source node doesn t receive the ACK for the transmitted data acket from its destination node for some redefined eriod, it will retransmit the data acket. The ACK can be transmitted searately or iggybacked. In the following, it is assumed that ACK transmission or retransmission also consumes energy. The state diagram for transmitting data ackets from the source node to its destination node M reliably with CSMA is in Fig.. The average total ower consumed by the nodes along the ath can be obtained, based on the state diagram, as: P,, + M j j P i,i+ j= P S,D = M + i,i+ M i,i+ M P i,i+ M i,i+ j,j+ i,i+ If we also consider the energy consumtion for receiving ackets as in [], we can modify Eq into: M j j P S,D =, P,,+,,,4 j= P i,i++p r i,i+ j,j+ M i,i+ M M P i,i++p r i,i+ + M,4 i,i+,,, M- Fig.. M, M State diagram for CSMA. M M, M. However, such one-way energy consumtion is still not enough since the source knows the acket arriving at its destination correctly only if it receives the ACK back. But.

3 the ACK can also be lost so the destination node needs to retransmit the ACK. Usually, the destination retransmits the ACK only after it receives the retransmitted data acket from the source correctly as in the case of sto-and-wait ARQ rotocol. That is, the number of ACK retransmissions equals the number of retransmitted data ackets arriving at the destination correctly. In such a case, the average total ower in sending a acket from the source to its destination successfully is: P S,D N D,S ACK+P D,S ACK, where N D,SACK is the average number of ACK retransmissions given by: N S,D = M i,i+ and P D,SACK is the average total ower for transmitting an ACK from the destination node to the source node correctly, which can be comuted as in Eq. Multile Access with Collision Avoidance MACA: MACA attemts to reduce collisions in CSMA by introducing two control messages: Request To Send RTS and Clear To Send CTS. A node transmits a RTS to its receiver before transmitting a data acket. Nodes in its neighborhood will defer their transmission until they receive the CTS or timeout. If the receiver receives the RTS, it will rely with a CTS. Nodes in the receiver s neighborhood will yield to allow the data ackets to be transmitted. Once the node receives the CTS, it will transmit the data ackets. If it doesn t receive the CTS, the whole rocess will be reeated. Let the acket error rate from node i to node j for RTS and CTS be r,i,j and c,i,j resectively. The state diagram for node i to transmit a data acket to one of its neighboring nodes, node j, isshown in Fig, where state S is the initial state, S is the state in which node j receives the RTS acket, S is the state in which node i receives the CTS acket, S is the state in which node j receives the data acket and S4 is the state in which the data acket from node i is lost. We assume that the nodes ; RTS and CTS acket sizes by N rts and N cts resectively, the hysical layer overhead size by N hy and the data acket size by N, then the average total ower in sending a acket from node i to node j can be exressed, based on the state diagram in Fig., as: N r+n c P T i, j =P i,j + P r,i,j m N m, 4 c,j,i r,i,j where N r = N rts+n hy, N c = N cts+n hy, N m = N +N maca+ N hy. Considering the scenario with M intermediate nodes between the source node and the destination node M, the average total ower in transmitting data ackets from node to node M reliably is: P S,D = M P T,,+ j j= + j P T i,i+ i,i+ j,j+ M i,i+ M M P T i,i+ i,i+ M i,i+. 5 Similar to the case for CSMA, if we also consider the energy consumtion for receiving the acket, we can modify Eq 4 to be: P T i, j =P i,j + P r +P m + P r N r + N c r,i,j N m. 6 c,j,i r,i,j In addition, the average number of source retransmission until the acket can reach the destination reliably is N S,D = M i,i+ Hence, as in the case for the end-to-end retransmission in CSMA, the average total ower in sending a acket and getting an ACK back successfully will be: P S,D N D,S ACK+P D,S ACK. 7. S c, j, i r, i, j r, i, j S c, j, i S i, j i, j S S4 B. Energy Consumtion Models for the HHR mode 8. is a tyical HHR scheme. There are two ways of transmitting data frames over a channel: the Two Frame Exchange scheme and the Four Frame Exchange scheme. In the following, we will analyze the energy consumtion for both schemes. To simlify the exressions in the analysis, we denote the 8. header size and ACK acket size by and N ack resectively. And we also define the following symbols: Fig.. State diagram for transmitting a acket from node i to node j in MACA. transmit data ackets at the minimum necessary ower level, but transmit RTS and CTS at the maximum ower level P m. Denote the MACA header size for data ackets by N maca, the = N + + N hy,n r = N rts + N hy N c = N cts + N hy, andn a = N ack + N hy. In 8., the number of retransmissions is limited e.g., the short retry limit is 7 and the long retry limit is 4 [6]. However, to simlify our analysis, we assume unlimited retransmissions

