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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 3 | Mar 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 7952
A PROFICIENT TIME SLOT ATTAINMENT ON THE HYBRID TDMA / CSMA
MULTI-CHANNEL MAC IN VANETS
Divya. S1and Prakash Narayanan. C2
divya95cse@gmail.com and cprakashmca@gmail.com
1PG Student and 2Assistant Professor, Department of Computer Science and Engineering
P.S.V. College of Engineering & Technology, Krishnagiri.
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - The multi-channel MACs increment the throughput and lessenthecrashlikelihoodcontrastedwiththe
single channel MACs However, coordination of different hubs crosswise over multi-channels is non-trifling. As of
late, a multi-channel MAC, Called HER-MAC, utilizes both TDMA and CSMA plans to improve dependability in
communicating wellbeing messages and proficiency in administration channel usage. By the by, HER-MAC
languishes a high crash likelihood over an expansive number of vehicle hubs .In this paper, we propose a half and
half TDMA/CSMAmulti-channelMACconventionforVANETsthatpermitseffectivetelecomofmessagesandbuilds
throughput on the control station .Further, our proposed MAC disposes of pointless control parcel, for example,
HELLO and SWITCH bundles in HER-MAC .Analysis and reproduction results demonstrate that the proposed MAC
can give quicker vacancy securing on the control station than HER-MAC.
Key Words: VANET, HER-MAC, multi-channel MAC
1. INTRODUCTION
One purpose of the Intelligent Transportation System (ITS)is to improve the quality and effectiveness of safety
messages in the future transportation systems.VehicularAdHocNetworks(VANETs)areanimportantcomponent
of ITS .Each vehicle is equipped with a radio interface, called an on board unit(OBU). A set of stationaryunits along
the road called Road Side Units (RSUs) allows vehicles to connect to the Internet. VANETs support two
communication type : Vehicle-to-Vehicle (V2V) and Vehicle-to-RSU (V2R). They can support a variety of safety
applications and non-safety applications, and provide comfort to drivers and passengers .Dedicated Short Range
Communications (DSRC) is exclusively used by V2V and V2R communications. The DSRC spectrum is divided into
seven channels: one Control channel(CCH) and six Service channels(SCHs).TheCCHisusedforhighprioritysafety
applications and network management .Service Channels mainly support the non-safety information and
entertainment applications .To provide timely and effective safety applications, theMediumAccessControl(MAC)
protocol needs an efficient broadcast service for safety messages. In addition, the multichannel MAC protocol is
proposed to ensure reliable transmission of safety messages by using interleave operation CCH and SCH and
priority access parameter. Some multichannel protocols are proposed to increase the safety broadcast reliability.
Performance matrices for multi-channel protocol are the collision probability and the throughput. A collision
probability is defined as an event where more than one node transmit at the same time slot. When a collision
occurs, the nodes must re-transmit the collided packets. This causes more delay. Thus, the collision probability is
important of safety message application and in this paper, we focus on the reducing the collision probability of
safety messages on the control channel .The basic multi-channel MAC is similar to IEEE 802.11 Distributed
Coordination Function (DCF) and EnhanceDistributedChannelAccess(EDCA).TheEDCAcanmapthetrafficwhich
has different priorities or different virtual stations and assign different channel access parameters to each virtual
station.However,thisschemeshasadrawbackinsupportingthroughput-sensitivenon-safetyapplicationshasbeen
proposed for a defaultmultichannelMACstandardforVANETs,asshowninFig.1c.InIEEE1609.4,nodesbroadcast
safetymessages or negotiatetheSCHsontheCCHduringtheControlChannelInterval(CCHI).IntheServiceChannel
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 3 | Mar 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 7953
Interval (SCHI), nodes switch to the negotiated SCHs for their non-safetymessagestransmissions.Thisschemehas
a high contention rate during the CCHI and the SCHI resources cannot be util.
