Towards Mobility-Aware Proactive Caching for Vehicular Ad hoc Networks

Transcription

1 Toward Mobility-Aware Proactive aching for Vehicular Ad hoc Network Youef AlNagar, Sameh Hony, Amr A. El-Sherif Wirele Intelligent Network enter (WIN), Nile Univerity, Giza, Egypt. Department of Electrical Engineering, Alexandria Univerity, Alexandria 21544, Egypt. arxiv: v1 [c.ni] 2 Oct 2018 Abtract Harneing information about the uer mobility pattern and daily demand can enhance the network capability to improve the quality of experience (QoE) at Vehicular Ad- Hoc Network (VANET). Proactive caching, a one of the key feature offered by 5G network, ha lately received much interet. However, more reearch i till needed to convey largeized multimedia content including video, audio and picture to the high peed moving vehicle. In thi paper, we tudy the gain achieved by proactive caching in Roadide Unit (RSU) where we take into conideration the effect of the vehicle velocity on the optimal caching deciion. Information about the uer demand and mobility i harneed to cache ome file in RSU, which will communicate with vehicle travering along the viited road before the actual demand. Our main objective i to minimize the total network latency. Toward thi objective, we formulate two optimization problem for non-cooperative and cooperative caching cheme to find the optimal caching policy to decide which file to be cached by the RSU. Due to the complexity of thee problem, we propoe a ub-optimal caching policy for each cheme. We compare the performance of the optimal caching policy to that of the uboptimal caching policy. Numerical reult how that proactive caching ha a ignificant performance gain when compared to the baeline reactive cenario. Moreover, reult reveal that the cooperative caching cheme i more efficient than the noncooperative cheme. I. INTRODUTION Global mobile data traffic reached 96 exabyte per month at the end of 2016 and i expected to reach 278 exabyte per month by The proliferation of online ocial network lead to an exploion of video traffic which i expected to reach 80% of the total internet traffic [1]. Uer demand increae dramatically and network traffic grow exponentially. Therefore, communication latency become a vital iue to conider. A promiing approach to meet thee challenge at cellular network i caching at the network edge to mitigate overload on the remote backhaul erver [2]. In caching, the mot frequent file are acceed from ome intermediate node to reduce load on the erver. A uer demand i not proceed by the erver, there i le time delay in retrieving the ervice. Today there i ignificant conenu that caching will play a fundamental role in the future communication ytem [3]. In particular, proactive caching i conidered one of the effective olution in 5G network. It relie on caching deired data before actual demand which can enhance traffic offloading, energy and pectrum efficiency [4]. However, preerving cache information, in order to provide the moving uer with the requeted data item, i a major challenge. Great effort are purued to look over mobility conequence on caching ytem [5], [6]. Vehicular Ad-Hoc Network, pecial wirele Ad-Hoc network in which communication node are moving vehicle, are conidered one of the mot prominent area for reearch and indutry application. VANET depend mainly on Vehicle-to-Vehicle (V2V) and Vehicle-to-Infratructure (V2I) communication to upport abundant application uch a intelligent tranportation, emergency ervice, elf driving, information haring and entertainment [7]. aching popular file in RSU with large torage capacity i tudied in [8]. Author try to tackle latency problem where the main objective i to minimize the mean time for On-Board Unit (OBU) to download a file. They propoe three algorithm to aign file at RSU, an optimal algorithm that achieve the bet performance and depend on exhautive earch, a ub-optimal algorithm, and a low-complexity greedy algorithm. On the other hand, a plit content caching cheme i addreed in [9] with an area controller located in the network backhaul which manage caching placement in the RSU layer. The author preent a imple analytic model to predict the probability for the content to be requeted at particular edge node. ooperative content caching between moving vehicle i introduced in [10]. The outage probability i conidered a a performance metric for the propoed caching model. The author alo dicu the outage analyi under random mobility cenario, and vehicular cenario where vehicle are aumed to move in traight freeway. Author