On the Effect of Group Mobility to Data
Replication in Ad Hoc Networks
Jiun-Long Huang and Ming-Syan Chen, Fellow, IEEE
Abstract—The growth in wireless communication technologies attracts a considerable amount of attention in mobile ad hoc networks. Since mobile hosts in an ad hoc network usually move freely, the topology of the network changes dynamically and disconnection occurs frequently. These characteristics make it likely for a mobile ad hoc network to be separated into several disconnected partitions, and the data accessibility is hence reduced. Several schemes are proposed to alleviate the reduction of data accessibility by replicating data items. However, little research effort was elaborated upon exploiting the group mobility where the group mobility refers to the phenomenon that several mobile nodes tend to move together. In this paper, we address the problem of replica allocation in a mobile ad hoc network by exploring group mobility. We first analyze the group mobility model and derive several theoretical results. In light of these results, we propose a replica allocation scheme to improve the data accessibility. Several experiments are conducted to evaluate the performance of the proposed scheme. The experimental results show that the proposed scheme is able to not only obtain higher data accessibility, but also produce lower network traffic than prior schemes.
Index Terms—Mobile data service, replica allocation, data accessibility, mobile computing, ad hoc networks.
æ
1
I
NTRODUCTIONT
HEadvance in wireless communication enables users toaccess information systems from anywhere at any time via various mobile devices such as notebooks, tablet PCs, personal digital assistants (PDAs), and GPRS-enabled cellular phones. Service providers are establishing a number of mobile services including weather forecasting, stock information dissemination, location-dependent query, and route guidance, to name a few. To provide such services, researchers have encountered and are endeavoring to overcome challenges in various research areas including mobile data management [1], wireless network infrastruc-ture [4], location-dependent data management [18], perva-sive computing [31], and so on.
A mobile ad hoc network (referred to as a MANET) is a self-organizing, rapidly deployable network which consists of wireless nodes without infrastructure. All nodes in a MANET are capable of moving actively and can be connected dynamically. Due to the lack of infrastructure, mobile nodes of a MANET also function as routers which discover and maintain routes, and forward packets to other nodes. A number of standards have been developed to support MANETs including IEEE 802.11 [17] and Bluetooth [8]. Example applications of MANETs include digital battle-field communications, personal area networks [32], and sensor networks. Most prior researches on MANETs focus on the development of routing protocols [22], [30] to overcome
the problems caused by node mobility. In addition, several cache frameworks are proposed to improve the performance of data access in MANETs [6], [21], [25], [39].
With the advance of technology, a mobile device is equipped with a small storage to store data items. In a collaborative work scenario, several mobile devices may work together and access data items stored in other devices. Since each node in a MANET can move freely, the topology and connectivity of the network often change dynamically. In addition, disconnection often occurs and causes frequent network division. Both characteristics will separate the network topology into several disconnected partitions and, hence, decrease the accessibility of data items. Consider the scenario in Fig. 1a, where there are six mobile devices (M1; M2; ; M6), and M1 and M6 store data items D1 and
D2, respectively. Assume that the link between M1and M4
disconnects due to the movement of mobile devices. Then, the network is divided into two partitions, P1¼
fM1; M2; M3g and P2¼ fM4; M5; M6g. The data access to D2
from a mobile device in P1(e.g., M1) will fail since P1and P2
are disconnected. Similarly, the data access to D1 from a
mobile device in P2will also fail.
Data replication is a promising technique to improve data accessibility and system performance in distributed database systems. However, in the literature of mobile computing, only a few works addressed the issues of data replication in MANETs. Xu et al. [36], [37] addressed the problem of the update of replicas in a MANET. However, each node is expected to replicate all data items in the MANET whose practicability may need further justifica-tions since the memory space is a scarce resource of mobile devices. Note that with the global topology of a fixed network, the replica allocation problem can be transformed into a minimum K-median problem which is NP-hard [14], [29]. Clearly, the problem of replica
. J.-L. Huang is with the Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan, ROC.
E-mail: jlhuang@csie.nctu.edu.tw.
. M.-S. Chen is with the Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, ROC.
E-mail: mschen@cc.ee.ntu.edu.tw.