4 which should not affect the accuracy too much as most of the acket retransmissions will not be over the limits. the Two Frame Exchange scheme: In the Two Frame Exchange scheme, a node transmits a data acket if the channel is idle for a eriod that exceeds the Distributed Inter Frame Sace DIFS. If the channel is busy, it will defer the transmission and kee monitoring the channel until it is idle for a eriod of DIFS. And then,it starts backoff with a random backoff time. The backoff timer will be aused if the channel is busy and continued once the channel is idle again for the DIFS eriod. Once the backoff timer reaches zero, the node will transmit the data acket immediately. The receiver relies with an ACK to the sender after receiving the data acket successfully. If the transmitter doesn t receive the ACK within a redefined time eriod, the whole rocess will be reeated. Let the ACK acket error rate from node i to node j be a,i,j. The state diagram for transmitting a data acket from node i to one of its neighboring nodes, node j, isinfig.,where S is the initial state, S is the state in which node j receives the data acket, S is the state in which node i receives the ACK acket. Then, the average total transmission ower in transmitting a acket from node i to node j successfully is given by P T i, j = P N i,j + P a j,i i,j. 8 i,j a,j,i Similiarly, the average total receiving ower in receiving a acket from node i at node j successfully is obtained as P R i, j =P r + N a. a,j,i Therefore, the average total ower in sending a acket from node i to node j successfully is Fig.. P i, j =P T i, j+p R i, j. S a, j, i i, j i, j a, j, i S S State diagram for the Two Frame Exchange scheme. The average total ower consumed along the ath from the source node to the destination node M is P total = M P T i, i ++P R i, i + the Four Frame Exchange scheme: In the Four Frame Exchange scheme, nodes exchange two more frames before transmitting data ackets: RTS and CTS. More secifically, the sender transmits a RTS acket after the channel is available for a eriod longer than DIFS or the backoff timer reaches zero. 9 The receiver resonds with a CTS acket after receiving a RTS acket. If the CTS is not received within a redetermined time interval, the sender retransmits the RTS acket. After receiving the CTS, the sender will send out the data acket and the receiver will rely with an ACK acket after receiving the data acket successfully. If the transmitter doesn t receive the ACK acket within a redefined time eriod, the whole rocess will be reeated. The state diagram for transmitting a data acket from node i to one of its neighboring nodes, node j, is shown in Fig 4, where S is the initial state, S is the state in which node j receives the RTS acket, S is the state in which node i receives the CTS acket, S is the state in which node j receives the data acket, and S4 is the state in which node i receives the ACK acket. S Fig. 4. c, j, i r, i, j r, i, j c, j, i S i, j a, j, i S i, j S a, j, i S4 State diagram for the Four Frame Exchange scheme. Therefore, the average total transmission ower in successfully transmitting a acket from node i to node j is P T i, j = P m Nr + Nc r,i,j + Pi,j + P N j,i a i,j r,i,j c,j,i i,j a,j,i. i,j a,j,i And the average total receiving ower in successfully receiving a acket from node i at node j is N r N P R i, j =P 8 + Nc N8 + i,j + Na i,j a,j,i c,j,i r. c,j,i i,j a,j,i The average total ower consumed along the ath from the source node to the destination node M isthus P total = M P T i, i ++P R i, i +. III. MINIMUM ENERGY ROUTING SCHEME A key element in any minimum energy routing scheme is the link cost assignment. The accuracy of link costs determines the erformance of these schemes in terms of energy consumtion as well as throughut. Therefore, we need to determine link costs that can reresent real energy consumtion in wireless networks as accurately as ossible. Once we get the link costs, we can then modify the traditional shortest ath routing If a node receives a RTS but can t rely with a CTS because the channel is busy, we treat it as a RTS acket error in our analysis even though the RTS acket is received correctly. We call this as the busy channel roblem.

