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An improved multicast based energy efficient opportunistic data scheduling algorithm for VANET
Accepted Manuscript Regular paper An Improved Multicast Based Energy Efficient Opportunistic Data Scheduling Algorithm for VANET Anurag Shrivastava, Prashant Bansod, Kamlesh Gupta, Shabbir N. Merchant PII: DOI: Reference:
S1434-8411(17)30775-6 https://doi.org/10.1016/j.aeue.2017.10.011 AEUE 52088
To appear in:
International Journal of Electronics and Communications
Received Date: Revised Date: Accepted Date:
6 April 2017 6 September 2017 8 October 2017
Please cite this article as: A. Shrivastava, P. Bansod, K. Gupta, S.N. Merchant, An Improved Multicast Based Energy Efficient Opportunistic Data Scheduling Algorithm for VANET, International Journal of Electronics and Communications (2017), doi: https://doi.org/10.1016/j.aeue.2017.10.011
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An Improved Multicast Based Energy Efficient Opportunistic Data Scheduling Algorithm for VANET Title Page
An Improved Multicast Based Energy Efficient Opportunistic Data Scheduling Algorithm for VANET
Following are the authors: (1) Anurag Shrivastava, M. Tech.
Department of Electronics & Telecommunication Engineering, SGSITS, Indore, MP, 452003, India ([email protected]). (2) Prashant Bansod, Ph.D.
Department of Electronics & Instrumentation Engineering, SGSITS, Indore, MP, 452003, India ([email protected]) (3) Kamlesh Gupta, Ph.D.
Department of Electronics & Communication Engineering, AITR, Indore, MP, 453771, India ([email protected]) (4) Shabbir N. Merchant, Ph.D.
Department of Electrical Engineering, IIT Bombay, Mumbai, MH, 400076, India ([email protected])
2 Anurag Shrivastavaa,*, Prashant Bansodb, Kamlesh GuptaC and Shabbir N. Merchantd a
Department of Electronics & Telecommunication Engineering, SGSITS, Indore, MP, 452003, India ([email protected])
b
Department of Electronics & Instrumentation Engineering, SGSITS, Indore, MP, 452003, India ([email protected])
c
Department of Electronics & Communication Engineering, AITR, Indore, MP, 453771, India ([email protected])
d
Department of Electrical Engineering, IIT Bombay, Mumbai, Maharashtra, 400076, India ([email protected])
Abstract—A road side unit in VANET is capable of providing various infotainment services. With the increase in demand for data download amongst the vehicular users, power consumption, both at vehicle end and the road side unit is also increasing proportionally. Hence, there is a need for improving energy efficiency as well as the throughput of the system. In this work, we focus on improving energy efficiency and throughput of the road side unit. We propose an improved multicast based energy efficient opportunistic data scheduling algorithm. We estimate optimum data rate and optimum number of users having good channel conditions, thus obviating the need to know the channel state information at the transmitter. The group of users so selected is served by multicasting the service at optimal data rate. Results show that the proposed algorithm is not only energy efficient but also throughput optimal. It is also possible to estimate the maximum throughput accurately and with low search complexity (O(N)) using the proposed method. Simulations are done for two different cases in order to test the flexibility of the algorithm—one, when no new user is entertained until all the initial users get served; two, new users can enter the system in every time slot. Keywords—VANET,
Wireless
communications,
Energy
efficiency,
Opportunistic
scheduling, Multicast 1. INTRODUCTION Vehicular Adhoc Network (VANET) is a wireless technology capable of providing infotainment services to the vehicles. There are two modes in VANET—Vehicle to Vehicle (V2V), and Vehicle to Infrastructure (V2I) also called road side unit (RSU). Energy
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consumption is not a major issue in V2V mode because vehicles continuously get recharged while in motion. In V2I mode, sources such as battery, sunlight and wind are used to power the RSU on the highways and rural areas where regular sources are not available. This introduces a challenge to reduce power consumption in transmission of data at RSU [1, 2]. One of the ways to achieve this reduction in power consumption is to do intelligent and energy efficient data scheduling. Data scheduling is a method to allocate resources amongst the users. A scheduling algorithm mainly decides which user will transmit or receive and the corresponding time of transmission or reception. Various data scheduling schemes are suggested in the literature [3], for achieving different Quality of Service (QoS) objectives such as minimizing delay, maximizing throughput or minimizing energy. Some authors [14, 15] consider speed, deadline, data size and number of users demanding a service for data scheduling in VANET. A
algorithm and its extension
algorithm are proposed
by Zhang et al. [14], where D is deadline and S is data size and pending requests (N) of a service. Here, N improves fairness of the system. Shrivastava et al. [15] propose a new priority based NDS algorithm with broadcast scheduling in VANET. The idea behind using broadcast is to improve throughput but they do not consider energy efficiency. In wireless communication, channel statistics are dynamic in nature due to fading and multipath. Zhao et al. [4] propose an energy efficient scheduling algorithm with transmission modulation and deadline constraint. The emphasis of this algorithm is on scheduling number of bits to be transmitted in a given time slot. Koutsakis et al. [5] propose a bandwidth scheduling algorithm along with call admission control aiming high speed wireless users for different multimedia traffic. They claim that by using channel prediction a better resource allocation can be done. The channel state remains constant for a fixed time slot, which is proportional to coherence time. Channels are assumed to be in two states, either good or bad. A data scheduling scheme which can exploit channel conditions of different users, such that the
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users with good channels are scheduled first, is called opportunistic data scheduling. This is so because when channel condition is good, less power is required for the transmission of data. Knopp and Humblet [6], proposed for the first time the opportunistic scheduling for improving capacity of the system using multi user diversity. Opportunistic schedulers for minimizing the transmission power are also proposed in the literature. Amongst the users who demand similar type of service, the users with good channel conditions form a multicast group. Instead of serving each user in a unicast manner, multicasting can be used to serve them simultaneously. An interesting analysis of multicast throughput and energy efficiency for wireless sensor networks using Extreme Value Theory (EVT) is done by Bahl et al. [7], however, in our work, we have done these analyses for adhoc networks without using EVT. A comparison between direct and multi-hop communication for energy efficient multicast scheduling is discussed by Qiang et al. [12]. In conventional method of multicast based opportunistic scheduling [10], the base station arranges all the received Signal-to-Noise Ratios (SNRs) in the descending order and multicast the service at a rate decided by the worst channel condition (lowest SNR). Another such algorithm is median opportunistic multicast scheduling (median OMS) [8, 9], in which top half of the users are served. Median OMS exhibits better throughput than the traditional opportunistic multicast scheduling. The problem with conventional and median OMS schemes is that they do not guarantee the optimal throughput or the optimal energy per bit. Veshi et al. [11] propose Opportunistic Multicast Optimal group Size (OppMC–OS) algorithm, which assumes that the Channel State Information (CSI) is available at the base station. In OppMC–OS strategy, the user with kth highest SNR value is targeted. In a time slot, k out of N users get served using multicast. Each of these k users are served with a data rate, R=B log2(1+ SNRk). The total throughput of the system is kB log2(1+ SNRk). Therefore, k should be chosen such that it maximizes the system throughput. In the multicast based opportunistic scheduling algorithms including OppMC– OS, the same data is transmitted in every time slot until it is received by all the requesting
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users. The major problem with such a strategy is that some users may get repeatedly selected and thus get redundant data, which decreases the throughput of the system. It is also assumed that CSI at the transmitter is known through the feedback channel in conventional and OppMC–OS schemes, which is not always practical. In view of these problems, Qian et al. [13] propose a multicast based scheduling algorithm based on adaptive user selection (A– OMS) with a view to improve the throughput and decrease the search complexity. Users once get selected and received desired data, are not considered in subsequent time slots, hence user selection becomes adaptive. In A–OMS algorithm, the adaptive selection of users is done by approximating the system throughput statistically using Estimated System Throughput Matrix (ESTM). The A–OMS algorithm is not effective for small number of users because the estimates are not very accurate. Also, for finding the maximum throughput in each time slot, a row of ESTM is scanned, which increases the search complexity with increased number of users. Looking at this, there is a need of an improved OMS algorithm which can estimate the maximum throughput more accurately and with low search complexity. Such an algorithm should work efficiently for any number of users. Considering these issues, we propose an improved multicast based opportunistic data scheduling algorithm for VANET in this paper. The rest of the paper is organized as follows: The system model is discussed in Section 2, whereas Section 3 has details of the proposed algorithm. In Section 4, results are shown where the proposed algorithm is compared with some existing algorithms. Finally, conclusion with possible extension of the work is presented in Section 5.