Manuscript received 1 Feb. 2004; revised 15 Sept. 2004; accepted 14 Jan. 2005; published online 15 Mar. 2006.
For information on obtaining reprints of this article, please send e-mail to: tmc@computer.org, and reference IEEECS Log Number TMC-0018-0204.
allocation in a MANET is even more complicated since the network topology changes frequently. Hara [9] proposed the scheme DCG to address the problem of replica allocation in a MANET. The experiments in [9] show that data replication can greatly improve the data accessibility for a partitioned network. In addition, scheme E-DCG was proposed in [11] to extend scheme DCG by considering the periodic update of data items.
In reality, the moving behavior of mobile users is usually regular and follows some mobility patterns [28], [35]. Group mobility refers to the scenario where several mobile nodes tend to move together. In practice, group mobility usually occurs in collaborative works [12], [19]. For example, a group of visitors visiting an art gallery with the same guide has similar movement behavior. In addition, in military, a team of soldiers moves together to accomplish a task. As a result, a number of research works have been elaborated upon the impact of group mobility [2], [26], [27], [33], [34]. Although reducing the degradation of data accessibility to some extent, both scheme DCG and scheme E-DCG have the following two major drawbacks.
1. Generation of a large amount of traffic. In essence, because of requiring the global network connectiv-ity, both schemes are centralized and require all data nodes to broadcast their information to all other nodes, which will undesirably cause a significant amount of network traffic. In this paper, we call this phenomenon blind flooding. This situation is more severe in a MANET due to the low network bandwidth.
2. Negligence of group mobility. Consider the scenario shown in Fig. 1b. Suppose that M1and M3are in the
same mobility group and M2 is in another. Also,
assume that both groups are of different moving behaviors. Therefore, M1 and M2tend to disconnect
in the near future and only allocating D0
2 in M2 will
lead to an unsuccessful access to D2 from M1. As a
result, replica allocation schemes without consider-ing group mobility are not able to allocate replicas effectively.
In view of this, we address in this paper the problem of replica allocation by exploring group mobility. The under-lying group mobility model is assumed to be RPGM
(standing for Reference Point Group Mobility model). By analyzing the characteristic of the employed group mobility model, several theoretical results are derived. In light of these results, we propose a replica allocation scheme (referred to as scheme DRAM) to allocate replicas by considering group mobility. To avoid blind flooding, scheme DRAM takes a bottom-up approach without requir-ing the global network connectivity. In scheme DRAM, each mobile node first exchanges its motion behavior with some neighbors. The coverage of the information exchange is limited by a predetermined parameter. Then, a decentralized clustering algorithm is proposed to cluster mobile nodes with similar motion behavior into mobility groups. Hence, clusters which are likely to connect with one another later will be merged into an allocation unit to save the aggregate storage cost. Finally, data items are replicated according to the resulting allocation units. Moreover, scheme DRAM maintains the mobility groups in an adaptive manner which keeps the number of information broadcasts as small as possible and, hence, reduces the generated network traffic. These characteristics distinguish our work from others. To evaluate the performance of the proposed schemes, several experiments are conducted. The experimental results show that scheme DRAM is able to not only achieve higher data accessibility, but also produce less network traffic than prior schemes.
The rest of this paper is organized as follows: Section 2 describes the employed mobility and system models. The proposed replica allocation scheme DRAM is described in Section 3. The performance study of DRAM is given in Section 4 and, finally, Section 5 concludes this paper.
2
P
RELIMINARIES2.1 Mobility Models
Several mobility models have been proposed to model the mobility behavior of mobile nodes [5], [15], and Waypoint mobility model [16] is a widely used one. The waypoint mobility model breaks the entire movement of a mobile node into repeating pause and motion periods. In a pause period, a mobile node will stay at the current location for a certain time period. When changing to a new movement period, one node will move toward a new random-chosen
destination at a speed uniformly distributed between ½vMin; vMax. After arriving at the destination, the mobile
node will enter another pause period.