5 rotocols e.g. Bellman-Ford, DSR, and AODV to suort minimum energy routing. Currently, there exist three tyes of link costs: Transmission Power Level P i,j in the MTTP rotocols; TransCeiving Power Level P i,j + P r in the MTTCP rotocols; P Reliable Transmission Power Level i,j i,j, where L = L,,,... in the Protocols. However, these link costs could not accurately reresent the energy consumtion since they do not take the extra energy consumtion in MAC and Physical layers into account. Therefore, we need to derive new link costs for our minimum energy routing scheme. In Section II, we have introduced more accurate energy consumtion models for wireless networks. In this section, we will derive new link costs for our minimum energy routing scheme based on these models. A. Link costs for the EER mode Based on the energy consumtion models for two MAC rotocols CSMA and MACA in the eer mode develoed earlier, the minimum energy routing scheme would find a ath that minimizes Eq for CSMA or Eq 7 for MACA. Given these two equations, the average total ower over the ath can not be exressed as a linear sum of individual ower levels. Therefore we need to simlify these two equations. By using the same assumtion as that in [4] that transmission errors on a link do not sto downstream nodes from relaying the acket, we can aroximate Eq in CSMA by: M P i,i+ + P r M, i,i+ i+,i and Eq 7 in MACA by M Nr +Nc r,i,i+ P i,i++p r+p m+p r Nm r,i,i+ c,i+,i M i,i+ i+,i. 4 Note that, the numerators in these two equations can be exressed as a linear sum of ower levels and the logarithm of the denominators can be exressed as a linear sum of the logarithm of acket error rates. Therefore, we can let each node advertise two different metrics: one is P i,j+p r for CSMA and P i,j + P r +P m + P r Nr+Nc r,i,j N m for MACA; the other r,i,j c,j,i is log i,j j,i. With these two metrics and their cumulative values, every node can calculate P and select the minimum energy ath. From Eqs and 4, we can see that the variation in the data acket error rates for each link i,i+ or i+,i has a significant effect on the total energy consumtion as P is roortional to, which can be aroximated as + i,i+ i,i+ by using the Taylor exansion. For examle, if the data acket error rate on one link changes from. to., the total energy consumtion will be increased for about ercent. If data acket error rates on more than one link change, the total energy consumtion will be affected more dramatically. For CSMA, this could be a big roblem as the data acket error rates are very senstive to environment change such as noise, interference, and number of cometing nodes so that they may change very fast. To kee track of data acket error rates in CSMA will require a lot of routing overhead, which may consume more energy than the savings from minimum energy ath. Therefore, CSMA is not suitable for minimum energy routing if the enviroment is not static enough. On the other hand, in MACA, the sender exchanges RTS and CTS with the receiver before sending a data acket, the data acket error rates will not vary too much to cause a major concern. B. Link costs for the HHR mode It is easier to derive the link costs for the HHR mode since the average total ower over the ath is a linear sum of ower levels in each link. More secifically, for 8., we can use P T i, j+p Ri, j as the link cost. For the Two Frame Exchange scheme, the link cost is + P r C i, j =P i,j + Na i,j i,j a,j,i a,j,i + Na. 5 For the Four Frame Exchange scheme, the link cost is P m Nr N + Nc C 4i, j = 8 N 8 r,i,j P i,j + Na N + 8 i,j r,i,j c,j,i i,j a,j,i i,j a,j,i Nr N + Nc +P 8 N8 c,j,i + c,j,i i,j + Na N 8 c,j,i i,j a,j,i r. 6 c,j,i i,j a,j,i From Eqs. 5 and 6, we can see that the variation in the acket error rates may have some high effects on the energy consumtion for transmitting the data acket from one node to another. However, this is not as significant as in EER since the energy consumtion in one link is far smaller than the total energy consumed along the ath from the source to the destination, esecially when the number of links is large enough. IV. SIMULATION RESULTS In this section, we evaluate the roosed energy consumtion models and comared several minimum energy routing schemes via simulations. A. Energy Consumtion Models In this set of simulations, We obtain the energy consumed for transmitting data ackets from the source node to the destination node,, 4, 5, or 6 using GlomoSim. The transmission ower level is mw for data ackets, and 5mW for RTS and CTS ackets. To exclude the imact of finding a route on the energy consumtion, we use static routing. In addition, we assume that there is no ower saving mode for the nodes, and accordingly, a receiving node will send the same amount of energy in monitoring the channel even if it doesn t receive a acket. In this way, we need to focus only on the transmission ower in simulations and comare that with the transmission ower redicted by various models. For this reason, we will only comare the accuracy of the energy consumtion models used in MTTP and with