2. SYSTEM MODEL An RSU is considered which provides infotainment services to the vehicles within its coverage area. The RSU collects requests from the vehicular users. Vehicles are assumed to be equipped with an On Board Unit (OBU) through which requests for services can be sent
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and data can be received. The GPS module in the OBU helps in collecting coordinates, speed and direction of a vehicle. Time is divided into slots. Each time slot is equivalent to the coherence time during which the channel remains constant. We assume slow Rayleigh fading channels. Further, we neglect the effect of shadowing as we consider a VANET scenario with the assumption that obstacles are fewer in number. The optimum value of SNR of a channel at which the throughput of the system is maximum or equivalently the energy per bit is minimum is calculated. This optimum SNR is used to decide the rate at which the data is to be transmitted; therefore, the knowledge of CSI is not required at RSU. The users with SNR greater than the optimum SNR can decode this data. The energy metric, which we define as energy per bit (U) is given by (1). U=
joule per bit
(1)
where P denotes the transmit power, which is a constant; and T denotes the throughput, which is calculated for a time slot and is given by (2). (2) In (2), k and R respectively denote the number of users with good channel conditions and the rate at which the data is multicast. The objective is to minimize U which can be stated as (3). =
=
joule per bit
(3)
From (1), U is inversely proportional to T. Since P is constant, the minimization of energy per bit is equivalent to maximizing the throughput. Accordingly, (3) can be restated as (4). (4)
The bit rate R can be given by Shannon’s formula as SNR of the channel. Substituting this expression of R in (4), we get
. Here,
denotes
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(5)
Further, to estimate k, we assume that there are n number of users with good channel conditions out of N users who have demanded certain service. The number of users, n, can be modeled as Binomial distribution with the probability mass function given in (6) (6) where
is the probability that a channel is good and this probability can be further calculated
as per (7). (7) A channel is considered as good if its SNR, ᴦ, is more than a threshold, γ. The cumulative distribution function of SNR is defined as (8) For the assumed Rayleigh channel, the SNR is exponentially distributed [7]. Since,
,
where N0 is power spectral density of Gaussian noise, B is bandwidth of the channel and |h|2 is the channel gain. Therefore,
, which on substitution in (7) gives (9)
As the number of users with good channel condition in a time slot is Binomial distributed, we estimate k as its mean value (10). (10) Equation (5) can be rewritten, after substituting this value of k, as (11)
The throughput, T, is a concave function; it has a unique maximum at an optimal value of the threshold SNR,
. This
can be calculated using (12), which in turn gives (13). (12)
8
(1+
(13)
For a given , by using (13), the corresponding
can be calculated for which the throughput
obtained is maximum. In a given time slot, a multicast group of k users is formed which is served at a rate,
. The maximum throughput and the corresponding
minimum energy per bit for the ith time slot are given by (14) and (15) respectively. (14) (15) In the next section, we discuss the proposed algorithm which uses various parameters such as optimal SNR, optimum multicast group size, optimal data rate and maximum throughput, derived in this section. 3. AN IMPROVED MULITICAST BASED ENERGY EFFICIENT OPPORTUNISTIC DATA SCHEDULING ALGORITHM
FOR VANET
In this section, we propose an improved multicast based energy efficient opportunistic data scheduling algorithm for VANET. The algorithm allows an RSU to schedule the data demanded by the users depending upon their channel conditions. The emphasis of the work is on improving the energy efficiency and equivalently the throughput of RSU. In the previous section, it was shown that the optimum average number of users with good channel conditions (k) and optimum threshold SNR (
depend upon the average channel SNR ( ).
After RSU collects the service request from different users, it runs Algorithm 1 in each time slot.
Algorithm 1 1. RSU forms an optimal multicast group of users with good channel conditions ( for one time slot 2. Data is transmitted at a rate
)
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3. Maximum throughput obtained in each time slot is 4. Users served in a time slot are not considered in subsequent time slots to avoid redundant data delivery. 5. Only un-served users are considered in subsequent time slots. 6. In each time slot, Steps 1 to 4 are repeated until all the users get served. _________________________________________________________________ In each time slot, a multicast group (of users with good channel conditions) is served. The users with bad channel conditions wait for their chance in subsequent time slots. In the proposed algorithm, the users with good channel conditions are estimated using
since the
CSI at the transmitter is not known. The users served in a time slot do not accept the data in subsequent time slots. This is so because the same data is transmitted in every time slot. We assume that l time slots are required to serve all the users who demand a service. The throughput averaged over l time slots is given by (16), whereas the average energy per bit (
is given by (17). (16) =
(17)
In the A–OMS strategy [13], an ESTM is formed a priori and in each time slot the maximum throughput is searched using this matrix. We define, the number of elements searched in a matrix in order to find the maximum throughput, as the search complexity. In the A–OMS algorithm the worst case search complexity for N users is
. Unlike A–
OMS algorithm, in the proposed algorithm, for calculating the maximum throughput, the estimation matrix is not required. The proposed algorithm uses (14) for calculating the maximum throughput, which makes the calculations fast, thereby reducing the search complexity of the system to
. We prove this in Appendix A.
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In the proposed work, the optimal number of users in the multicast group is also estimated in each time slot. Obviously, this estimation should be close to the actual value (i.e., the value when CSI is known). Let there be n number of users in the multicast group out of N users, with CSI known. As per the proposed algorithm, the optimal number of users in the multicast group without CSI is estimated as k = Np. The accuracy of estimation with 90% confidence interval is calculated using Hoeffding bound [16]. This is given by (18). (18) where
is a real non-negative value. A plot between
and the corresponding minimum
number of users required in the multicast group for 90% confidence interval considering a 60% probability of the channel being good is shown in Figure 1. From the figure, it is clear that as
increases from 0.1 to 1, the minimum multicast group size required to maintain 90%
confidence interval decreases. It may be noted that
represents the difference between the
actual multicast group size (n) and the estimated multicast group size (k). Even for high values of
(nearly 1), the group size is very small (2 or 3 users). This ensures a good
estimation accuracy of the proposed algorithm. A comparison between the proposed OMS with Hoeffding bound and A–OMS algorithm is also shown in the same figure. It can be concluded that as
increases, the difference between the minimum number of users in
multicast groups for both of the algorithms also increases. This increase in the difference is due to the fact that A–OMS does not work well for small group sizes.