In real cases, mobile nodes may collaborate and, hence, move as a group instead of independently. RPGM is proposed in [12] to model this kind of team collaboration behavior. RPGM and its variations [19], [20], [34] are widely used to model the group mobility in a MANET [12], [26], [27], [33], [34]. In RPGM, all mobile nodes are divided into several mobility groups and all mobile nodes within the same mobility group are of similar moving behavior. Suppose that the time is divided into several slots, Tð1Þ; T ð2Þ; . Each time slot is of equal time interval . Each node is assigned to a virtual reference node. The movement of a reference node in a time slot is called a global motion vector. The global motion vectors of all reference nodes in the same mobility group are the same. The location of a mobile node is uniformly distributed in the circle centered by the location of the corresponding reference node with radius . For each mobile node, the vector from the position of the corresponding reference node to the position of the mobile node is called a random motion vector. Fig. 2 shows an example movement of the mobile nodes (i.e., M1, M2, and M3) of a mobility group which follows
RPGM model in a motion period. In each time slot, each black node represents a mobile node and the gray node with an equal number represents the corresponding reference node. The dotted circle centered by a reference node is the possible area where the mobile node will actually appear. Let PN
i ðkÞ and PiRðkÞ represent the positions of the mobile
node Miand the corresponding reference node in time T ðkÞ,
respectively. The global and random motion vectors of M3
are GM!3ðkÞ and RM!3ðkÞ, respectively. We then have
PiRðk þ 1Þ ¼ PR i ðkÞ þ GM!iðkÞ and PiNðk þ 1Þ ¼ PR i ðk þ 1Þ þ RM!iðk þ 1Þ: 2.2 System Model
Suppose that there are m mobile devices, M1; M2; ; Mm.
Each device stores and acts as the original host of several data items. There are n data items, D1; D2; ; Dn. Similar to
[9], all data items are of equal size, and each data item is held by a particular mobile host as its original host. In addition to original data items, each mobile host has an extra memory space to store SRep replicas. Similar to [11],
each data item Di is updated by its original host
periodically with period i. The access frequency of mobile
host Mito data item Djis assumed to be fijwhich is known
in advance [9], [10], [11]. We assume that each node is equipped with a GPS device and, hence, the position of the node is always available. It is possible that not all mobile nodes are equipped with GPS devices, and under such case, scheme APS [23], [24] can be employed for the mobile nodes without GPS devices to obtain their locations.
In this paper, we take RPGM as the group mobility model and the movement of each group follows a waypoint model. The speed of a group within a motion period will be a constant which follows a uniform distribution over ½vMin; vMax. We also assume that the
lengths of pause and motion periods are two exponential distributions with mean P ause and Motion time slots,
respectively. For a mobile node Mi in time T ðkÞ, we have
a global motion vector GM!iðkÞ and random motion vector
RMi
!ðkÞ. Let j j represent the length of a vector, and then we have vMin jGM!iðkÞj vMax in each motion
period and jGM!iðkÞj ¼ jRM!iðkÞj ¼ 0 in each pause period.
3
D
ESIGN OFD
ECENTRALIZEDR
EPLICAA
LLOCATION WITHG
ROUPM
OBILITYIn this section, by considering group mobility, we propose a decentralized algorithm, scheme DRAM (standing for Decentralized Replica Allocation with group Mobility), to produce effective replica allocation efficiently. Section 3.1 gives an overview of scheme DRAM. Two major phases of scheme DRAM, the allocation unit construction and replica
allocation phases, are described in Sections 3.2 and 3.3, respectively.
3.1 An Overview
Since the network connectivity changes frequently, scheme DRAM is executed periodically with period r time slots to adapt the replica allocation according to the network connectivity. This time period is referred to as a relocation period. The tasks for each mobile node in a relocation period consist of two major phases: the allocation unit construction phase and the replica allocation phase.
In the allocation unit construction phase, all mobile nodes in the network are divided into several disjoint allocation units. The formal definition of an allocation unit is as follows:
Definition 1.An allocation unit is a set of mobile nodes which share their storage and do not store repeated data item unless all data items have been allocated in this allocation unit. Then, in the following replica allocation phase, the replicas of all data items are allocated in accordance with the access frequencies of the data items and the derived allocation units of the previous allocation unit construction phase.