6 our models. Note that, in terms of redicting the transmission ower, the model used in MTTCP is as inaccurate as the model used in MTTP. In terms of redicting the total energy consumtion, the model used in MTTCP is more accurate than that in MTTP and, but still not as accurate as our model as the energy needed for receiving control ackets is ignored in the model used in MTTCP as well as MTTP and. Energy Consumtion Models for EER: In this mode, we use FTP File Transfer Protocol to transmit 6, data ackets with 5 bytes er acket. To reduce the imact on the energy consumtion due to FTP control ackets, we set the size of FTP control ackets to one byte. The acket error rates for CSMA and MACA are set to.5 and. resectively. The simulation results and the energy consumtion estimated by each model are shown in Figs. 5 and 6. It is clear that our models match the simulation results very well in both CSMA and MACA. On the other hand, both MTTP and models, which resulted in almost the same energy consumtion estimate due to the low acket error rate esecially in the case of MACA, are seen to underestimate the energy consumtion significantly and the underestimation increases with the number of intermediate nodes. In addition, the underestimation is much more in MACA than in CSMA. The reason is that the MTTP and models in MACA not only do not consider the energy consumtion by ACK and the number of ACK retransmissions on the Transort layer, but also ignore the energy consumtion for RTS and CTS in the MAC layer. Energy Consumtion mwhr Simulation Our Model MTTP Energy Consumtion mwhr Fig Simulation Our Model MTTP 4 5 M Energy consumtion for simulation and analysis with MACA. and the underestimation is more serious as the number of intermediate nodes increases. In addition, the underestimation is much larger in the Four Frame Exchange scheme than in the Two Frame Exchange scheme. Energy Consumtion mwhr Simulation Our Model MTTP M Fig. 7. Energy consumtion for simulation and analysis with Two Frame Exchange scheme. Fig M Energy consumtion for simulation and analysis with CSMA. Energy Consumtion Models for HHR: In this mode, we use CBR Constant Bit Rate to transmit 65,56 data ackets. The acket error rate is set to. for both the Two Frame Exchange scheme and the Four Frame Exchange scheme. The simulation results and the energy consumtion estimated by each model are shown in Figs. 7 and 8. Our models match the simulation results quite well in both schemes. Again, MTTP and models underestimate the energy consumtion B. Minimum Energy Routing Schemes In this set of simulations, we modified AODV to suort minimum energy routing schemes in GlomoSim. We changed the battery model in GlomoSim by setting the battery efficiency to, and in addition removed the energy consumtion for receiving ackets or monitoring the channel. The area simulated is m m, the received ower threshold is set to 8 dbm, the available transmission ower levels are, 5,, 5,, 5, and 5mW, and the rocessing ower level is.5mw. The nodes are uniformly distributed and the airs of source and destination nodes are randomly selected. The connection requests arrive according to a Poisson rocess

7 .7.6 Simulation Our model MTTP 7 x 5 6 Energy Consumtion mwhr Energy Consumtion er Packet mwhr M Fig. 8. Energy consumtion for simulation and analysis with Four Frame exchange scheme. Fig. 9. Energy consumtion er acket in MACA. and the connection duration is exonentially distributed. The data acket size is 5 bytes and the data rate is Mbs. Since the authors in [4] already showed that the is better than the MTTP, we will only comare our rotocol to and Scheme, which uses AODV as the routing rotocol and adjusts the transmission ower according to the distance between the sender and the receiver. We study two erformance metrics for these three rotocols. For the EER mode, these two metrics are: Energy consumtion er acket, which is defined as the total energy consumtion divided by the total number of ackets transmitted successfully; Number of ackets transmitted, which reresents the effective throughut. For the HHR mode, the two erformance metrics are: Energy consumtion er acket;percentage of ackets transmitted, which is defined as the number of ackets received by the destination correctly divided by the number of ackets transmitted by the source. This metric also reflects the throughut if the end-to-end delay is almost the same for each acket. The higher the ercentage of the ackets transmitted, the higher the throughut. EER mode: In this mode, we use FTP as our alication rotocol. The connection arrival rate is er hour and the average connection duration is 6 minutes. We simulate each rotocol for hours in MACA. The amount of energy consumed and number of ackets transmitted are collected. The simulation results are shown in Figs. 9 and. As can be seen from Fig. 9, our rotocol has the least energy consumtion er acket, followed by and the Power Control scheme. However, in terms of the number of ackets transmitted, The scheme erforms the best, followed by our rotocol and. That is because the number of ackets transmitted is mainly determined by endto-end delay and acket error rate. The larger end-to-end delay and acket error rate, the less number of ackets transmitted. As the uses the least number of intermediate nodes, it will have the least delay and end-to-end acket error Number of Packets transmitted 4 x Fig.. Number of ackets transmitted in MACA. rate. Therefore it has the most number of ackets transmitted. It is worthwhile to oint out that we simulated the rotocols using toologies with different density and only allowed discrete transmit ower levels so that the curve for each rotocol is not so smooth. However, as we are only interested in comaring the erformance of three rotocols with the same number of nodes, but not the erformance of any given rotocol with different numbers of nodes, this henomena doesn t affect our analysis. HHR mode: In this mode, we used CBR 5 ackets er second as our alication rotocol. The connection arrival rate is 5 er hour and the average connection duration is minutes. We simulated each rotocol for one hour using the Two Frame Exchange scheme and the Four Frame Exchange scheme. The amount of energy consumed, the number of ackets transmitted and the number of ackets received correctly are monitored. The simulation results are deicted in Fig. through 4.