in [11] preent a caching placement policy to maximize the caching gain baed on the cloud-baed VANET at the vehicular layer and RSU. Vehicle are aumed to travel in platoon and RSU are deployed uniformly along the road. A new caching allocation policy i uggeted to jointly conider the vehicle and RSU cache. An optimization problem i formulated to minimize the latency for vehicle to receive their deired data item. Although previou work tudied convenient caching cheme at both vehicle and RSU, they didn t capture the effect of vehicle velocity and how to exploit uer mobility pattern to enhance the ytem performance. There i a trong evidence in the literature that many people follow certain daily routine and hence their behavior (mobility pattern and demand) i highly predictable over the time a a prior

2 information [12] [15]. In thi work, we principally focu on deploying a cooperative proactive caching cheme between RSU to minimize the communication latency and enhance quality of ervice (QoS) in VANET. We how that exploiting the information about uer mobility and demand tatitic help u to addre the latency problem and reinforce the network capacity. The main contribution are: 1) We propoe a non-cooperative caching cheme where each RSU find it optimal caching deciion independently. The optimization problem i formulated in order to minimize the total expected delay of the network. A reactive network i conidered a a baeline model to evaluate the performance of the propoed model. 2) Due to the complexity of the optimization problem, we introduce a ub-optimal caching policy which achieve a high caching gain compared to the baeline reactive cheme. 3) We extend our work by conidering a cooperative caching cheme where RSU collaborate to get their optimal caching deciion after conidering the vehicle updated demand and location information. We propoe a greedy algorithm which outperform the noncooperative caching cheme. We how that cooperation between RSU enhance the network performance and minimize the total expected delay. The ret of the paper i organized a follow. In Section II, we introduce the ytem model and tate the underlying aumption. The problem i formulated in Section III. We dicu the non-cooperative caching cheme in Section IV. In Section V, we propoe the cooperative caching cheme and introduce a ub-optimal caching policy. Numerical reult and dicuion are provided in Section VI. The paper i concluded in Section VII. II. SYSTEM MODEL We conider a et of S Roadide Unit, S = {1, 2,, S}, that are located equiditantly with ditance L over a certain road, a hown in Fig 1. Each RSU S i equipped with a limited cache of ize Z which i ued to cache a number of data item. Along the road, there i a et of V moving vehicle, V = {1, 2,, V }. Vehicle are intereted in a et of M uncorrelated data item, M = {1, 2,, M}. For implicity, we aume that all data item have the ame ize of byte. Each RSU erve connected vehicle, which are moving within it coverage area, with data rate α byte/ec. In the free-flow tate when the traffic denity i low, we aume that vehicle velocitie are independent and identically ditributed ince driver can chooe their appropriate peed, which are generated randomly by truncated Gauian ditribution and each vehicle keep it aigned peed u v while it move along the highway [16],[17]. It i widely acceptable that velocity ditribution of vehicle in freeway follow Gauian ditribution [18]. Without lo of generality, we aume that any vehicle i moving with a velocity u that i limited by minimum and maximum peed, i.e. u min u u max. Fig. 1: Sytem Model. Therefore, we have truncated normal ditribution with mean µ and variance σ 2 where ( ) (x µ) 2 exp 2 2σ 2 ( ) ( 2πσ 2( erf umax µ umin σ f(u) = µ )), erf 2 σ 2 u min u u max, 0, otherwie. Let θv be the probability that vehicle v i located at the coverage area of RSU. Due to their mobility, vehicle will be connected to any RSU for a certain amount of time and then handover to the next RSU. We define the contact time vector h := (h 1, h 2,, h v) where h v i the contact time between vehicle v and RSU in econd. We aume that the RSU can track, learn and predict the vehicle behavior, hence, contruct a demand profile for each vehicle v denoted by p v := ( ) p 1 v, p 2 v,, p M v where p m v i the probability that vehicle v requet data item m. The demand of vehicle v i captured by a random variable expreed by { I m 1, with probability p m v, v = 0, with probability 1 p m v, where I m v = 1 mean that data item m i requeted by vehicle v while I m v = 0 mean that it i