1. HTC-MAC PROTOCOL sized during this interval
We assume that each node has one transceiver which can switch between CCH and SCHs.Eachnodemustbeonthe
CCH in order to broadcast safety message or exchange WSA/RFS message. For safety application, each node must
acquire exactly one time slot in the TDMA-based reservation period. As such, each node must transmit an
announcement packet (ANC) on the reservation period2, the ANC packet contains seven fields: (i) Node ID, (ii)its
reserved time slot, (iii) switched time slot, (iv) a number of time slots, (v) IDs of neighbor nodes, (vi) time slot are
allocated by neighbor nodes, (vii) safety applicationpacket .Once a node acquires a timeslot,itkeepsaccessingthe
same slot on the TDMA-based reservation period if its transceiver is not tuned to the service channel to receive or
transmit non safety application packets .ConsideringANCpayloadsizeof SbytesandatransmissionrateofRMbps,
the ANC packet requires a transmission time of t payload = (S_8)=R. The sum of the guard periods, the preamble
and the physic layer header is t add. Then, a time slot it slot = t payload + t add . We assume that there are K nodes
which broadcast in the reservation period. Hence, the reservation period is TRE =K_ slot . When the nodedensityis
high, the payload size S increases because the neighbor information field becomes bigger. The reservation period
TRE also increases and the contention period (TCON = 50ms � TRE) will be decreased. Consequently, the collision
probability wili increase due to many nodes attempt to broadcast packets in as small contention period.
3. ANALYTICAL MODEL FOR TIME SLOT ACQUISITION
A. Markov chain in HTC-MAC
For comparison with HER-MAC, we determine the averagenumberofnodeswhichacquireatimeslotwithinasync
interval and the probability that all the nodes acquire a timeslot within n frames. Let K denotes the number of
contending nodes in 2-hop neighborhood because if nodes are located at least three hop away, they can reuse the
same time slot [7].The Markov chain of HTC-MAC is inherited from the MAC, as shown in Fig. 3a. Let N be the
number of initially available time slots in async-interval,andbethetotalnumberofnodeswhichacquireatimeslot
within n sync interval. X is a stationary discrete-time Markov chain with the transition probabilities illustrated in
Fig. 3a.In this paper, we consider the case where K _ N. For the case K > N, it is useful to determine an optimal value
for a number of time slots on the reservation period. Let P be the one-step transition probability matrix, and Pn be
the n-step transition probability matrix. Then ,p( Xn = i) = Pn1;i+1; i = 0; :::;K: (1)The probability that all nodes
acquire a time slot within n sync interval is Falln ; HTC�MAC = p(Xn = K) = Pn1;K+1: In this paper, we consider the
case where K _ N. For the case K > N, it is useful to determine an optimal value for a number of time slots on the
reservation period. Let P be the one-step transition probability matrix, and Pn be the n-step transition probability
matrix. Then,
p (Xn = i) = Pn
1;i+1; i = 0; :::;K: (1)
The probability that all nodes acquire a time slot within n sync interval is
Fall
n;HTC�MAC = p(Xn = K) = Pn
1;K+1: (2)
Let Y be the average number of nodes which successfully
acquire a time slot within n frames. Then, we have
E[Yn] = ΣK
i=0, iP n
1;i+1:
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 3 | Mar 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 7954
B. Markov chain in HER-MAC
In this section, we determine formulas of the average number of nodes which acquire a time slot within a sync
interval and the probability that all the nodes acquire a timeslot within n frames in HER-MAC. From the Markov
chain [9] it is clear that the probability _ that a node transmits a HELLO or safety application packet in an arbitrary
time slot can be expressed as
Let p be the collision probability when more than one node transmit at the same time slot. Hence, we have
Consequently, based on (4) and (5), variable _ and p can solved by the numerical methods as in [9].Note that 0 _ p _
1and 0 _ _ _ 1.In every time slot during the HELLO interval, an agreement will be successfullymadewithprobability
p suc, thus, we have p suc = K_ (1 � _ )K�1: (6)In the p-persistent CSMA/CA, the back off interval is based on the
geometric distribution with probability p suc [10].