Clearly, the more mobile nodes each allocation unit contains, the higher data accessibility we have. However, an unstable allocation unit which will be separated into disconnected partitions later will not take advantage of storage sharing which will, in turn, cause severe degrada-tion of data accessibility. Although setting a shorter relocation period can reduce the degradation in data accessibility, this approach will produce more network traffic. Therefore, constructing large and stable allocation units is important to achieve high data accessibility.
In the allocation construction phase, scheme DRAM constructs the allocation units in a bottom-up manner by considering the group mobility. In addition to producing less traffic than prior schemes by avoiding blind flooding, scheme DRAM is able to construct more stable allocation units since mobile nodes in each resulting allocation unit are likely connected later. Moreover, scheme DRAM maintains the mobility groups in an adaptive manner which keeps the number of information broadcasts as small
as possible and, hence, reduces the generated network traffic. The details of scheme DRAM are described in the following sections. For better readability, a list of symbols used is shown in Table 1.
3.2 Allocation Unit Construction Phase
Fig. 3 shows the state transition diagram of mobile nodes in scheme DRAM. The tasks of mobile nodes in these states are described in the following sections.
3.2.1 INITIAL State
Before describing the task of nodes the INITIAL state, we first define a broadcast zone as follows:
Definition 2.The broadcast zone of a mobile node Miis a set of
mobile nodes whose distances to Mi are smaller than or equal
to a predefined T T L.
When a mobile node wants to join the MANET, it will enter the INITIAL state. In addition, a mobile node in the CLUSTER-MASTER state will enter the INITIAL state when there is no member of its cluster within its broadcast zone. A mobile node in the CLUSTER-MEMBER state will also enter the INITIAL state when its mobility group master is not within its broadcast zone. A detailed description of the CLUSTER-MASTER and CLUSTER-MEMBER states will be given in Section 3.2.3.
A mobile node in the INITIAL state will broadcast info messages to all mobile nodes in its broadcast zone. Unlike scheme E-DCG, each info message contains a time-to-live which is a predetermined constant T T L. When a mobile host Mi receives an info message of Mj, Mi will accept this
info message and forward this message to all its neighbors if the distance between Miand Mjis smaller than or equal to
T T L. Otherwise, Mi will discard the message. Therefore,
only mobile nodes connected to Mjwith a distance smaller
than or equal to T T L (i.e., those mobile nodes within the broadcast zone of Mj) will receive the info message of Mj.
The employment of T T L can avoid blind flooding and produce less network traffic.
Let an actual motion vector AM!iðx; yÞ represent the
motion of Mi from time T ðxÞ to T ðyÞ (i.e., the vector from
PN
i ðxÞ to PiNðyÞ). Suppose that T ðk 1Þ and T ðkÞ are within
the same motion period, and consider the movement scenario of Mi as shown in Fig. 4. Since 0 jRM!iðkÞj
always holds for all mobile host Mi, we have:
TABLE 1 Description of Symbols
jAM!iðk 1; kÞj jGM!iðk 1Þj 2
and
jAM!iðk 1; kÞj jGM!iðk 1Þj þ 2:
Assume that jGM!iðk 1Þj > 2 and, hence, jAM!iðk
1; kÞj > 0 when T ðk 1Þ and T ðkÞ are in the same motion period. Since the speed of each mobile node is zero only in pause periods, each mobile node Mi is in
the same pause period from T ðxÞ to T ðyÞ if and only if PN
i ðxÞ ¼ PiNðx þ 1Þ ¼ ¼ PiNðyÞ. Therefore, the pause
and motion periods of each mobile node can be recognized from its historical locations.
To achieve this, each mobile node Mimaintains a list of
its historical locations (i.e., PN
i ðkÞ) called a position list. For
each time slot, Mi will retrieve its current location, denoted
as PN
i ðk1Þ, from its GPS device and insert it into the position
list. Oweing to the limitation in storage, the capacity of a position list is limited. Suppose that the maximal capacity of a position list is SList, the current time stamp is T ðk1Þ, and
the largest time stamp among all elements in the position list is T ðk2Þ, where k2< k1. If PiNðk1Þ ¼ PiNðk2Þ, PiNðk1Þ is
discarded since T ðk1Þ and T ðk2Þ are in the same pause
period. Otherwise, PN
i ðk1Þ is inserted into the position list. If
the position list is full, the element with the smallest time stamp will be removed.