not requeted. We aume that I m1 v i independent of I m2 v, m 1, m 2 M. Moreover, for any v 1 v 2, I m v 1 i independent of I m v 2, m M, v 1, v 2 V. Let x m be the caching deciion of data item m at RSU where x m {0, 1}, m M, S. (2) In particular, x m = 0 mean that the RSU doe not cache data item m while x m = 1 mean the data item m i cached at RSU. It i worth to notice that the ize of the cached item hould be le than or equal to the total RSU torage Z. Therefore, we have M x m Z, S. (3) When a vehicle requet a data item, the erving RSU tranmit the requeted data item to the vehicle, in α econd, if the data item i available in it local cache. If not found locally, the RSU requet thi data item from the (1)

3 network backhaul. In thi cae, every data item m require time (τ + α ) econd to be erved, where τ i the time to fetch the requeted data item from backhaul to the RSU. We aim to find an optimal caching policy {x m } that pecifie the data item to be be cached at the RSU to minimize the total latency. III. PROBLEM FORMULATION RSU take the vehicle mobility and demand tatitic into conideration to find an optimal caching policy. To tudy the potential gain achieved by the proactive caching approach, we compare the propoed model with a baeline reactive cheme. Let h v repreent the contact time between the vehicle v and the erving RSU where A. Reactive Network h v = L u v. (4) We conider a reactive network a a baeline cenario where the requet are erved directly from the network backhaul without caching at the RSU. Let Mv be the maximum number of data item that can be received by vehicle v from RSU, where ( ) M v := min h v α + τ, M. (5) Each data item will be delivered from the network backhaul within ( α + τ) econd. Hence, each vehicle can receive up to data item but can not exceed the library ize M. h v α +τ In particualr, each vehicle can requet k data item where 0 k Mv. Therefore, the expected total delay incurred by all vehicle for RSU will be given by W R = M v θv v=1 k=0 G k ( τ) k q i,k +, (6) α i=1 where R repreent the reactive network and G k = ( ) M k i the number of all poible combination to requet k file from the library M. We denote by q i,k the probability that combination i of requeting k data item i elected. Suppoe that combination i ha the indice a i,k = {l i,1, l i,2,, l i,k }. Hence, q i,k will be given by q i,k = ( ) 1 p r v. (7) l a i,k p l v. r / a i,k The RSU conider all the vehicle which are located within it coverage area and conider it correponding contact time. It alo conider the elected combination of requeted data item. Each data item in the requeted combination will be delivered within α + τ econd. B. Proactive Network In proactive network, each RSU exploit it limited memory to proactively cache ome of the data item. For a RSU to erve a vehicle requet from it cache, it require α econd. If the requeted data item i not available in the RSU local cache, the data item will be delivered from the network backhaul within ( α + τ) econd. Since vehicle v will be connected to the erving RSU for h v econd, the vehicle can receive at mot ˆM v data item from the RSU local cache where ( ) M ˆM v := min,. (8) h v α Since ˆM v i the minimum between mot amount of cached file that can be received by vehicle v and total cached item. If the contact time allow the vehicle to receive more data, the RSU will be able to deliver at mot M v data item from the network backhaul where h M v v ˆM v α := + τ α x m. (9) h Since the maximum of ˆM v i v which mean that α content item can by delivered from the backhaul M v equal zero. Now, each vehicle can receive at mot M v data item but can not exceed the library ize M, where ( M v := min ˆM v + M ) v, M. (10) Therefore, the expected total delay incurred by all vehicle for RSU will be given by W P = θv v=1 k=0 i=1 M v G k q i,k t i,k, (11) where P repreent the propoed proactive network, and t i,k i the tranmiion time for combination i. In general, ( ) t i,k = k + τ τ x l α, (12) l a i,k where the firt term repreent total time if the uer i erved directly from the backhaul and the econd term refer to aved time due to the cached file. We aim to minimize the latency over all uer under the proactive network by finding an optimal caching policy x m, m M, S. To evaluate the potential gain of proactive caching and it effect on the expected total delay, we characterize caching gain W := W R V W P v=1 M v V M a our performance metric for v=1 v the propoed model a the difference between the expected time delay per file at reactive and proactive model.