8 7 x Energy Consumtion er Packet mwhr 5 4 Fig.. Percentage transmitted Fig.. Energy Consumtion er Packet mwhr Energy consumtion er acket in two frame scheme Percentages of ackets transmitted in two frame scheme. 7 x Percentage transmitted Fig Percentages of ackets transmitted in four frame scheme. As can be seen from these figures, our scheme also has the best erformance in terms of energy consumtion er acket, followed by and the scheme. Our scheme can also transmit a higher ercentage of ackets as comared to. However, the scheme has the lowest ercentage of ackets transmitted in the Two Frame Exchange scheme but the highest ercentage of ackets transmitted in the Four Frame Exchange scheme. This is exlained as follows. In the Two Frame Exchange scheme, most of the ackets lost are caused by the asymmetric ower roblem.inthe scheme, the transmission ower can vary between the minimum and the maximum, hence the asymmetric roblem is very serious. and our rotocol use more short-distance links to save energy, hence the transmission ower for each link does not change significantly. However, uses more intermediate nodes than our scheme. Therefore, our rotocol has the highest ercentage of ackets transmitted, followed by and the ower control scheme. In the Four Frame Exchange scheme, as the nodes exchange RTS and CTS at the maximum ower level, the asymmetric ower roblem can be ignored. However, it has the busy channel roblem see footnote. If the number of RTS retransmissions is over the limit because of the busy channel roblem, the node has to discard the data acket. Most of the ackets are lost in this way in the Four Frame Exchange scheme. Obviously, more radio transmissions would make the busy channel roblem more serious. Therefore, has the lowest ercentage of ackets transmitted because it uses the largest number of intermediate nodes that generate the highest number of radio transmissions. And the ower control scheme has the highest ercentage of ackets transmitted, followed by our rotocol. Fig.. Energy consumtion er acket in four frame scheme. One node cannot sense other nodes radio transmission because they use a low transmission ower, however this node can cause collision if it sends ackets to one of its neighboring nodes using a high transmission ower.

9 V. CONCLUSION In this aer, we have develoed, for the first time, energy consumtion models for common wireless ad hoc networks that take the energy consumtion in sending control ackets into account as well. These theoretical models have been verified to be much more accurate than existing models used by the minimum total tranmission ower routing rotocols, the minimum total transceiving ower routing rotocols, and the minimum total reliable transmission ower routing rotocols. Based on our models, we have also roosed a minimum energy routing scheme. Our simulation results have shown that our scheme erforms better than other existing schemes in terms of both the energy consumtion and the effective throughut. As many current 8. cards already suort the functions of received ower measurement and transmission ower setting, it is easy to imlement our scheme in real alications. REFERENCES [] S. Singh and C. Raghavendra, Pamas-ower aware routing in mobile ad-hoc networks, In Proceedings of Mobicom, Oct [] S. Doshi, S. Bhandare, and T. X Brown, An on-demand minimum energy routing rotocol for a wireless ad hoc network, in ACM Mobile Comuting and Communications Review, vol. 6, no., July. [] V. Rodolu and T. Meng, Minimum energy mobile wireless networks, IEEE Journal on Selected Areas on Communications, vol. 7, Aug [4] S. Banerjee and A. Misra, Minimum energy aths for reliable communication in multi-ho wireless networks, MOBIHOC, June. [5] J. Gomez, A. T. Cambell, M. Naghshineh, and C. Bisdikian, Conserving transmission ower in wireless ad hoc networks, in Proc. of IEEE Conference on Network Protocols, Nov. [6] ANSI/IEEE Std 8., 999 Edition. [7] E. Jung and N. H. Vaidya, A ower control MAC rotocol for ad hoc networks, MOBICOM, Set.. [8] V. Kawadia and P. R. Kumar, Power control and clustering in ad hoc networks, in Proceedings of IEEE INFOCOM,. [9] C. E. Perkins, E. M. Belding-royer, and S. R. Das, Ad hoc On-demand Distance Vector AODV routing, Mobile Ad Hoc Networking Working Grou Internet Draft, 4 Nov.. [] E. M. Royer, and C. K. Toh, A review of current routing rotocols for ad hoc mobile wireless networks, IEEE Personal Communications, Aril 999. [] Theodore S. Raaort, Wireless communications rinciles and ractice, PRENTICE HALL.