In the method to store and process historical location information mentioned above, only a small portion of historical location information (the location information of the last period) is required by scheme DRAM. Hence, it is unnecessary to store all historical location information. In addition, owing to the employment of SList, the volume of
stored historical location information is limited and can be controlled by mobile nodes.
For each mobile node, an info message contains the following fields which can be obtained from its position list:
. id: The host id.
. tsNow: The time stamp of the current relocation
period.
. PiNðtsNowÞ: The location of Mi in time T ðtsNowÞ.
. tsP auseStart; tsP auseEnd : The time stamps of the start and end
time of the latest pause period.
. tsMotion
Start ; tsMotionEnd : The time stamps of the start and end
time of the latest motion period.
. AM!iðtsMotionStart ; tsMotionEnd Þ: The actual motion vector of
the latest motion period.
Example.Consider an example position list shown in Fig. 5. This list records the positions of a mobile host Mi from
Tð2Þ to T ð15Þ. The motion of Mi can be divided into
two pause periods (i.e., from T ð2Þ to T ð5Þ and from T ð7Þ to T ð9Þ) and two motion periods (i.e., from T ð5Þ to T ð7Þ and from T ð9Þ to T ð15Þ). Since PN
i ð9Þ is not in the
position list, we have PN
i ð9Þ ¼ PiNð7Þ ¼ ð5; 4Þ and
AMi
!ð9; 15Þ ¼ ð1 5; 7 4Þ ¼ ð6; 3Þ. As a result, the content of the info message broadcast by Mi in T ð15Þ is:
fi; 15; h1; 7i; 7; 9; 9; 15; h6; 3ig.
3.2.2 ZONE-MASTER and ZONE-MEMBER States After broadcasting info messages, the mobile nodes are classified into two groups by the lowest-id clustering algorithm proposed in [7]. Each node in the INITIAL state whose host id is the smallest one among all nodes within its broadcast zone (obtained from the id field of all received info messages) is selected as the master of its broadcast zone and, hence, enters the ZONE-MASTER state. On the other hand, the other nodes enter the ZONE-MEMBER state. A node Miin the ZONE-MEMBER state will join the node Mj
in the ZONE-MASTER state with the smallest id among the nodes within the broadcast zone of Mi by sending a join
messages to Mj.
Each node Miin the ZONE-MASTER state then clusters
its member nodes (i.e., those node which send the join messages to Mi) into clusters, and all nodes within a cluster
are expected to have similar motion behaviors. The employed clustering algorithm is as follows: First, all nodes are clustered by the periods of the latest pause and motion periods recorded in info messages since all mobile nodes in the same cluster are of equal records of latest pause and motion periods (i.e., have the same tsP ause
Start, tsP auseEnd , tsMotionStart ,
and tsMotion
End in their info messages). However, several
mobile nodes within different mobility groups (i.e., of different motion behaviors) may be placed into the same cluster especially when the length of a motion period is larger than the length of position lists. To achieve better results, the master node should recluster the resulting clusters again by considering motion vectors. With the scenario shown in Fig. 4, we have the following lemmas. Lemma 1. The expectation of AM!iðk 1; kÞ is equal to
GMi
!ðk 1Þ.
Fig. 4. The locations of a mobile host Miin Tðk 1Þ and T ðkÞ.