4 IV. NON-OOPERATIVE AHING SHEME In thi cheme, each RSU find it optimal caching deciion regardle of the other RSU deciion. We aume that there i no cooperation nor coordination between the RSU. Therefore, the optimization problem for RSU can be defined a follow min x m W P V M v=1 v.t. (2), (3), + γ M x m (13) where γ i a factor capturing the caching cot per data item at any RSU. The firt term repreent the expected time per file and the econd term refer to the total caching cot. We aim to minimize the expected time and cot while maximizing the total number of file that uer can receive. Due to the complexity of the problem, it i not eay to find the global optimal of (13) a it i difficult to prove the convexity of the objective function. To overcome thi difficulty, we find the optimal olution by launching an exhautive earch algorithm to attain the optimal combination of file that the RSU hould cache. Therefore, we calculate the total expected time (main operation at the algorithm) by going over all different poible combination of cached item from the library M to give 2 M iteration. Moreover, we take into conideration different demand combination over all uer which lead to olution x m V M ( v M v=1 i=1 i brute force algorithm i O ) operation. ( Hence, the complexity of the 2 M V v=1 M ( v M ) ) i=1 i. It i clear that the complexity of the optimization problem increae exponentially a the number of vehicle and data item increae. Therefore, we propoe an efficient greedy algorithm to tackle thi iue. The key of thi greedy algorithm i the term V v=1 θ vp m v in (11), which i conidered a a weight factor for each data item. Moreover, the effect of vehicle velocity hould be conidered in the ytem by defining λ v := h v V. Thi factor capture the vehicle velocity and v=1 h v give high priority for low peed vehicle aiming to maximize the network throughput. The data item which receive high value of V v=1 θ vp m v and λ v will be more probable to be cached firt. Therefore, by orting the data item baed on thee value, the RSU fill it local cache memory until it reache the minimum between it cache ize Z and α h, which refer to the average number of cached item received by uer due to their mobility, ince h i the average of contact time vector. Thi allow u to guarantee that the caching cot tay reaonable and the caching proce i efficient. The propoed algorithm give promiing reult when compared to the exhautive earch a hown in Section VI. It achieve lower complexity O(MV + M 2 ), where (MV ) i the iteration for finding π m and M 2 i the complexity of the orting algorithm [19]. Algorithm 1 tate the detail of the propoed ub-optimal caching policy for the non-cooperative cheme. Algorithm 1 Sub-optimal noncooperative caching policy Initialize p m v, θv, h v, v V, m M Set x m = 0, m M Evaluate π m := V v=1 θ vp m v λ v, m M Sort π m decendingly and ave orting indice in ζ Set m = 1 while M xm min ( Z, α ) h do Set x ζ(m) = 1 Set m = m + 1 end Output x m. V. O-OPERATIVE AHING SHEME In thi cheme, we aume that the RSU cooperate together through information ignal to enhance the uer experience by caching file which are expected to be requeted at the coverage area of the next RSU. Therefore, we can rewrite (6) a follow ˆθ v = W R = M ˆθ v v=1 v G k q i,k ˆ k k=0 i=1 ( ) + τ, (14) α { 1, v wa previouly located at RSU 1, 0, otherwie, (15) where ˆθ v i the updated location probability which become determinitic and we denote to previou RSU by 1. ˆq i,k i the updated demand probability ince the prior RSU pae the information about the file delivered to each uer. Therefore, the current RSU update p v to ˆp v by making p m 1 v = 0, m ˆM v, where ˆM 1 v i the et file downloaded by vehicle v at the coverage area of RSU 1, which mean that the uer will not requet a file that had been received. By finding conditional ditribution on previou demand of probability vector, we keep M ˆpm v = 1. Moreover, the total expected delay under the proactive caching cheme for RSU i given by W P = ˆθ v v=1 M v G k q i,k ˆ t i,k. (16) k=0 i=1 For implicity, we conider two RSU only and then generalize the olution for all RSU. In thi cae, the optimization problem for the two RSU and 1 i min W P x m V M,xm 1 v=1 v + γ + W 1 P V 1 v=1 M v M ( x m + x m 1).t. (2), (3). (17) Inpired by the olution of the non-cooperative caching cheme dicued in Algorithm 1, we propoe a ub-optimal