Fig. 3.1 Markov chain in HER-MAC
4. PERFORMANCE EVALUATION
To validate HTC-MAC, we use an event-driven simulation program written in Mat lab. For comparison with HTC-
MAC, we also simulate HER-MAC where a HELLO packet configured to useAccessClass3(AC3)withCW=8andCW
= 4 due to it is a safety message using the highest priority scheme [11]. In Fig. 4, we compare HTC-MAC with HER-
MAC for CW = 8 and CW = 4 in a dense scenario (N = 20; K = 10). In HER-MAC, if nodes use CW = 8, all nodes can
successfully acquire a time slot after6frames.However,nodesusing CW=4need12framestosuccessfullyacquirea
time slot. In the same condition, in HTC-MAC, after5 frames, all nodes have successfully acquired their time slots.
Using Eq. (10) and (2), the probability that all nodes acquire time slots within n frames is presented in. The
averagenumber of nodes which successfully acquire a time slot and Fall have same results. Hence, the rate of
successful time slot acquisitioncan be shown by using the probability or average numberofnodeswhichacquirea
time slot. we evaluate Eq. (5) and (10) with the same thenumberofavailabletimeslots, N=20.Wetaketheaverage
number of nodes which acquire a time slot within each frame by running100times.Inaddition,inEq.(10),wetake
the floor function ⌊E[Xi]⌋. Hence, the average number of nodes which acquire a time slot within 3 framesasshown
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 3 | Mar 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 7955
in Fig. 6 with K= 5 and K = 10, which are close together. Consequently, than alsoclosetogetherasshowninFig.5.If
we take the ceiling
function ⌈E[Xi]⌉, the rate of time slot acquisition is faster than taking the floor function .In Fig. 6, we fix the number
of available time slots andvary the number of contending nodes, K. Forcomparison,wesimulateHER-MACwithits
best performing parameter ,CW = 8. If K is 5, HTC-MAC and HER-MAC have the same rate of successful time slot
acquisition. When K increases,the rate of successful time slot acquisition in HTC-MAC Is higher than HER-MAC.
WhenK equals N, the collision probability when more than one node transmit at the same time slot in Eq (5)
increases. Hence, the probability that all
p[Xi = E[Xi]] =8>><>>:0;
Fig. 4.1 Performance Evaluation
5. CONCLUSION
In this paper, we propose an efficient time slot acquisition on the hybrid TDMA/CSMA mutli-channel MAC in
VANETs. HTC-MAC not only eliminates unnecessary control overhead but also increases the throughput on the
control channel. The analysis and simulation results prove that HTC-MAC outperforms HER-MAC in terms of the
average number of nodes which acquire a time slot. However, HTC-MAC requires a larger ANC’s payload size to
broadcast its neighbors’ information when the node density is high.
REFERENCES
[1] H. Wu, A. Wang, Q. Zhang, and X. Shen, “IEEE 802.11e enhanced distributed channel access (EDCA) throughput
analysis,” in Communications, 2006. ICC ’06. IEEE International Conference on, vol. 1, 2006, pp. 223–228.
[2] [2] IEEE Standard for Wireless Access in Vehicular Environments (WAVE) Multi-channelOperation,Sep,2010.
[3] D. N. M. Dang, H. N. Dang, V. Nguyen, Z. Htike, and C. S. Hong, “HER-MAC: A hybrid efficient and reliable MACfor
vehicular ad hoc networks,” in Advanced Information Networking and Applications (AINA), 2014 IEEE 28th
International Conference on, May 2014, pp. 186–193.
[4] F. Borgonovo, A. Capone, M. Cesana, and L. Fratta, “ADHOC MAC: New MAC architecture for ad hoc networks
providing efficient and reliable point-to-point and broadcast service.” Wireless Netw., 2004, pp. 359–366 Vol.
