10 M)and consider Zipf distribution,i.e=,where np=uandIIn this case,each content is requested by a 0 is the exponent of Zipf distribution and H(M)= u clients.Under fast mobility,from Theorem 1,we obtain (∑-) is a normalization constant.From Theorem the optimal throughput and delay tradeoff 1,we obtain the following optimal throughput-delay tradeoff Under slow mobility,from Theorem 3,we obtain the optimal under fast mobility throughput and delay tradeoff).These results 百(1) a≥2 recover the optimal throughput-delay tradeoffs in [10]. Finally,we consider the content-centric case in [17]by 1<a<2 (30) setting pi=and K 1.In this case,the content 0 () a≤1 popularity follows a Zipf distribution.Since [17]assumes free content placement and a limited cache size,we further set Comparing(29)and(30),we find that mobility improves the p 0 and n e(1).From Theorem 5,we obtain the performance when a<1,while it degrades the performance following throughput-delay tradeoffs,which recover the results when a∈(1,2).Fora≥2，it is possible to achieve the best in[17刀]. (1)throughput and (1)delay in both the mobile and static ( 白(1)， a≥2 cases 6(),1<a<2 (32) In addition,from Theorem 3,we obtain the following optimal throughput-delay tradeoff under slow mobility 6(), a≤1 Moreover,we find that even when content placement is not 白(1) a2是 free (i.e.,p 0),our scheme can improve the maximum 1<a<是 (31) throughput up to a factor of when the cache size )： is scalable.This gain demonstrates the benefit of caching in a≤1 content-centric MANETs. From(29),(30)and (31),we find that slow mobility leads to a better performance than both fast mobility and the static case.This is because there are more possible routing VI.CONCLUSION AND FUTURE WORK schemes when nodes move in a much slower time scale than content transmissions.This observation seems to be different from that in [17],which shows that mobility may hurt the In this paper,we investigate the asymptotic performance performance when the cache size is limited.The intuition is of content-centric MANETs.Different from previous work which considers content retrieval cost only,this paper jointly as follows.In the static case,contents are forwarded to clients hop by hop,and the required cache size is constant in the order considers the delay costs in both content placement and con- tent retrieval.We study two mobility models in different time- sense.In the mobile case,contents are delivered to clients using the "store-carry-forward"paradigm,i.e.,contents are scales,i.e.,fast and slow mobility.Under each mobility model, first stored and carried by mobile servers,and then forwarded by optimizing the number of replicas and retrieval ranges to mobile clients by one hop.Therefore,the storage of servers for contents of different popularity,we analyze the optimal throughput and delay,and design a near-optimal scheme. plays a more important role on content delivery in the mobile case.If the cache size is limited (nb =e(1)),the number Furthermore,we introduce a more general weighted sum delay of contents carried by each mobile server is bounded by metric,to capture content placement and content retrieval e(1).Then during the inter-meeting time (larger than e(1)), of possibly different delay costs.Our results provide useful insights into the performance of content-centric MANETs in a mobile server does not always have contents to forward, different scenarios. even though it has a transmission opportunity.Thus mobile servers with limited cache sizes cannot effectively exploit the There are several interesting directions for future research. transmission opportunities. For instance,when energy consumption is considered,there Observation 2:By considering an arbitrary content pop- may exist a tradeoff among energy,throughput and delay.It is thus meaningful to investigate the optimal tradeoff and design ularity distribution,we establish more general results.The following discussions demonstrate that our results can recover an energy-aware scheme which achieves a tradeoff close to the analytical results for the unicast [8],[9]and multicast [10] the optimal one.In addition,if content popularity is time- traffic patterns,and are more general than the results in [17]. varying,the proposed scheduling scheme designed for fixed First,we consider the unicast case in [8].[9]by setting popularity may no longer be effective.This highlights the need for designing dynamic placement and retrieval strategies npi =1 and I=n.In this case,each content is requested by a single client.Under fast mobility,from Theorem 1,we obtain for time-varying popularity.Finally,the proposed scheme can also be generalized to vehicle-to-vehicle (V2V)networks.in the optimal throughput and delay tradeoff入-6（√t), which real time data traffic and inhomogeneous vehicle density Under slow mobility,from Theorem 3,we obtain the optimal should be considered.It is interesting to see how local content throughput and delay tradeoff.These results sharing is affected by high spatial variations of vehicle density recover the optimal throughput-delay tradeoffs in [8].