5 caching policy for the cooperative caching cheme. RSU 1 find it optimal caching policy baed on Algorithm 1. RSU modifie the calculation of π m to capture the updated information about the vehicle location and demand from RSU 1 and proceed with the ame approach a in Algorithm 1. In particular, RSU fill it cache memory with the updated information about the location and demand of the paing vehicle after being erved by RSU 1. Algorithm 2 how the detail of the propoed ub-optimal caching policy under the cooperative cheme for two RSU. The ame approach can be applied to generalize the propoed olution for all RSU. The caching deciion of RSU will be affected by the deciion of RSU 1, 2,, 1. Algorithm 2 Sub-optimal ooperative aching Policy Initialize p m v, ˆp m v, θv 1, ˆθ v, h 1 v, h v v V, m M, 1, S Set x m 1 = 0, m M Evaluate π 1 m := V v=1 θ 1 v p m v λ 1 v, m M Sort π 1 m decendingly and ave orting indice in ζ 1 Set m = 1 while M xm 1 min ( Z 1, α ) 1 h 1 do Set x ζ 1(m) 1 = 1 Set m = m + 1 end Set x m = 0, m M Evaluate π m := V ˆθ v=1 v ˆp m v λ v, m M Sort π m decendingly and ave orting indice in ζ while M xm min ( Z, α ) h do Set x ζ(m) = 1 Set m = m + 1 end Output x m 1, x m. VI. NUMERIAL RESULTS AND DISUSSION In thi ection, we compare the performance of the propoed model to the reactive baeline model. We conider the cae of two RSU with equal coverage ditance L = 50 meter and are erving 3 vehicle. We aume that the vehicle are intereted in M = 20 data item each of ize = 1000 kbyte. Vehicle velocitie are generated by a truncated Gauian ditribution with mean µ = 55, variance σ 2 = 10, minimum velocity u min = 10 km/h and maximum velocity u max = 120 km/h. Both RSU have the ame data rate α = 1000 kbyte/, S. For implicity, we conider τ = /α = 1 econd and γ ha three different value {0.1, 0.01, 0.001}. We aume that each uer ha different interet from other. We model the demand probabilitie for the uer uing Zipf ditribution with different parameter. Moreover, to guarantee that the file demanded don t have the ame order at all uer, we permute the generated file rank randomly to attain a different demand vector for each uer. A. Non-cooperative veru cooperative caching cheme Fig. 2 how the expected time per file for different cheme veru the cache ize Z. It i clear that the reactive baeline cenario ha the wort performance due to abence of caching. In cae of non-cooperative caching cheme, each RSU take it deciion independently, neglecting previou information about demand and location tatitic. The figure how that the expected time decreae a the RSU cache ize increae to give a high caching gain W of 45% at cache ize = 10 file. On the other hand, in cae of the cooperative caching cheme, each RSU collaborate with the previou RSU to update it information about the vehicle mobility and demand pattern. Thi collaboration allow the RSU to increae their certainty about uer behaviour and enhance their caching deciion. It i noticeable that the cooperative caching cheme outperform the non-cooperative caching cheme for all cache ize. For intance, the cooperative caching cheme achieve caching gain of 64% at cache ize = 10 file. Moreover, the propoed ub-optimal greedy algorithm achieve nearly the ame performance a the high complexity optimal exhautive earch algorithm. B. Impact of aching cot on the ytem We characterize our model by conidering that caching a file at the RSU caue ome ort of cot uch a time, energy or memory, etc. In our model, γ i the factor that capture the caching cot. In Fig. 3, we plot the objective function at noncooperative caching cheme (13) veru the cache ize for different value of γ. At a high value of caching cot factor, γ = 0.1, the minimum value of total cot i achieved at cache ize = 1 file, which indicate that the optimal deciion i to cache one file. While at intermediate value of caching cot factor, at γ = 0.01, we get minimum total cot value at cache ize = 7 file, which i approximately the average number of cached file that uer can receive α h, ince RSU doen t need to cache beyond thi number to avoid any extra cot. At low caching cot factor, γ = 0.001, the optimal deciion i to cache all of the file in the library. aching cot factor value may differ from time to time a it depend on abundant factor uch a available memory, battery lifetime, and even peak and off-peak time. VII. ONLUSION We tudy the gain achieved by proactive caching in RSU to minimize the communication latency in VANET. Information about the uer demand and mobility i harneed to cache a number of file at the RSU before the actual demand. We capture the vehicle velocity in our model, which follow Gauian ditribution, to tudy it effect. We evaluate the propoed model by conidering the expected network delay a a performance metric. Optimization problem are formulated to minimize the expected network delay for non-cooperative and cooperative caching cheme. To overcome the complexity of thee problem, we propoe an efficient greedy algorithm for each cheme. We compare the