10.

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IRJET- A Proficient Time Slot Attainment on the Hybrid TDMA / CSMA Multi-Channel Mac in Vanets

  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 3 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 7952 A PROFICIENT TIME SLOT ATTAINMENT ON THE HYBRID TDMA / CSMA MULTI-CHANNEL MAC IN VANETS Divya. S1and Prakash Narayanan. C2 divya95cse@gmail.com and cprakashmca@gmail.com 1PG Student and 2Assistant Professor, Department of Computer Science and Engineering P.S.V. College of Engineering & Technology, Krishnagiri. ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - The multi-channel MACs increment the throughput and lessenthecrashlikelihoodcontrastedwiththe single channel MACs However, coordination of different hubs crosswise over multi-channels is non-trifling. As of late, a multi-channel MAC, Called HER-MAC, utilizes both TDMA and CSMA plans to improve dependability in communicating wellbeing messages and proficiency in administration channel usage. By the by, HER-MAC languishes a high crash likelihood over an expansive number of vehicle hubs .In this paper, we propose a half and half TDMA/CSMAmulti-channelMACconventionforVANETsthatpermitseffectivetelecomofmessagesandbuilds throughput on the control station .Further, our proposed MAC disposes of pointless control parcel, for example, HELLO and SWITCH bundles in HER-MAC .Analysis and reproduction results demonstrate that the proposed MAC can give quicker vacancy securing on the control station than HER-MAC. Key Words: VANET, HER-MAC, multi-channel MAC 1. INTRODUCTION One purpose of the Intelligent Transportation System (ITS)is to improve the quality and effectiveness of safety messages in the future transportation systems.VehicularAdHocNetworks(VANETs)areanimportantcomponent of ITS .Each vehicle is equipped with a radio interface, called an on board unit(OBU). A set of stationaryunits along the road called Road Side Units (RSUs) allows vehicles to connect to the Internet. VANETs support two communication type : Vehicle-to-Vehicle (V2V) and Vehicle-to-RSU (V2R). They can support a variety of safety applications and non-safety applications, and provide comfort to drivers and passengers .Dedicated Short Range Communications (DSRC) is exclusively used by V2V and V2R communications. The DSRC spectrum is divided into seven channels: one Control channel(CCH) and six Service channels(SCHs).TheCCHisusedforhighprioritysafety applications and network management .Service Channels mainly support the non-safety information and entertainment applications .To provide timely and effective safety applications, theMediumAccessControl(MAC) protocol needs an efficient broadcast service for safety messages. In addition, the multichannel MAC protocol is proposed to ensure reliable transmission of safety messages by using interleave operation CCH and SCH and priority access parameter. Some multichannel protocols are proposed to increase the safety broadcast reliability. Performance matrices for multi-channel protocol are the collision probability and the throughput. A collision probability is defined as an event where more than one node transmit at the same time slot. When a collision occurs, the nodes must re-transmit the collided packets. This causes more delay. Thus, the collision probability is important of safety message application and in this paper, we focus on the reducing the collision probability of safety messages on the control channel .The basic multi-channel MAC is similar to IEEE 802.11 Distributed Coordination Function (DCF) and EnhanceDistributedChannelAccess(EDCA).TheEDCAcanmapthetrafficwhich has different priorities or different virtual stations and assign different channel access parameters to each virtual station.However,thisschemeshasadrawbackinsupportingthroughput-sensitivenon-safetyapplicationshasbeen proposed for a defaultmultichannelMACstandardforVANETs,asshowninFig.1c.InIEEE1609.4,nodesbroadcast safetymessages or negotiatetheSCHsontheCCHduringtheControlChannelInterval(CCHI).IntheServiceChannel