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Fig.1. Hoeffding bound applied on Proposed and A–OMS algorithms 4. SIMULATIONS AND DISCUSSIONS In this section, we present the simulation results and analysis of the proposed algorithm and its comparison with the OppMC–OS and A–OMS schemes. We consider the Rayleigh fading channels and show the simulation results for two different cases. Case-I: No new arrivals are allowed until all the previous users get served. Case-II: New arrivals in the beginning of every time slot is permitted. For both of these cases, the proposed algorithm is compared with OppMC–OS and A–OMS on the basis of two parameters, namely, the average throughput and the average energy per bit. The simulation setting is summarized in Table 1. Table 1 Simulation parameters System Bandwidth (W)
10 MHz
Noise Power Spectral Density (N0)
-174 (dBm/Hz)
Cell Radius
500 m
Time Slot (Ts)
10 ms
Average SNR ( )
5 to 20
Average Arrival Rate (λ)
2 arrivals/time slot and
(Poisson distribution)
5 arrivals/time slot
Transmission Power (P)
1W
Data Rate (R)
3 to 40 Mbps
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4.1 Performance comparison on the basis of average throughput For the OppMC–OS and the A–OMS algorithms, (19) and (20) respectively are used to calculate the average throughput. (19) where
denotes the number of users in the multicast group in the ith time slot such that it
gives the maximum throughput. (20) where
is the number of users in the multicast group selected out of
users in the ith time
slot such that it gives the maximum throughput. As already mentioned, the simulations are done for two cases (Case-I and Case-II). In Case-I, there is an initial number of users with similar data (service) requests. In each time slot, the selected users (with good channel conditions) form a multicast group and are served. This continues until all the users with initial requests get served. No new user is entertained during this time. In Case-II, similar to Case-I, there are initial users requesting the same data. However, in every time slot new users can also be entertained and if their channel conditions are good, they are considered for receiving the service. These new users, along with the initial users are served by the RSU. The number of new users arriving at the start of each time slot is random and is modeled as a Poisson random variable with average arrival rate (per time slot) of λ. Case-II, which makes the system flexible and more practical, is the general form of Case-I. In other words, Case-I may be treated as a special case of Case-II with λ=0. Figures 2(a), (b) and (c) show the simulation and analytical (theoretical) results for the proposed as well as the other two algorithms as applied for Case-I. These results are shown in the form of graphs between the average throughput and the number of users requesting a service, for
=5, 10 and 20. The analytical results are obtained using
(16), (19) and (20). The Monte Carlo simulation results are obtained by averaging the
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maximum throughput over 10,000 trials. It can be observed from the figures that the analytical results closely match with the simulation results thereby validating them. Results in Figures 2(a), (b) and (c) further show that for all the three algorithms, the average throughput increases with the increase in the number of users as well as the increase in
. It is evident from (14) and (16) that the average throughput mainly depends upon the
number of users in the multicast group (
) and the number of time slots required to
serve all the requesting users (l). With the increase in
and the number of requesting users,
the multicast group size formed in each time slot is large, therefore, all the users get served with small value of l. This results in high average throughput. It is also observed from Figures 2(a), (b) and (c), that the proposed algorithm has better average throughput as compared to A–OMS and OppMC–OS. The throughput of OppMC–OS is poor, as the multicast group formed in each time slot may select users already served, multiple times. Thus, a particular user may get redundant data, which affects the throughput. The A–OMS has better throughput as compared to OppMC–OS, since the user once served is not considered in subsequent time slots. However, A–OMS scheme does not perform efficiently for small multicast group sizes. This is so because for small group sizes the average throughput is poor for A–OMS according to (20). The proposed algorithm, on the other hand, gives better throughput even for small group sizes and it also ensures that the users do not get repeatedly selected for receiving the same data. It is also seen that when the number of users are fewer, the difference between the average throughputs of all the three algorithms is very small. This difference increases with the increase in the number of users.
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Fig. 2. Average throughput vs. number of users for Case-I with (a)
=5, (b)
=10 and (c)
=20
Figures 3(a), (b) and (c) depict the average throughput plots for Case-II for different values of λ and . All the plots are obtained with some initial number of users demanding a service. For Case-II, in every time slot, new users for the same service are also included with λ =2 and 5. From these figures, it is clear that in this case also, with the increase in the number of initial users and that in
, the average throughput increases. The reason behind
this increase is the same as that is discussed for Case-I. However, because of the inclusion of new users in every time slot, the number of slots (l) required to serve all the users (initial and newly included) is more than that required for Case-I. Therefore, the average throughput for Case-II is less than that for Case-I, which is also evident from (16). For the same value of if we compare the plots for different values of λ (including λ=0, Case-I), it is observed that
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with the increase in λ the average throughput decreases. This decrease is due to the fact that with the increase in λ, more users enter in each time slot, which makes the system slow.
Fig. 3. Average Throughput for Case-II with λ =2 and 5, (a)
=5, (b)
=10 and (c)
=20
Table 2 Variation in average throughput for different cases Percentage change in average throughput when the number of users varies from 5 to 40 for :
Simulated Algorithms
Case-I
Case-II
Case-II
λ= 0
λ= 2
λ= 5
=5
=10
=20
=5
=10
=20
=5
=10
=20
Proposed Algorithm
337.5 %
400.0 %
400.0 %
80.8 %
150.0 %
151.2 %
14.2%
20.0 %
21.6%
A–OMS
273.3 %
400.0 %
410.0 %
74.4 %
108.0 %
125.6 %
12.5%
16.1 %
17.5%
OppMC–OS
266.7 %
250.0 %
300.0 %
16.3 %
20.0 %
25.7 %
10.0%
15.0 %
16.1%
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In Table 2, the percentage increase in the average throughput of the three algorithms is presented, for the number of users varying from 5 to 40 and for both the cases. For Case-I, it is observed that there is a rapid increase in the average throughput with the number of users. With the increase in that with higher
the change in average throughput is also fast. The reason for it is
large multicast groups can be formed and served quickly. Further, in
OppMC–OS the effect of variation in the number of users is not significant and thus, the change in average throughput is small. From Table 2, it can also be concluded that for CaseII, the increase in the average throughput is not as significant as it is for Case-I. This is so because of the addition of new users in every time slot. This is also the reason for decrease in the variation in throughput with the increase in λ. As discussed for Case-I, for Case-II also there is an increase in the average throughput with the increase in
however, this change is small. Results also show that for
both the cases, the average throughput changes most rapidly in the proposed algorithm. Overall, from Figures 2 and 3, it can be seen that the average throughput of the proposed algorithm is better than that of A–OMS and OppMC–OS algorithms. It can also be observed that in both the cases, for small number of requesting users, the average throughputs of the three algorithms are nearly same with the proposed algorithm exhibiting slightly better performance. However, as the number of users increases, the proposed algorithm exhibits significantly improved performance. The reason behind the similar performance of the algorithms for small number of users is that to serve small number of users, the number of time slots (l) required are nearly same. However, for larger number of users, the time slots (l) required is fewer in the proposed algorithm as compared to the other two algorithms. Table 3 gives a comparison of the three algorithms for different values of 40 users requesting a service. For Case-I, with the increase in
for
the difference in the average
throughput of the proposed and A–OMS algorithms decreases. Also, the difference between the proposed and OppMC–OS algorithms increases with the increase in .
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Table 3 Comparison of average throughput (in Mbps) for 40 users at different -
Proposed
Case-I
Case-II
Case-II
λ= 0
λ= 2
λ= 5
A-OMS
OppMC–
Proposed
A-OMS
OS
OppMC–
Proposed
A-OMS
OS
OppMC-OS
=5
19.0
15.0
13.2
8.5
7.5
3.2
4.0
2.3
1.1
=10
26.0
20.0
14.0
15.0
12.5
4.8
4.2
3.6
2.3
=20
32.5
29.0
19.7
20.1
17.6
6.3
7.3
4.7
3.1
4.2 Performance comparison on the basis of average energy per bit An algorithm that requires minimum energy per bit ( energy efficient algorithm. From (17),
in transmission is the most
is inversely proportional to the maximum
throughput. Therefore, it is obvious that whichever algorithm has better throughput, it is more energy efficient as it has less transmission energy per bit. For the cases (Case-I and Case-II), plots between average energy per bit and the number of requesting users are shown in Figures 4 and 5 respectively. The average energy per bit
is reciprocal of the average throughput. The result
analysis for the average throughput of different algorithms is already discussed in the previous sub-section. In this sub-section, we present the analysis related to average energy per bit. It may also be observed from Figure 4 that the average energy per bit plots with respect to the number of users, as obtained through Monte Carlo simulations closely match the ones obtained analytically.