Proof.Suppose that the polar coordinate representations of the random motion vectors in T ðk 1Þ and T ðkÞ in Fig. 4 are RM!iðk 1Þ ¼ ðr1; 1Þ and RM!iðkÞ ¼ ðr2; 2Þ,
respec-tively. Also, let the density function of r1, r2, 1, and 2be
fr1, fr2, f1, and f2, respectively. We have
fr1ðaÞ ¼ d daP robfr1 g ¼ d da 2 a2 22 ¼2a 2; and f1ðbÞ ¼ 1 2: Similarly, we also have fr2ðcÞ ¼
2c
2 and f2ðdÞ ¼
1
2. tu
Since r1, 1, r2, and 2are independent, the joint density
function of r1, 1, r2, and 2is
fr1;1;r2;2ða; b; c; dÞ ¼ fr1ðaÞ f1ðbÞ fr2ðcÞ f2ðdÞ
¼a c 24 :
Let the locations of PR
i ðk 1Þ and P R
i ðkÞ be ðx1; y1Þ
and ðx2; y2Þ, respectively. Clearly, the Cartesian
coordi-nate of GM!iðk 1Þ is hx2 x1; y2 y1i. Suppose that
AM!iðk 1; kÞ ¼ h; i. We have
E½r2cos 2 r1cos 1 ¼
Z 0 Z 0 Z 2 0 Z 2 0 a c 24 r2cos 2 r1cos 1 d1d2dr1dr2¼ Z 0 Z 0 a c 24 r2 Z 2 0 cos 2 d2r1 Z 2 0 cos 1d 1 dr1dr2 ¼ 0:
Then, we can derive the following equation: E½ ¼ E½the x coordinate of PR
i ðkÞ
the x coordinate of PR i ðk 1Þ
¼ E½x2þ r2cos ðx1 r1cos Þ
¼ x2 x1þ E½r2cos 2 r1cos 1
¼ x2 x1:
Similarly, we can also show that E½ ¼ y2 y1 and,
finally, we have:
E½AM!iðk 1; kÞ ¼ E½h; i
¼ hE½; E½ i ¼ hx2 x1; y2 y1i
¼ GM!iðk 1Þ:
From Lemma 1, we have the following observation. If the length of position lists (i.e., SList) is large enough and the
length motion period is long enough, the global motion vector of each mobile node can be approximated. However, it is impractical to store too many previous positions of a mobile node. Therefore, we propose a vector clustering algorithm below. To facilitate our presentation, we denote the global
motion vector of Mifrom T ðk1Þ to T ðk2Þ (i.e., the vector from
PiRðk1Þ to PiRðk2Þ) as Vi
!
ðk1; k2Þ. For Mi, if T ðk1Þ and T ðk2Þ are
in the same motion period and T ðk2Þ > T ðk1Þ, we have
Vi
!
ðk1; k2Þ ¼ ðk2 k1Þ GM!iðk1Þ. In addition, we represent
motion vectors as polar coordinates (i.e., length-angle forms) and T ðk1Þ and T ðk2Þ are assumed to be in the same motion
period and k2> k1.
Lemma 2.For a mobile host Mi, the maximum absolute value of the
difference between the angles of AM!iðk1; k2Þ and Vi
! ðk1; k2Þ is sin1 ðk2 k1Þ vMin ;
where vMin, , and represent, respectively, the minimum
speed of mobile nodes, the length of a time slot, and the maximal length of random vectors.
Proof.Consider the scenario shown in Fig. 6. Let be the absolute value of the difference between the angles of AMi
!ðk
1; k2Þ and Vi
!
ðk1; k2Þ. is maximal when PiNðk1Þ ¼
P1and PiNðk2Þ ¼ P2 or P3. Since 0, we have
sinðÞ jVi ! ðk1; k2Þj ¼ ðk2 k1Þ jGM!iðk1Þj ðk2 k1Þ vMin : Finally, we have 0 sin1 ðk2 k1Þ vMin : t u
Lemma 3.For a mobile host Mi, the maximal absolute value of
the differences between the lengths of AM!iðk1; k2Þ and
Vi
!
ðk1; k2Þ is 2.
Proof.The distance between PR
i ðk1Þ and PiRðk2Þ is jVi ! ðk1; k2Þj ¼ ðk2 k1Þ jGM!iðk1Þj: A Mi !ð k
1; k2Þ is maximal when PiNð k1Þ ¼ P5 and
PiNðk2Þ ¼ P6, and, therefore, we have
AM!iðk1; k2Þj jVi ! ðk1; k2j jVi ! ðk1; k2Þj þ 2 jVi ! ðk1; k2Þj ¼ 2:
Similarly, AM!iðk1; k2Þ is minimal when PiNðk1Þ ¼ P1and
PN
i ðk2Þ ¼ P4. Again, we have the following equation:
jAM!iðk1; k2Þj jVi ! ðk1; k2j jVi ! ðk1; k2Þj 2 jVi ! ðk1; k2Þj ¼ 2:
Finally, we have 0 jAM!iðk1; k2Þj jVi
! ðk1; k2j
2. tu For vectors vi¼ ðri; iÞ and vj¼ ðrj; jÞ, vjis said to be “a
neighbor in angle with maximal difference of vj” if
ji jj . Similarly, vjis said to be “a neighbor in length
with maximal difference dist of vj” if jri rjj dist. For
each mobile node Mi, AM!iðk1; k2Þ is a neighbor in angle
with a maximal difference of of Vi
!