[9]. and how to design efficient scheduling schemes for inter- Second,we consider the multicast case in [10]by setting vehicle content sharing.10 M = I) and consider Zipf distribution, i.e., pi = H(M) iα , where α ≥ 0 is the exponent of Zipf distribution and H(M) = €PM i=1 i −α Š−1 is a normalization constant. From Theorem 1, we obtain the following optimal throughput-delay tradeoff under fast mobility λ¯ = 8 >>< >>: Θ (1) ˜ , α ≥ 2 Θ˜ È W¯ M2−α  , 1 < α < 2 Θ˜ ÈW¯ M  , α ≤ 1 . (30) Comparing (29) and (30), we find that mobility improves the performance when α ≤ 1, while it degrades the performance when α ∈ (1, 2). For α ≥ 2, it is possible to achieve the best Θ (1) ˜ throughput and Θ (1) ˜ delay in both the mobile and static cases. In addition, from Theorem 3, we obtain the following optimal throughput-delay tradeoff under slow mobility λ¯ = 8 >>< >>: Θ (1) ˜ , α ≥ 3 2 Θ˜  3 È W¯ M3−2α  , 1 < α < 3 2 Θ˜  3 ÈW¯ M  , α ≤ 1 . (31) From (29), (30) and (31), we find that slow mobility leads to a better performance than both fast mobility and the static case. This is because there are more possible routing schemes when nodes move in a much slower time scale than content transmissions. This observation seems to be different from that in [17], which shows that mobility may hurt the performance when the cache size is limited. The intuition is as follows. In the static case, contents are forwarded to clients hop by hop, and the required cache size is constant in the order sense. In the mobile case, contents are delivered to clients using the “store-carry-forward” paradigm, i.e., contents are first stored and carried by mobile servers, and then forwarded to mobile clients by one hop. Therefore, the storage of servers plays a more important role on content delivery in the mobile case. If the cache size is limited (nb = Θ(1)), the number of contents carried by each mobile server is bounded by Θ(1). Then during the inter-meeting time (larger than Θ(1)), a mobile server does not always have contents to forward, even though it has a transmission opportunity. Thus mobile servers with limited cache sizes cannot effectively exploit the transmission opportunities. Observation 2: By considering an arbitrary content pop￾ularity distribution, we establish more general results. The following discussions demonstrate that our results can recover the analytical results for the unicast [8], [9] and multicast [10] traffic patterns, and are more general than the results in [17]. First, we consider the unicast case in [8], [9] by setting npi = 1 and I = n. In this case, each content is requested by a single client. Under fast mobility, from Theorem 1, we obtain the optimal throughput and delay tradeoff λ¯ = Θ˜ €ÈW¯ n Š . Under slow mobility, from Theorem 3, we obtain the optimal throughput and delay tradeoff λ¯ = Θ˜ € 3 ÈW¯ n Š . These results recover the optimal throughput-delay tradeoffs in [8], [9]. Second, we consider the multicast case in [10] by setting npi = u and I = n u . In this case, each content is requested by u clients. Under fast mobility, from Theorem 1, we obtain the optimal throughput and delay tradeoff λ¯ = Θ˜ €È W¯ un Š . Under slow mobility, from Theorem 3, we obtain the optimal throughput and delay tradeoff λ¯ = Θ˜ € 3 È W¯ u2n Š . These results recover the optimal throughput-delay tradeoffs in [10]. Finally, we consider the content-centric case in [17] by setting pi = H(I) iα and K = 1. In this case, the content popularity follows a Zipf distribution. Since [17] assumes free content placement and a limited cache size, we further set ρ = 0 and nb = Θ(1). From Theorem 5, we obtain the following throughput-delay tradeoffs, which recover the results in [17]. λ¯ = 8 >< >: Θ (1) ˜ , α ≥ 2 Θ˜ € W¯ M2−α Š , 1 < α < 2 Θ˜ € W¯ M Š , α ≤ 1 . (32) Moreover, we find that even when content placement is not free (i.e., ρ ̸= 0), our scheme can improve the maximum throughput up to a factor of Θ˜ €È M W¯ Š when the cache size is scalable. This gain demonstrates the benefit of caching in content-centric MANETs. VI. CONCLUSION AND FUTURE WORK In this paper, we investigate the asymptotic performance of content-centric MANETs. Different from previous work which considers content retrieval cost only, this paper jointly considers the delay costs in both content placement and con￾tent retrieval. We study two mobility models in different time￾scales, i.e., fast and slow mobility. Under each mobility model, by optimizing the number of replicas and retrieval ranges for contents of different popularity, we analyze the optimal throughput and delay, and design a near-optimal scheme. Furthermore, we introduce a more general weighted sum delay metric, to capture content placement and content retrieval of possibly different delay costs. Our results provide useful insights into the performance of content-centric MANETs in different scenarios. There are several interesting directions for future research. For instance, when energy consumption is considered, there may exist a tradeoff among energy, throughput and delay. It is thus meaningful to investigate the optimal tradeoff and design an energy-aware scheme which achieves a tradeoff close to the optimal one. In addition, if content popularity is time￾varying, the proposed scheduling scheme designed for fixed popularity may no longer be effective. This highlights the need for designing dynamic placement and retrieval strategies for time-varying popularity. Finally, the proposed scheme can also be generalized to vehicle-to-vehicle (V2V) networks, in which real time data traffic and inhomogeneous vehicle density should be considered. It is interesting to see how local content sharing is affected by high spatial variations of vehicle density and how to design efficient scheduling schemes for inter￾vehicle content sharing