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Fig. 4. Average energy per bit vs. number of users for Case-I with (a)
=5, (b)
=10 and (c)
=20
It can be inferred from Figures 4 and 5, that the requirement of the average energy per bit (Uavg) decreases with the increase in the number of initial users as well as . This is due to the fact that as the number of initial users and
increases, large multicast groups are
formed in each time slot. Therefore, in the same amount of energy, more bits are transmitted. For Case-I, for large number of users, the proposed and A–OMS algorithms have nearly the same Uavg. This is so because the difference in the average throughput of these two algorithms is also small for the large number of users (see Table 3). Figures 5(a), (b) and(c) depict Case-II for = 5, 10 and 20. From the plots it is clear that the proposed algorithm is most energy efficient. For λ=2, Uavg of the proposed algorithm is smaller than that for λ=5. For Case-II, the proposed algorithm is more energy efficient when λ=2. Across all the plots in Figure 5, for λ=2, with increase in the number of initial users, Uavg decreases for the proposed and A-OMS algorithms but remains nearly constant for OppMC-OS algorithm. The energy
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efficiency for Case-I is better than that for Case-II with λ=2 and λ=5 in all the algorithms. It can be observed from Table 3, which is for 40 initial users, that the average throughput for Case-I is better than that for Case-II and hence less energy per bit is consumed for Case-I.
Fig. 5. Average energy per bit for Case-II with λ =2 and 5, (a)
=5, (b)
=10 and (c)
=20
5. CONCLUSION In this paper, we proposed an improved multicast based energy efficient opportunistic data scheduling algorithm for VANET. We gave a formulation for obtaining the optimum value of SNR (γ*), which maximizes the average throughput (minimizes the average energy per bit) of a V2I system. The optimal SNR is also useful in the estimation of the optimal multicast group size without the knowledge of channel state at the road side unit. This optimal multicast group is served in a time slot at an
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optimal rate. The road side unit keeps on forming multicast groups and serving them until all the users get served. The algorithm that we suggest is compared with two recently proposed algorithms, on the basis of average throughput and the average energy per bit. The comparison is made for two cases (one—no new service request is accepted until the initial ones get served, two—new service requests may be accepted in every time slot). In both the cases, with increase in the number of users and average SNR, the throughput increases rapidly in the proposed algorithm as compared to the other two algorithms. As average transmission energy per bit is inversely proportional to the average throughput, it is concluded that the proposed algorithm outperforms the other two algorithms, since it requires minimum average energy per bit. In particular, Case-I is found to be more energy efficient than Case-II, for large number of users. It may be noted that not only does the proposed algorithm work for multicast groups, it also works well for unicast and broadcast groups. All the algorithms mentioned in this work consider only single-hop communication, which has the advantage of small service delay. However, single-hop communication can only serve a small geographical area.
This problem can be
addressed using multi-hop communication with relays. But multi-hop communication poses other problems such as increased delay and power consumption. The increase in delay is caused due to the need for relay selection in each time slot and also due to the Amplify and Forward, or Decode and Forward modes at relays. This latter mode also results in the increased power consumption. It will be interesting to address these problems associated with multi-hop communication. Once it is done, multi-hop communication could be a better alternative for the data scheduling problem as it covers a larger geographical area. However, it may be noted that the estimation of channel state information for such cases would become extremely challenging. These issues are currently being investigated.
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Appendix A. Computation of worst case search complexity We compare worst case search complexities of A-OMS and the proposed algorithms for N users. In A-OMS algorithm, the search of maximum throughput is done in each time slot by scanning a row of ESTM. The elements of ESTM are calculated using (20), for all possible combinations of (
and
. The rows of ESTM corresponds to the number of users
) in the beginning of a time slot, whereas the columns denote the number of users selected
to be served ( ) such that the maximum throughput in a particular time slot is obtained. Elements for which
≥
is assigned a value zero, since
should be smaller than
. On
the other hand, for the proposed algorithm the estimation matrix is not formed; rather, in each time slot, (14) is used to calculate the maximum throughput. Now, we calculate the worst case search complexity for A-OMS and Case-I of the proposed algorithm. The worst case in multicast occurs when multicast group size is one (i.e., unicast). The ESTM is a lower triangular matrix, therefore, in each time slot, fewer elements in a row are to be scanned to find the maximum throughput. In the first time slot, N-1 elements, and in the last time slot only one element is scanned. To find the total number of elements scanned to serve all the N requesting users in the worst case for O-AMS algorithm, we sum up the number of elements scanned in each time slot as shown in (A.1) (A.1) (A.2) (A.3) Hence, for A-OMS, the search complexity for serving all the N users is for large N. Similarly, in the worst case for the proposed algorithm, only one user is served in each time slot; therefore, for serving all N users the search complexity is
.
22
References [1] Eze EC, Sijing Zhang , Enjie Liu. Vehicular ad hoc networks (VANETs): Current state, challenges, potentials and way forward. In: 20th IEEE International Conference on Automation and Computing (ICAC): Sept. 2014, p 176-18. [2] Younghyun Kim, Jaeduck Ko, Wonjung Kim, Sangheon Pack. A measurement study on internet access in vehicular Wi-Fi networks.
In: 72nd IEEE Vehicular Technology
Conference Fall (VTC 2010-Fall): Sept. 2010, pp.1-5. [3] Goldsmith AJ, Wicker SB. Design challenges for energy-constrained ad hoc wireless networks. IEEE Wireless Communications Aug. 2002; 9(4): 8-27. [4] Zhao X, Wang Jun, Feng M, Wang Jin.
Energy-Efficient Scheduling over Fading
Channels with Transmission Modulation and Deadline Constraints.
AEU-International
Journal of Electronics and Communications Jun 2012; 66(6): 491-94. [5] Koutsakis P, Vafiadis M, Papadakis H. Prediction-based resource allocation for multimedia traffic over high-speed wireless networks. AEU-International Journal of Electronics and Communications. Nov 2006; 60(10): 681-9. [6] Knopp R , Humblet P. Information capacity and power control in single cell multiuser communications. In: Proceedings 1995 of IEEE ICC, p. 331-335. [7] Bahl N, Sharma AK, Verma HK. Asymptotic multicast throughput analysis and energy efficiency in WSN under double Nakagami fading channel using Extreme value theory. AEU-International Journal of Electronics and Communications. Sep 2015;69(9):1346-53. [8] Asadi A, Mancuso V.
A Survey on Opportunistic Scheduling in wireless
communications. Communications: Surveys & Tutorials, IEEE 2013; 15(4): 1671-88. [9] Gopala PK, Gamal HE. Opportunistic multicasting. In: Proceedings 2004 of IEEE 38th Asilomar Conference on Signals, Systems and Computers, p. 845-849.
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[10] Zhang, Xing Li, Qinzi, Huang Yu, Wang Wenbo. An energy-efficient opportunistic multicast scheduling based on superposition coding for mixed traffics in wireless networks. EURASIP Journal on Wireless Communications and Networking 2012; 2012 (1): 1-12. [11] Veshi, Erzim Kuehne, Alexander , Klein Anja. Comparison of different multicast strategies in wireless identically distributed channels. In: IEEE Wireless Communication and Networking Conference (WCNC): April2013, p. 3001-3006. [12] Qiang Xue, Pantelidou A, Matti Latva-aho. Energy Efficient scheduling and power control for multicast data. In: IEEE Wireless Communication and Networking Conference (WCNC): March 2011, p. 144-149. [13] Qian Li, Zhiyong Feng, Wei Li, Aaron Gulliver T. A new multicast scheduling scheme for cellular networks. IEEE Wireless Communications Letters 2014; 3(1): 26-29. [14] Zhang Y, Zhao J, Guohong Cao. On scheduling vehicle roadside data access. In : Proceedings 2007 of the fourth ACM international workshop on Vehicular ad hoc networks, p. 9-18. [15] Shrivastava A, Merchant SN, Desai UB, Pandya B. Priority based NDS data scheduling algorithm for vehicle to hotspot communication. In: IEEE International Conference on Vehicular Electronics and Safety (ICVES) 2009: p.25-30. [16] Hoeffding W. Probability inequalities for sums of bounded random variables. Journal of the American statistical association 1963; 58(301): 13-30.