ðk1; k2Þ, where is equal
to the result in Lemma 2. Similarly, according to Lemma 3, AM!iðk1; k2Þ is the neighbor in length with maximal
difference 2 of Vi
! ðk1; k2Þ.
In a mobility group, the number of the neighbors in angle with maximal difference of Vi
!
ðk1; k2Þ is maximal among all
actual motion vectors of all group members. Similarly, the number of the neighbors in length with maximal difference 2of Vi
!
ðk1; k2Þ is maximal among all actual motion vectors
of all group members. With the result of Lemma 1 and the above observations, we have the following two heuristics:
1. In a mobility group, an actual motion vector is close to the global motion vector if it has the maximal
number of neighbors in angle with maximal difference .
2. In a mobility group, an actual motion vector is close to the global motion vector if it has the maximal number of neighbors in length with maximal difference 2.
In accordance with the above heuristics, we develop algorithm VectorCluster which is an efficient node clustering algorithm comprised of two major procedures, ClusterByAngle and ClusterByLength. The algorithmic form of algorithm VectorCluster is shown in Fig. 7.
After executing the algorithm VectorCluster, each zone master will select one cluster master for each resulting cluster. Then, the selected mobile nodes will enter the CLUSTER-MASTER state, and the other nodes will enter the CLUSTER-MEMBER state.
Example 2. Consider the scenario shown in Fig. 8. Clustering by the time of latest pause and motion periods (i.e., line one of Algorithm VectorCluster in Fig. 7) will form two clusters: fM1; M2; ; M10g and
fM11g. M11 is separated from other nodes since it has
different latest pause and motion periods.
Then, fM1; M2; ; M10g will be reclustered by angle.
The actual motion vectors of M1; M2; ; M10are drawn in
Fig. 9 in a counterclockwise order. Assume that vMin¼ 5,
vMax¼ 7, and ¼ 2. According to Lemma 2, we have
¼ jsin1ð 2
532Þj ¼ 0:1545. The number of neighbors in
angle with maximal difference 0:1545 for each vector is then calculated. v1 is a neighbor of v3 since the absolute
value of the difference between angles of them is j0:42 0:56j ¼ 0:14 < 0:1545. On the other hand, v5 is not
a neighbor of v3 since the absolute value of the difference
between angles of them is j0:9 0:56j ¼ 0:34 > 0:1545. Since the actual motion vector of M7 (i.e., v7) is of the
maximal number of neighbors, M7 and its neighbors in
angle form a cluster. The rest actual motion vectors are processed analogously. The results of procedure Cluster-ByAngle on fM1; M2; ; M10g are fM1; M2; M3; M4g and
fM5; M6; ; M10g as shown in Fig. 9a.
All resulting clusters of procedure ClusterByAngle are reclustered again by procedure ClusterByLength. From Lemma 3, we have dist ¼ 2 ¼ 4. Similarly, the number of neighbors in length with maximal difference 4 for each motion vector is calculated. v5is a neighbor of v7 since the
absolute value of the difference between the lengths of them is j15:7 15:1j ¼ 0:6 < 4. On the other hand, v6 is not a
neighbor of v5 since j31:2 15:1j ¼ 16:1 > 4. Therefore,
fM5; M6; ; M10g is reclustered into fM5; M7; M10g and
fM6; M8; M9g by procedure ClusterByLength as shown in
Fig. 9b. The result of algorithm VectorCluster on fM1; M2,
; M10g is shown in Fig. 9c and, finally, these 11 mobile
nodes are clustered into four clusters: fM1; M2; M3; M4g,
fM5; M7; M10g, fM6; M8; M9g and fM11g.