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 3 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 7953 Interval (SCHI), nodes switch to the negotiated SCHs for their non-safetymessagestransmissions.Thisschemehas a high contention rate during the CCHI and the SCHI resources cannot be util. 1. HTC-MAC PROTOCOL sized during this interval We assume that each node has one transceiver which can switch between CCH and SCHs.Eachnodemustbeonthe CCH in order to broadcast safety message or exchange WSA/RFS message. For safety application, each node must acquire exactly one time slot in the TDMA-based reservation period. As such, each node must transmit an announcement packet (ANC) on the reservation period2, the ANC packet contains seven fields: (i) Node ID, (ii)its reserved time slot, (iii) switched time slot, (iv) a number of time slots, (v) IDs of neighbor nodes, (vi) time slot are allocated by neighbor nodes, (vii) safety applicationpacket .Once a node acquires a timeslot,itkeepsaccessingthe same slot on the TDMA-based reservation period if its transceiver is not tuned to the service channel to receive or transmit non safety application packets .ConsideringANCpayloadsizeof SbytesandatransmissionrateofRMbps, the ANC packet requires a transmission time of t payload = (S_8)=R. The sum of the guard periods, the preamble and the physic layer header is t add. Then, a time slot it slot = t payload + t add . We assume that there are K nodes which broadcast in the reservation period. Hence, the reservation period is TRE =K_ slot . When the nodedensityis high, the payload size S increases because the neighbor information field becomes bigger. The reservation period TRE also increases and the contention period (TCON = 50ms � TRE) will be decreased. Consequently, the collision probability wili increase due to many nodes attempt to broadcast packets in as small contention period. 3. ANALYTICAL MODEL FOR TIME SLOT ACQUISITION A. Markov chain in HTC-MAC For comparison with HER-MAC, we determine the averagenumberofnodeswhichacquireatimeslotwithinasync interval and the probability that all the nodes acquire a timeslot within n frames. Let K denotes the number of contending nodes in 2-hop neighborhood because if nodes are located at least three hop away, they can reuse the same time slot [7].The Markov chain of HTC-MAC is inherited from the MAC, as shown in Fig. 3a. Let N be the number of initially available time slots in async-interval,andbethetotalnumberofnodeswhichacquireatimeslot within n sync interval. X is a stationary discrete-time Markov chain with the transition probabilities illustrated in Fig. 3a.In this paper, we consider the case where K _ N. For the case K > N, it is useful to determine an optimal value for a number of time slots on the reservation period. Let P be the one-step transition probability matrix, and Pn be the n-step transition probability matrix. Then ,p( Xn = i) = Pn1;i+1; i = 0; :::;K: (1)The probability that all nodes acquire a time slot within n sync interval is Falln ; HTC�MAC = p(Xn = K) = Pn1;K+1: In this paper, we consider the case where K _ N. For the case K > N, it is useful to determine an optimal value for a number of time slots on the reservation period. Let P be the one-step transition probability matrix, and Pn be the n-step transition probability matrix. Then, p (Xn = i) = Pn 1;i+1; i = 0; :::;K: (1) The probability that all nodes acquire a time slot within n sync interval is Fall n;HTC�MAC = p(Xn = K) = Pn 1;K+1: (2) Let Y be the average number of nodes which successfully acquire a time slot within n frames. Then, we have E[Yn] = ΣK i=0, iP n 1;i+1:
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 3 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 7954 B. Markov chain in HER-MAC In this section, we determine formulas of the average number of nodes which acquire a time slot within a sync interval and the probability that all the nodes acquire a timeslot within n frames in HER-MAC. From the Markov chain [9] it is clear that the probability _ that a node transmits a HELLO or safety application packet in an arbitrary time slot can be expressed as Let p be the collision probability when more than one node transmit at the same time slot. Hence, we have Consequently, based on (4) and (5), variable _ and p can solved by the numerical methods as in [9].Note that 0 _ p _ 1and 0 _ _ _ 1.In every time slot during the HELLO interval, an agreement will be successfullymadewithprobability p suc, thus, we have p suc = K_ (1 � _ )K�1: (6)In the p-persistent CSMA/CA, the back off interval is based on the geometric distribution with probability p suc [10]. Fig. 3.1 Markov chain in HER-MAC 4. PERFORMANCE EVALUATION To validate HTC-MAC, we use an event-driven simulation program written in Mat lab. For comparison with HTC- MAC, we also simulate HER-MAC where a HELLO packet configured to useAccessClass3(AC3)withCW=8andCW = 4 due to it is a safety message using the highest priority scheme [11]. In Fig. 4, we compare HTC-MAC with HER- MAC for CW = 8 and CW = 4 in a dense scenario (N = 20; K = 10). In HER-MAC, if nodes use CW = 8, all nodes can successfully acquire a time slot after6frames.However,nodesusing CW=4need12framestosuccessfullyacquirea time slot. In the same condition, in HTC-MAC, after5 frames, all nodes have successfully acquired their time slots. Using Eq. (10) and (2), the probability that all nodes acquire time slots within n frames is presented in. The averagenumber of nodes which successfully acquire a time slot and Fall have same results. Hence, the rate of successful time slot acquisitioncan be shown by using the probability or average numberofnodeswhichacquirea time slot. we evaluate Eq. (5) and (10) with the same thenumberofavailabletimeslots, N=20.Wetaketheaverage number of nodes which acquire a time slot within each frame by running100times.Inaddition,inEq.(10),wetake the floor function ⌊E[Xi]⌋. Hence, the average number of nodes which acquire a time slot within 3 framesasshown
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 3 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 7955 in Fig. 6 with K= 5 and K = 10, which are close together. Consequently, than alsoclosetogetherasshowninFig.5.If we take the ceiling function ⌈E[Xi]⌉, the rate of time slot acquisition is faster than taking the floor function .In Fig. 6, we fix the number of available time slots andvary the number of contending nodes, K. Forcomparison,wesimulateHER-MACwithits best performing parameter ,CW = 8. If K is 5, HTC-MAC and HER-MAC have the same rate of successful time slot acquisition. When K increases,the rate of successful time slot acquisition in HTC-MAC Is higher than HER-MAC. WhenK equals N, the collision probability when more than one node transmit at the same time slot in Eq (5) increases. Hence, the probability that all p[Xi = E[Xi]] =8>><>>:0; Fig. 4.1 Performance Evaluation 5. CONCLUSION In this paper, we propose an efficient time slot acquisition on the hybrid TDMA/CSMA mutli-channel MAC in VANETs. HTC-MAC not only eliminates unnecessary control overhead but also increases the throughput on the control channel. The analysis and simulation results prove that HTC-MAC outperforms HER-MAC in terms of the average number of nodes which acquire a time slot. However, HTC-MAC requires a larger ANC’s payload size to broadcast its neighbors’ information when the node density is high. REFERENCES [1] H. Wu, A. Wang, Q. Zhang, and X. Shen, “IEEE 802.11e enhanced distributed channel access (EDCA) throughput analysis,” in Communications, 2006. ICC ’06. IEEE International Conference on, vol. 1, 2006, pp. 223–228. [2] [2] IEEE Standard for Wireless Access in Vehicular Environments (WAVE) Multi-channelOperation,Sep,2010. [3] D. N. M. Dang, H. N. Dang, V. Nguyen, Z. Htike, and C. S. Hong, “HER-MAC: A hybrid efficient and reliable MACfor vehicular ad hoc networks,” in Advanced Information Networking and Applications (AINA), 2014 IEEE 28th International Conference on, May 2014, pp. 186–193. [4] F. Borgonovo, A. Capone, M. Cesana, and L. Fratta, “ADHOC MAC: New MAC architecture for ad hoc networks providing efficient and reliable point-to-point and broadcast service.” Wireless Netw., 2004, pp. 359–366 Vol. 10.