S1434-8411(17)30775-6 https://doi.org/10.1016/j.aeue.2017.10.011 AEUE 52088
To appear in:
International Journal of Electronics and Communications
Received Date: Revised Date: Accepted Date:
6 April 2017 6 September 2017 8 October 2017
Please cite this article as: A. Shrivastava, P. Bansod, K. Gupta, S.N. Merchant, An Improved Multicast Based Energy Efficient Opportunistic Data Scheduling Algorithm for VANET, International Journal of Electronics and Communications (2017), doi: https://doi.org/10.1016/j.aeue.2017.10.011
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1
An Improved Multicast Based Energy Efficient Opportunistic Data Scheduling Algorithm for VANET Title Page
An Improved Multicast Based Energy Efficient Opportunistic Data Scheduling Algorithm for VANET
Following are the authors: (1) Anurag Shrivastava, M. Tech.
Department of Electronics & Telecommunication Engineering, SGSITS, Indore, MP, 452003, India ([email protected]). (2) Prashant Bansod, Ph.D.
Department of Electronics & Instrumentation Engineering, SGSITS, Indore, MP, 452003, India ([email protected]) (3) Kamlesh Gupta, Ph.D.
Department of Electronics & Communication Engineering, AITR, Indore, MP, 453771, India ([email protected]) (4) Shabbir N. Merchant, Ph.D.
Department of Electrical Engineering, IIT Bombay, Mumbai, MH, 400076, India ([email protected])
2 Anurag Shrivastavaa,*, Prashant Bansodb, Kamlesh GuptaC and Shabbir N. Merchantd a
Department of Electronics & Telecommunication Engineering, SGSITS, Indore, MP, 452003, India ([email protected])
b
Department of Electronics & Instrumentation Engineering, SGSITS, Indore, MP, 452003, India ([email protected])
c
Department of Electronics & Communication Engineering, AITR, Indore, MP, 453771, India ([email protected])
d
Department of Electrical Engineering, IIT Bombay, Mumbai, Maharashtra, 400076, India ([email protected])
Abstract—A road side unit in VANET is capable of providing various infotainment services. With the increase in demand for data download amongst the vehicular users, power consumption, both at vehicle end and the road side unit is also increasing proportionally. Hence, there is a need for improving energy efficiency as well as the throughput of the system. In this work, we focus on improving energy efficiency and throughput of the road side unit. We propose an improved multicast based energy efficient opportunistic data scheduling algorithm. We estimate optimum data rate and optimum number of users having good channel conditions, thus obviating the need to know the channel state information at the transmitter. The group of users so selected is served by multicasting the service at optimal data rate. Results show that the proposed algorithm is not only energy efficient but also throughput optimal. It is also possible to estimate the maximum throughput accurately and with low search complexity (O(N)) using the proposed method. Simulations are done for two different cases in order to test the flexibility of the algorithm—one, when no new user is entertained until all the initial users get served; two, new users can enter the system in every time slot. Keywords—VANET,
Wireless
communications,
Energy
efficiency,
Opportunistic
scheduling, Multicast 1. INTRODUCTION Vehicular Adhoc Network (VANET) is a wireless technology capable of providing infotainment services to the vehicles. There are two modes in VANET—Vehicle to Vehicle (V2V), and Vehicle to Infrastructure (V2I) also called road side unit (RSU). Energy
3
consumption is not a major issue in V2V mode because vehicles continuously get recharged while in motion. In V2I mode, sources such as battery, sunlight and wind are used to power the RSU on the highways and rural areas where regular sources are not available. This introduces a challenge to reduce power consumption in transmission of data at RSU [1, 2]. One of the ways to achieve this reduction in power consumption is to do intelligent and energy efficient data scheduling. Data scheduling is a method to allocate resources amongst the users. A scheduling algorithm mainly decides which user will transmit or receive and the corresponding time of transmission or reception. Various data scheduling schemes are suggested in the literature [3], for achieving different Quality of Service (QoS) objectives such as minimizing delay, maximizing throughput or minimizing energy. Some authors [14, 15] consider speed, deadline, data size and number of users demanding a service for data scheduling in VANET. A
algorithm and its extension
algorithm are proposed
by Zhang et al. [14], where D is deadline and S is data size and pending requests (N) of a service. Here, N improves fairness of the system. Shrivastava et al. [15] propose a new priority based NDS algorithm with broadcast scheduling in VANET. The idea behind using broadcast is to improve throughput but they do not consider energy efficiency. In wireless communication, channel statistics are dynamic in nature due to fading and multipath. Zhao et al. [4] propose an energy efficient scheduling algorithm with transmission modulation and deadline constraint. The emphasis of this algorithm is on scheduling number of bits to be transmitted in a given time slot. Koutsakis et al. [5] propose a bandwidth scheduling algorithm along with call admission control aiming high speed wireless users for different multimedia traffic. They claim that by using channel prediction a better resource allocation can be done. The channel state remains constant for a fixed time slot, which is proportional to coherence time. Channels are assumed to be in two states, either good or bad. A data scheduling scheme which can exploit channel conditions of different users, such that the
4
users with good channels are scheduled first, is called opportunistic data scheduling. This is so because when channel condition is good, less power is required for the transmission of data. Knopp and Humblet [6], proposed for the first time the opportunistic scheduling for improving capacity of the system using multi user diversity. Opportunistic schedulers for minimizing the transmission power are also proposed in the literature. Amongst the users who demand similar type of service, the users with good channel conditions form a multicast group. Instead of serving each user in a unicast manner, multicasting can be used to serve them simultaneously. An interesting analysis of multicast throughput and energy efficiency for wireless sensor networks using Extreme Value Theory (EVT) is done by Bahl et al. [7], however, in our work, we have done these analyses for adhoc networks without using EVT. A comparison between direct and multi-hop communication for energy efficient multicast scheduling is discussed by Qiang et al. [12]. In conventional method of multicast based opportunistic scheduling [10], the base station arranges all the received Signal-to-Noise Ratios (SNRs) in the descending order and multicast the service at a rate decided by the worst channel condition (lowest SNR). Another such algorithm is median opportunistic multicast scheduling (median OMS) [8, 9], in which top half of the users are served. Median OMS exhibits better throughput than the traditional opportunistic multicast scheduling. The problem with conventional and median OMS schemes is that they do not guarantee the optimal throughput or the optimal energy per bit. Veshi et al. [11] propose Opportunistic Multicast Optimal group Size (OppMC–OS) algorithm, which assumes that the Channel State Information (CSI) is available at the base station. In OppMC–OS strategy, the user with kth highest SNR value is targeted. In a time slot, k out of N users get served using multicast. Each of these k users are served with a data rate, R=B log2(1+ SNRk). The total throughput of the system is kB log2(1+ SNRk). Therefore, k should be chosen such that it maximizes the system throughput. In the multicast based opportunistic scheduling algorithms including OppMC– OS, the same data is transmitted in every time slot until it is received by all the requesting
5
users. The major problem with such a strategy is that some users may get repeatedly selected and thus get redundant data, which decreases the throughput of the system. It is also assumed that CSI at the transmitter is known through the feedback channel in conventional and OppMC–OS schemes, which is not always practical. In view of these problems, Qian et al. [13] propose a multicast based scheduling algorithm based on adaptive user selection (A– OMS) with a view to improve the throughput and decrease the search complexity. Users once get selected and received desired data, are not considered in subsequent time slots, hence user selection becomes adaptive. In A–OMS algorithm, the adaptive selection of users is done by approximating the system throughput statistically using Estimated System Throughput Matrix (ESTM). The A–OMS algorithm is not effective for small number of users because the estimates are not very accurate. Also, for finding the maximum throughput in each time slot, a row of ESTM is scanned, which increases the search complexity with increased number of users. Looking at this, there is a need of an improved OMS algorithm which can estimate the maximum throughput more accurately and with low search complexity. Such an algorithm should work efficiently for any number of users. Considering these issues, we propose an improved multicast based opportunistic data scheduling algorithm for VANET in this paper. The rest of the paper is organized as follows: The system model is discussed in Section 2, whereas Section 3 has details of the proposed algorithm. In Section 4, results are shown where the proposed algorithm is compared with some existing algorithms. Finally, conclusion with possible extension of the work is presented in Section 5.
