Guanglin Zhang, Jian Liu, Jiajie Ren

College of Information Science and Technology, Donghua University, Shanghai, 201620, China Engineering Research Center of Digitized Textile and Apparel Technology, Ministry of Education

* The corresponding author, email： glzhang@dhu.edu.cn

I. INTRODUCTION

Caching plays an important role in the applications of wireless networks, for instance, retrieving the cached contents which are closest the requesting nodes can improve the throughput capacity due to decreasing the number of hops between the requester and desired content. Recently, the content-centric networking architectures such as Named Data Networking (NDN) [9] and Content-Centric Networking (CCN) [10] have been developed for popularity content objects distribution making use of caching. It is of great interest to characterize the performance and scaling in large-scale content-centric wireless networks.In [11], Liu et al. obtain the scaling laws of the throughout capacity for cache enabled content distribution wireless ad hoc networks by proposing a nearest caching node scheme and transparent enroute caching scheme. They show that increasing the cache size of nodes can improve the throughput capacity under certain conditions. In [12], the authors study the per-node throughput capacity of an information-centric network while the content cached in each node has limited lifetimes. In[13], Mahdian et.al. study the the throughput and delay scaling behavior of content-centric wireless networks. By assuming that all contents follow a Zipf content popularity distribution, and each node has a limited capacity content storage, they give the solution of a cache optimization problem and minimize the average network delay and maximize the network throughput simultaneously. In[14], Alfano et al. study the throughput-delay tradeoffs of content-centric mobile ad-hoc networks for Zipf content popularity distributions. In [15], Do et al. investigate the optimal throughput-delay tradeoffs in content-centric mobile heterogeneous networks. In [16], Luo et al. study the throughput and delay of the content-centric MANETs under two operations regarding content placement and content retrieval. In [17], Liu et al. show that the impact of correlated mobility on the asymptotic scaling laws of MANETs. They propose two network regimes, which contain two mobility time scales in each regime.

In this paper, we first study the multicast throughput capacity of content-centric two-level hierarchical routing strategy. We first study the upper bound on multicast capacity of content-centric wireless ad hoc networks under the homogenous content access scheme,where the content objects are equally likely cached and requested. Then, we derive the multicast capacity of under the heterogenous content access scheme where the probability that them-th content is cached in a node is

The rest of this paper is organized as follows. Section II presents the system model. In Section III and IV, we derive the upper bound on multicast capacity of content-centric wireless ad hoc networks homogeneous hierarchical routing strategy and heterogeneous hierarchical routing strategy, respectively. Finally,we conclude the paper in Section V.This paper investigates the upper bound multicast capacity of content-centric wireless ad hoc networks with content-centric hierarchical routing strategy.By investigating two routing strategies,the authors prove the upper bounds of multicast capacity, respectively.

II. SYSTEM MODEL

2.1 Interference model

For the wireless interference in content-centric ad hoc networks, we adopt the protocol model fied：

Fig. 1 Example of multicast flows in a content-centric wireless ad hoc network

2.2 Content access scheme and routing strategy

We assumepusers originate request for given content object in a request. We adopt a content-centric two-level hierarchical routing strategy. Each requesting node forwards an interest packet toward the cluster head in each cluster using multi-hop pattern. Then each cluster head transmits the same interest packet to the closest caching node. When the interest packet is received by the closest caching node, the caching node routing a Data Packet containing the desired content objects to each cluster head in the reverse direction, then each cluster head forward the Data Packet to the requesting nodes in each cluster, respectively.For the sake of simplicity but without loss of generality, the route strategy is shown in Fig.1.

III. UPPER BOUND ON MULTICAST CAPACITY OF HOMOGENOUS CONTENT ACCESS SCHEME

In this section, we derive the upper bound on multicast capacity of content-centric wireless ad hoc networks under the homogenous content access scheme with content-centric two-level hierarchical routing strategy.

Proof:Consider an arbitrary clusterk, let

Lemma 3:The total number of hops from a caching node to itsprequesting nodes under the homogenous content scheme with content-centric two-level hierarchical routing strategy is

Theorem 1:The upper bound on multicast capacity under the homogenous content access scheme with content-centric two-level hierarchical routing strategy is

Fig. 2 The multicast capacity with various values of cache size C vs. the number of nodes n

Fig. 3 The multicast capacity with various values of cache size C vs. the number of nodes n

Theorem 2:Under the homogenous content access scheme with content-centric two-level hierarchical routing strategy, each content object is requested with equal probability. Since there areMdistinct content objects and each node can hold theCunit content object, the probability that each content object is requestupper bound on multicast capacity about the number of contentMand the cache sizeCby changing equation (4).

Discussion of result:Note that capacity result as shown in equation (7), the upper bound capacity on multicast capacity just about the cache size of each node and the number of content. The multicast capacity can be improved by enhancing the cache size of nodes as shown in Fig. 3.

IV. UPPER BOUND ON MULTICAST CAPACITY OF HETEROGENOUS CONTENT ACCESS SCHEME

In this section, we consider the random caching scheme where the probability that them-th is given by [14].

Lemma 5:The total number of hops from a caching node ofm-th content object to itsprequesting nodes under the content-centric hierarchical routing strategy is

The total number of hops from the closest caching node to the requesting nodes under heterogenous content access sceheme is

Theorem 3:The upper bound on multicast capacity under the heterogenous content access scheme with content-centric two-level hierarchical routing strategy is

Proof:Since the number of simultaneous transmission in the network is at most assume each node can generate traffic at a rate ity with content-centric two-level hierarchical routing strategy is (13) shown in the bottom at this page.

Recall that the number of cluster in the

(14) shown in the top at next page.

Fig. 4 The upper-bound of multicast capacity for various values of p, vs. the probability of random caching qm

Fig. 5 The multicast capacity for wireless ad hoc networks for various values of ,vs. cache probability qm

Theorem 4:Under the heterogenous content access scheme with content-centric two-level hierarchical routing strategy, the equation (12).

V. CONCLUSION

ACKNOWLEDGEMENT

This work is supported by the NSF of China under Grant No. 61301118 and No. 71171045;the International S&T Cooperation Program of Shanghai Science and Technology Commission under Grant No.15220710600; the Innovation Program of Shanghai Municipal Education Commission under Grant No.14YZ130;and the Fundamental Research Funds for the Central Universities.

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