6 Expected Time /File (ec) Reactive baeline Greedy algorithm (Non-cooperative) Optimal algorithm (Non-cooperative) Greedy algorithm (ooperative) Optimal algorithm (ooperative) ache Size (file) Fig. 2: omparion between the performance of reactive, optimal non-cooperative and optimal cooperative caching cheme and propoed greedy algorithm. Objective Function γ=0.1 γ=0.01 γ= ache ize (file) Fig. 3: Impact of different cot factor in cae of noncooperative caching cheme. performance of the optimal and ub-optimal caching policie. Moreover, we invetigate the effect of uing different caching cot factor on it performance. Reult reveal that the cooperative caching cheme outperform the non-cooperative caching cheme for all cache ize. Furthermore, proactive caching i proven to be highly efficient at vehicular network when compared to the baeline reactive cheme. In thi work, we conidered a ingle highway road to tudy the effect of proactive caching on the network performance. We plan to extend our work to conider a complete city model coniting of multiple road. We expect to achieve more gain by conidering larger network ize. Moreover, conidering the mobility of vehicle acro multiple road may help u to addre proactive caching more efficiently. REFERENES [1] ico, ico viual networking index: Forecat and methodology, , [online] [2] N. Golrezaei, K. Shanmugam, A. G. Dimaki, A. F. Molich, and G. aire, Femtocaching: Wirele video content delivery through ditributed caching helper, in 2012 Proceeding IEEE INFOOM, March 2012, pp [3] G. S. Pacho, G. Ioifidi, M. Tao, D. Towley, and G. aire, The Role of aching in Future ommunication Sytem and Network, ArXiv e-print, May [4] E. Batug, M. Benni, and M. Debbah, Living on the edge: The role of proactive caching in 5g wirele network, IEEE ommunication Magazine, vol. 52, no. 8, pp , Aug [5] Y. Guan, Y. Xiao, H. Feng,.. Shen, and L. J. imini, Mobicacher: Mobility-aware content caching in mall-cell network, in 2014 IEEE Global ommunication onference, Dec 2014, pp [6] S. Hony, A. Eryilmaz, and H. E. Gamal, Impact of uer mobility on d2d caching network, in 2016 IEEE Global ommunication onference (GLOBEOM), Dec 2016, pp [7] H. Hartentein and L. P. Laberteaux, A tutorial urvey on vehicular ad hoc network, IEEE ommunication Magazine, vol. 46, no. 6, pp , June [8] R. Ding, T. Wang, L. Song, Z. Han, and J. Wu, Roadide-unit caching in vehicular ad hoc network for efficient popular content delivery, in 2015 IEEE Wirele ommunication and Networking onference (WN), March 2015, pp [9] A. Mahmood,. aetti,. F. hiaerini, P. Giaccone, and J. Harri, Mobility-aware edge caching for connected car, in th Annual onference on Wirele On-demand Network Sytem and Service (WONS), Jan 2016, pp [10] O. Attia and T. ElBatt, On the role of vehicular mobility in cooperative content caching, in 2012 IEEE Wirele ommunication and Networking onference Workhop (WNW), April 2012, pp [11] J. Ma, J. Wang, G. Liu, and P. Fan, Low latency caching placement policy for cloud-baed vanet with both vehicle cache and ru cache, in 2017 IEEE Globecom Workhop (G Wkhp), Dec 2017, pp [12] J. B. T. amp and V. Davie, A urvey of mobility model for ad hoc network reearch, in Wirele ommunication and Mobile omputing(wm)), vol. 2, no. 5, Aug 2002, p [13] I. F. Akyildiz and W. Wang, The predictive uer mobility profile framework for wirele multimedia network, IEEE/AM Tranaction on Networking, vol. 12, no. 6, pp , Dec [14]. Song, Z. Qu, N. Blumm, and A.-L. Barabái, Limit of predictability in human mobility, Science, vol. 327, no. 5968, pp , [Online]. [15] O. B. Fikir, I. O. Yaz, and T. Özyer, A movie rating prediction algorithm with collaborative filtering, in 2010 International onference on Advance in Social Network Analyi and Mining, Aug [16] Y. Zhang, H. Zhang, W. Sun, and. Pan, onnectivity analyi for vehicular ad hoc network baed on the exponential random geometric graph, in 2014 IEEE Intelligent Vehicle Sympoium Proceeding, June 2014, pp [17] S. Youefi, E. Altman, R. El-Azouzi, and M. Fathy, Analytical model for connectivity in vehicular ad hoc network, IEEE Tranaction on Vehicular Technology, vol. 57, no. 6, pp , Nov [18] S. M. Abuelenin and A. Y. Abul-Magd, Empirical tudy of traffic velocity ditribution and it effect on vanet connectivity, in 2014 International onference on onnected Vehicle and Expo (IVE), Nov 2014, pp [19] T. H. ormen,. E. Leieron, R. L. Rivet, and. Stein, Introduction to Algorithm, Third Edition, 3rd ed. The MIT Pre, 2009.