2. SYSTEM MODEL An RSU is considered which provides infotainment services to the vehicles within its coverage area. The RSU collects requests from the vehicular users. Vehicles are assumed to be equipped with an On Board Unit (OBU) through which requests for services can be sent
6
and data can be received. The GPS module in the OBU helps in collecting coordinates, speed and direction of a vehicle. Time is divided into slots. Each time slot is equivalent to the coherence time during which the channel remains constant. We assume slow Rayleigh fading channels. Further, we neglect the effect of shadowing as we consider a VANET scenario with the assumption that obstacles are fewer in number. The optimum value of SNR of a channel at which the throughput of the system is maximum or equivalently the energy per bit is minimum is calculated. This optimum SNR is used to decide the rate at which the data is to be transmitted; therefore, the knowledge of CSI is not required at RSU. The users with SNR greater than the optimum SNR can decode this data. The energy metric, which we define as energy per bit (U) is given by (1). U=
joule per bit
(1)
where P denotes the transmit power, which is a constant; and T denotes the throughput, which is calculated for a time slot and is given by (2). (2) In (2), k and R respectively denote the number of users with good channel conditions and the rate at which the data is multicast. The objective is to minimize U which can be stated as (3). =
=
joule per bit
(3)
From (1), U is inversely proportional to T. Since P is constant, the minimization of energy per bit is equivalent to maximizing the throughput. Accordingly, (3) can be restated as (4). (4)
The bit rate R can be given by Shannon’s formula as SNR of the channel. Substituting this expression of R in (4), we get
. Here,
denotes
7
(5)
Further, to estimate k, we assume that there are n number of users with good channel conditions out of N users who have demanded certain service. The number of users, n, can be modeled as Binomial distribution with the probability mass function given in (6) (6) where
is the probability that a channel is good and this probability can be further calculated
as per (7). (7) A channel is considered as good if its SNR, ᴦ, is more than a threshold, γ. The cumulative distribution function of SNR is defined as (8) For the assumed Rayleigh channel, the SNR is exponentially distributed [7]. Since,
,
where N0 is power spectral density of Gaussian noise, B is bandwidth of the channel and |h|2 is the channel gain. Therefore,
, which on substitution in (7) gives (9)
As the number of users with good channel condition in a time slot is Binomial distributed, we estimate k as its mean value (10). (10) Equation (5) can be rewritten, after substituting this value of k, as (11)
The throughput, T, is a concave function; it has a unique maximum at an optimal value of the threshold SNR,
. This
can be calculated using (12), which in turn gives (13). (12)
8
(1+
(13)
For a given , by using (13), the corresponding
can be calculated for which the throughput
obtained is maximum. In a given time slot, a multicast group of k users is formed which is served at a rate,
. The maximum throughput and the corresponding
minimum energy per bit for the ith time slot are given by (14) and (15) respectively. (14) (15) In the next section, we discuss the proposed algorithm which uses various parameters such as optimal SNR, optimum multicast group size, optimal data rate and maximum throughput, derived in this section. 3. AN IMPROVED MULITICAST BASED ENERGY EFFICIENT OPPORTUNISTIC DATA SCHEDULING ALGORITHM
FOR VANET
In this section, we propose an improved multicast based energy efficient opportunistic data scheduling algorithm for VANET. The algorithm allows an RSU to schedule the data demanded by the users depending upon their channel conditions. The emphasis of the work is on improving the energy efficiency and equivalently the throughput of RSU. In the previous section, it was shown that the optimum average number of users with good channel conditions (k) and optimum threshold SNR (
depend upon the average channel SNR ( ).
After RSU collects the service request from different users, it runs Algorithm 1 in each time slot.
Algorithm 1 1. RSU forms an optimal multicast group of users with good channel conditions ( for one time slot 2. Data is transmitted at a rate
)
9
3. Maximum throughput obtained in each time slot is 4. Users served in a time slot are not considered in subsequent time slots to avoid redundant data delivery. 5. Only un-served users are considered in subsequent time slots. 6. In each time slot, Steps 1 to 4 are repeated until all the users get served. _________________________________________________________________ In each time slot, a multicast group (of users with good channel conditions) is served. The users with bad channel conditions wait for their chance in subsequent time slots. In the proposed algorithm, the users with good channel conditions are estimated using
since the
CSI at the transmitter is not known. The users served in a time slot do not accept the data in subsequent time slots. This is so because the same data is transmitted in every time slot. We assume that l time slots are required to serve all the users who demand a service. The throughput averaged over l time slots is given by (16), whereas the average energy per bit (
is given by (17). (16) =
(17)
In the A–OMS strategy [13], an ESTM is formed a priori and in each time slot the maximum throughput is searched using this matrix. We define, the number of elements searched in a matrix in order to find the maximum throughput, as the search complexity. In the A–OMS algorithm the worst case search complexity for N users is
. Unlike A–
OMS algorithm, in the proposed algorithm, for calculating the maximum throughput, the estimation matrix is not required. The proposed algorithm uses (14) for calculating the maximum throughput, which makes the calculations fast, thereby reducing the search complexity of the system to
. We prove this in Appendix A.
10
In the proposed work, the optimal number of users in the multicast group is also estimated in each time slot. Obviously, this estimation should be close to the actual value (i.e., the value when CSI is known). Let there be n number of users in the multicast group out of N users, with CSI known. As per the proposed algorithm, the optimal number of users in the multicast group without CSI is estimated as k = Np. The accuracy of estimation with 90% confidence interval is calculated using Hoeffding bound [16]. This is given by (18). (18) where
is a real non-negative value. A plot between
and the corresponding minimum
number of users required in the multicast group for 90% confidence interval considering a 60% probability of the channel being good is shown in Figure 1. From the figure, it is clear that as
increases from 0.1 to 1, the minimum multicast group size required to maintain 90%
confidence interval decreases. It may be noted that
represents the difference between the
actual multicast group size (n) and the estimated multicast group size (k). Even for high values of
(nearly 1), the group size is very small (2 or 3 users). This ensures a good
estimation accuracy of the proposed algorithm. A comparison between the proposed OMS with Hoeffding bound and A–OMS algorithm is also shown in the same figure. It can be concluded that as
increases, the difference between the minimum number of users in
multicast groups for both of the algorithms also increases. This increase in the difference is due to the fact that A–OMS does not work well for small group sizes.
11
Fig.1. Hoeffding bound applied on Proposed and A–OMS algorithms 4. SIMULATIONS AND DISCUSSIONS In this section, we present the simulation results and analysis of the proposed algorithm and its comparison with the OppMC–OS and A–OMS schemes. We consider the Rayleigh fading channels and show the simulation results for two different cases. Case-I: No new arrivals are allowed until all the previous users get served. Case-II: New arrivals in the beginning of every time slot is permitted. For both of these cases, the proposed algorithm is compared with OppMC–OS and A–OMS on the basis of two parameters, namely, the average throughput and the average energy per bit. The simulation setting is summarized in Table 1. Table 1 Simulation parameters System Bandwidth (W)
10 MHz
Noise Power Spectral Density (N0)
-174 (dBm/Hz)
Cell Radius
500 m
Time Slot (Ts)
10 ms
Average SNR ( )
5 to 20
Average Arrival Rate (λ)
2 arrivals/time slot and
(Poisson distribution)
5 arrivals/time slot
Transmission Power (P)
1W
Data Rate (R)
3 to 40 Mbps
12
4.1 Performance comparison on the basis of average throughput For the OppMC–OS and the A–OMS algorithms, (19) and (20) respectively are used to calculate the average throughput. (19) where
denotes the number of users in the multicast group in the ith time slot such that it
gives the maximum throughput. (20) where
is the number of users in the multicast group selected out of
users in the ith time
slot such that it gives the maximum throughput. As already mentioned, the simulations are done for two cases (Case-I and Case-II). In Case-I, there is an initial number of users with similar data (service) requests. In each time slot, the selected users (with good channel conditions) form a multicast group and are served. This continues until all the users with initial requests get served. No new user is entertained during this time. In Case-II, similar to Case-I, there are initial users requesting the same data. However, in every time slot new users can also be entertained and if their channel conditions are good, they are considered for receiving the service. These new users, along with the initial users are served by the RSU. The number of new users arriving at the start of each time slot is random and is modeled as a Poisson random variable with average arrival rate (per time slot) of λ. Case-II, which makes the system flexible and more practical, is the general form of Case-I. In other words, Case-I may be treated as a special case of Case-II with λ=0. Figures 2(a), (b) and (c) show the simulation and analytical (theoretical) results for the proposed as well as the other two algorithms as applied for Case-I. These results are shown in the form of graphs between the average throughput and the number of users requesting a service, for
=5, 10 and 20. The analytical results are obtained using
(16), (19) and (20). The Monte Carlo simulation results are obtained by averaging the
13
maximum throughput over 10,000 trials. It can be observed from the figures that the analytical results closely match with the simulation results thereby validating them. Results in Figures 2(a), (b) and (c) further show that for all the three algorithms, the average throughput increases with the increase in the number of users as well as the increase in
. It is evident from (14) and (16) that the average throughput mainly depends upon the
number of users in the multicast group (
) and the number of time slots required to
serve all the requesting users (l). With the increase in
and the number of requesting users,
the multicast group size formed in each time slot is large, therefore, all the users get served with small value of l. This results in high average throughput. It is also observed from Figures 2(a), (b) and (c), that the proposed algorithm has better average throughput as compared to A–OMS and OppMC–OS. The throughput of OppMC–OS is poor, as the multicast group formed in each time slot may select users already served, multiple times. Thus, a particular user may get redundant data, which affects the throughput. The A–OMS has better throughput as compared to OppMC–OS, since the user once served is not considered in subsequent time slots. However, A–OMS scheme does not perform efficiently for small multicast group sizes. This is so because for small group sizes the average throughput is poor for A–OMS according to (20). The proposed algorithm, on the other hand, gives better throughput even for small group sizes and it also ensures that the users do not get repeatedly selected for receiving the same data. It is also seen that when the number of users are fewer, the difference between the average throughputs of all the three algorithms is very small. This difference increases with the increase in the number of users.
14
Fig. 2. Average throughput vs. number of users for Case-I with (a)
=5, (b)
=10 and (c)
=20
Figures 3(a), (b) and (c) depict the average throughput plots for Case-II for different values of λ and . All the plots are obtained with some initial number of users demanding a service. For Case-II, in every time slot, new users for the same service are also included with λ =2 and 5. From these figures, it is clear that in this case also, with the increase in the number of initial users and that in
, the average throughput increases. The reason behind
this increase is the same as that is discussed for Case-I. However, because of the inclusion of new users in every time slot, the number of slots (l) required to serve all the users (initial and newly included) is more than that required for Case-I. Therefore, the average throughput for Case-II is less than that for Case-I, which is also evident from (16). For the same value of if we compare the plots for different values of λ (including λ=0, Case-I), it is observed that
15
with the increase in λ the average throughput decreases. This decrease is due to the fact that with the increase in λ, more users enter in each time slot, which makes the system slow.
Fig. 3. Average Throughput for Case-II with λ =2 and 5, (a)
=5, (b)
=10 and (c)
=20
Table 2 Variation in average throughput for different cases Percentage change in average throughput when the number of users varies from 5 to 40 for :
Simulated Algorithms
Case-I
Case-II
Case-II
λ= 0
λ= 2
λ= 5
=5
=10
=20
=5
=10
=20
=5
=10
=20
Proposed Algorithm
337.5 %
400.0 %
400.0 %
80.8 %
150.0 %
151.2 %
14.2%
20.0 %
21.6%
A–OMS
273.3 %
400.0 %
410.0 %
74.4 %
108.0 %
125.6 %
12.5%
16.1 %
17.5%
OppMC–OS
266.7 %
250.0 %
300.0 %
16.3 %
20.0 %
25.7 %
10.0%
15.0 %
16.1%
16
In Table 2, the percentage increase in the average throughput of the three algorithms is presented, for the number of users varying from 5 to 40 and for both the cases. For Case-I, it is observed that there is a rapid increase in the average throughput with the number of users. With the increase in that with higher
the change in average throughput is also fast. The reason for it is
large multicast groups can be formed and served quickly. Further, in
OppMC–OS the effect of variation in the number of users is not significant and thus, the change in average throughput is small. From Table 2, it can also be concluded that for CaseII, the increase in the average throughput is not as significant as it is for Case-I. This is so because of the addition of new users in every time slot. This is also the reason for decrease in the variation in throughput with the increase in λ. As discussed for Case-I, for Case-II also there is an increase in the average throughput with the increase in
however, this change is small. Results also show that for
both the cases, the average throughput changes most rapidly in the proposed algorithm. Overall, from Figures 2 and 3, it can be seen that the average throughput of the proposed algorithm is better than that of A–OMS and OppMC–OS algorithms. It can also be observed that in both the cases, for small number of requesting users, the average throughputs of the three algorithms are nearly same with the proposed algorithm exhibiting slightly better performance. However, as the number of users increases, the proposed algorithm exhibits significantly improved performance. The reason behind the similar performance of the algorithms for small number of users is that to serve small number of users, the number of time slots (l) required are nearly same. However, for larger number of users, the time slots (l) required is fewer in the proposed algorithm as compared to the other two algorithms. Table 3 gives a comparison of the three algorithms for different values of 40 users requesting a service. For Case-I, with the increase in
for
the difference in the average
throughput of the proposed and A–OMS algorithms decreases. Also, the difference between the proposed and OppMC–OS algorithms increases with the increase in .
17
Table 3 Comparison of average throughput (in Mbps) for 40 users at different -
Proposed
Case-I
Case-II
Case-II
λ= 0
λ= 2
λ= 5
A-OMS
OppMC–
Proposed
A-OMS
OS
OppMC–
Proposed
A-OMS
OS
OppMC-OS
=5
19.0
15.0
13.2
8.5
7.5
3.2
4.0
2.3
1.1
=10
26.0
20.0
14.0
15.0
12.5
4.8
4.2
3.6
2.3
=20
32.5
29.0
19.7
20.1
17.6
6.3
7.3
4.7
3.1
4.2 Performance comparison on the basis of average energy per bit An algorithm that requires minimum energy per bit ( energy efficient algorithm. From (17),
in transmission is the most
is inversely proportional to the maximum
throughput. Therefore, it is obvious that whichever algorithm has better throughput, it is more energy efficient as it has less transmission energy per bit. For the cases (Case-I and Case-II), plots between average energy per bit and the number of requesting users are shown in Figures 4 and 5 respectively. The average energy per bit
is reciprocal of the average throughput. The result
analysis for the average throughput of different algorithms is already discussed in the previous sub-section. In this sub-section, we present the analysis related to average energy per bit. It may also be observed from Figure 4 that the average energy per bit plots with respect to the number of users, as obtained through Monte Carlo simulations closely match the ones obtained analytically.
18
Fig. 4. Average energy per bit vs. number of users for Case-I with (a)
=5, (b)
=10 and (c)
=20
It can be inferred from Figures 4 and 5, that the requirement of the average energy per bit (Uavg) decreases with the increase in the number of initial users as well as . This is due to the fact that as the number of initial users and
increases, large multicast groups are
formed in each time slot. Therefore, in the same amount of energy, more bits are transmitted. For Case-I, for large number of users, the proposed and A–OMS algorithms have nearly the same Uavg. This is so because the difference in the average throughput of these two algorithms is also small for the large number of users (see Table 3). Figures 5(a), (b) and(c) depict Case-II for = 5, 10 and 20. From the plots it is clear that the proposed algorithm is most energy efficient. For λ=2, Uavg of the proposed algorithm is smaller than that for λ=5. For Case-II, the proposed algorithm is more energy efficient when λ=2. Across all the plots in Figure 5, for λ=2, with increase in the number of initial users, Uavg decreases for the proposed and A-OMS algorithms but remains nearly constant for OppMC-OS algorithm. The energy
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efficiency for Case-I is better than that for Case-II with λ=2 and λ=5 in all the algorithms. It can be observed from Table 3, which is for 40 initial users, that the average throughput for Case-I is better than that for Case-II and hence less energy per bit is consumed for Case-I.
Fig. 5. Average energy per bit for Case-II with λ =2 and 5, (a)
=5, (b)
=10 and (c)
=20
5. CONCLUSION In this paper, we proposed an improved multicast based energy efficient opportunistic data scheduling algorithm for VANET. We gave a formulation for obtaining the optimum value of SNR (γ*), which maximizes the average throughput (minimizes the average energy per bit) of a V2I system. The optimal SNR is also useful in the estimation of the optimal multicast group size without the knowledge of channel state at the road side unit. This optimal multicast group is served in a time slot at an
20
optimal rate. The road side unit keeps on forming multicast groups and serving them until all the users get served. The algorithm that we suggest is compared with two recently proposed algorithms, on the basis of average throughput and the average energy per bit. The comparison is made for two cases (one—no new service request is accepted until the initial ones get served, two—new service requests may be accepted in every time slot). In both the cases, with increase in the number of users and average SNR, the throughput increases rapidly in the proposed algorithm as compared to the other two algorithms. As average transmission energy per bit is inversely proportional to the average throughput, it is concluded that the proposed algorithm outperforms the other two algorithms, since it requires minimum average energy per bit. In particular, Case-I is found to be more energy efficient than Case-II, for large number of users. It may be noted that not only does the proposed algorithm work for multicast groups, it also works well for unicast and broadcast groups. All the algorithms mentioned in this work consider only single-hop communication, which has the advantage of small service delay. However, single-hop communication can only serve a small geographical area.
This problem can be
addressed using multi-hop communication with relays. But multi-hop communication poses other problems such as increased delay and power consumption. The increase in delay is caused due to the need for relay selection in each time slot and also due to the Amplify and Forward, or Decode and Forward modes at relays. This latter mode also results in the increased power consumption. It will be interesting to address these problems associated with multi-hop communication. Once it is done, multi-hop communication could be a better alternative for the data scheduling problem as it covers a larger geographical area. However, it may be noted that the estimation of channel state information for such cases would become extremely challenging. These issues are currently being investigated.
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Appendix A. Computation of worst case search complexity We compare worst case search complexities of A-OMS and the proposed algorithms for N users. In A-OMS algorithm, the search of maximum throughput is done in each time slot by scanning a row of ESTM. The elements of ESTM are calculated using (20), for all possible combinations of (
and
. The rows of ESTM corresponds to the number of users
) in the beginning of a time slot, whereas the columns denote the number of users selected
to be served ( ) such that the maximum throughput in a particular time slot is obtained. Elements for which
≥
is assigned a value zero, since
should be smaller than
. On
the other hand, for the proposed algorithm the estimation matrix is not formed; rather, in each time slot, (14) is used to calculate the maximum throughput. Now, we calculate the worst case search complexity for A-OMS and Case-I of the proposed algorithm. The worst case in multicast occurs when multicast group size is one (i.e., unicast). The ESTM is a lower triangular matrix, therefore, in each time slot, fewer elements in a row are to be scanned to find the maximum throughput. In the first time slot, N-1 elements, and in the last time slot only one element is scanned. To find the total number of elements scanned to serve all the N requesting users in the worst case for O-AMS algorithm, we sum up the number of elements scanned in each time slot as shown in (A.1) (A.1) (A.2) (A.3) Hence, for A-OMS, the search complexity for serving all the N users is for large N. Similarly, in the worst case for the proposed algorithm, only one user is served in each time slot; therefore, for serving all N users the search complexity is
.
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References [1] Eze EC, Sijing Zhang , Enjie Liu. Vehicular ad hoc networks (VANETs): Current state, challenges, potentials and way forward. In: 20th IEEE International Conference on Automation and Computing (ICAC): Sept. 2014, p 176-18. [2] Younghyun Kim, Jaeduck Ko, Wonjung Kim, Sangheon Pack. A measurement study on internet access in vehicular Wi-Fi networks.
In: 72nd IEEE Vehicular Technology
Conference Fall (VTC 2010-Fall): Sept. 2010, pp.1-5. [3] Goldsmith AJ, Wicker SB. Design challenges for energy-constrained ad hoc wireless networks. IEEE Wireless Communications Aug. 2002; 9(4): 8-27. [4] Zhao X, Wang Jun, Feng M, Wang Jin.
Energy-Efficient Scheduling over Fading
Channels with Transmission Modulation and Deadline Constraints.
AEU-International
Journal of Electronics and Communications Jun 2012; 66(6): 491-94. [5] Koutsakis P, Vafiadis M, Papadakis H. Prediction-based resource allocation for multimedia traffic over high-speed wireless networks. AEU-International Journal of Electronics and Communications. Nov 2006; 60(10): 681-9. [6] Knopp R , Humblet P. Information capacity and power control in single cell multiuser communications. In: Proceedings 1995 of IEEE ICC, p. 331-335. [7] Bahl N, Sharma AK, Verma HK. Asymptotic multicast throughput analysis and energy efficiency in WSN under double Nakagami fading channel using Extreme value theory. AEU-International Journal of Electronics and Communications. Sep 2015;69(9):1346-53. [8] Asadi A, Mancuso V.
A Survey on Opportunistic Scheduling in wireless
communications. Communications: Surveys & Tutorials, IEEE 2013; 15(4): 1671-88. [9] Gopala PK, Gamal HE. Opportunistic multicasting. In: Proceedings 2004 of IEEE 38th Asilomar Conference on Signals, Systems and Computers, p. 845-849.
23
[10] Zhang, Xing Li, Qinzi, Huang Yu, Wang Wenbo. An energy-efficient opportunistic multicast scheduling based on superposition coding for mixed traffics in wireless networks. EURASIP Journal on Wireless Communications and Networking 2012; 2012 (1): 1-12. [11] Veshi, Erzim Kuehne, Alexander , Klein Anja. Comparison of different multicast strategies in wireless identically distributed channels. In: IEEE Wireless Communication and Networking Conference (WCNC): April2013, p. 3001-3006. [12] Qiang Xue, Pantelidou A, Matti Latva-aho. Energy Efficient scheduling and power control for multicast data. In: IEEE Wireless Communication and Networking Conference (WCNC): March 2011, p. 144-149. [13] Qian Li, Zhiyong Feng, Wei Li, Aaron Gulliver T. A new multicast scheduling scheme for cellular networks. IEEE Wireless Communications Letters 2014; 3(1): 26-29. [14] Zhang Y, Zhao J, Guohong Cao. On scheduling vehicle roadside data access. In : Proceedings 2007 of the fourth ACM international workshop on Vehicular ad hoc networks, p. 9-18. [15] Shrivastava A, Merchant SN, Desai UB, Pandya B. Priority based NDS data scheduling algorithm for vehicle to hotspot communication. In: IEEE International Conference on Vehicular Electronics and Safety (ICVES) 2009: p.25-30. [16] Hoeffding W. Probability inequalities for sums of bounded random variables. Journal of the American statistical association 1963; 58(301): 13-30.