3.2.3 CLUSTER-MASTER and CLUSTER-MEMBER States
The tasks of cluster masters and members consist of two steps, cluster maintenance and cluster merge, which are described below.
Cluster Maintenance. Mobile nodes which enter the CLUSTER-MASTER and CLUSTER-MEMBER states in current allocation unit construction phase will skip the cluster maintenance step and execute the cluster merge step in this allocation unit construction phase. The other mobile nodes will execute cluster maintenance step before execut-ing cluster merge step. Since the clusters are constructed by considering group mobility, each cluster is likely to be connected in the near future. These clusters are maintained in the following adaptive fashion.
Each cluster member first sends a status message to its cluster master. The contents of status messages are similar to those of info messages. If the mobile node and its cluster master are disconnected, the mobile node will leave the current cluster and enter the INITIAL state. At the same time, the cluster master will remove the mobile hosts which do not send status messages to it from its member list.
The cluster master then checks whether the moving behaviors recorded in received status messages are similar to one another by the following procedure. The cluster master first clusters the motion behaviors stored in received status messages by the clustering algorithm proposed in Section 3.2.2. If each cluster member keeps similar motion behavior to what it used to have, the result of the execution of the clustering algorithm is one cluster which contains all cluster members. If some cluster members change their motion behaviors, the result will consist of several clusters. Let the dominating cluster of the resulting clusters be the cluster with the most nodes among all resulting clusters. Those mobile nodes not in the dominating cluster will then receive reject messages from the cluster master, and enter the INITIAL state. Note that only mobile nodes with different moving behavior from the majority of the original cluster will not be in the dominating cluster. If the original cluster master is not in the dominating cluster, it will assign one node in the dominating cluster as the new cluster master. The new cluster master will then send reject messages to the mobile nodes which are not in the dominating cluster.
Fig. 8. An illustrative example.
Fig. 9. An example of motion vector clustering onfM1; M2; ; M10g. (a) The results of procedure ClusterByAngle. (b) The results of procedure
Except the first execution of scheme DRAM, most mobile nodes will be in the MASTER or CLUSTER-MEMBER state since only mobile nodes disconnected with its cluster master or with different moving behavior from its cluster members will enter the INITIAL state. Therefore, the successive execution of scheme DRAM will produce less network traffic than the first execution because only the first execution of scheme DRAM requires all mobile nodes to broadcast messages. As shown in Section 4, the adaptive cluster maintenance is able to effectively reduce produced network traffic.
Cluster Merge.If two mobile nodes, M1and M2, tend to
connect to each other, replicating one data item in M1 also
makes this data item accessible for M2. Hence, M2 can
replicate another data item which will be also accessible for M1. As mentioned in Section 3.1, merging clusters which
tend to be connected in the near future into a big allocation unit makes the mobile nodes within different clusters share their storage and, hence, improve the data accessibility.
In replica allocation construction, only the resulting clusters which are likely to connect with one another until the next execution of scheme DRAM will be merged into the same allocation unit. Initially, each resulting cluster is assigned to be an allocation unit. Assume that the current and next executions of scheme DRAM are in T ðkÞ and Tðk þ rÞ, respectively. Then, we have the following definitions.
Definition 3.The bounding rectangle of an allocation unit is a rectangle which contains all nodes of the allocation unit. Denote the bounding rectangle of cluster Ci in T ðkÞ as
BRiðkÞ. Let BRiðkÞ be represented by four values: topiðkÞ,
bottomiðkÞ, leftiðkÞ, and rightiðkÞ. Then, we have
topiðkÞ ¼ max 8Mjin Ci
fthe y Coordinate ofMjin TðkÞg;
bottomiðkÞ ¼ min 8Mjin Ci fthe y coordinate of Mjin TðkÞg; leftiðkÞ ¼ min 8Mjin Ci fthe x coordinate of Mjin TðkÞg; rightiðkÞ ¼ max 8Mjin Ci fthe x coordinate of Mjin TðkÞg: Definition 4. Let BR
iðk þ rÞ be the estimated bounding
rectangle of the allocation unit Ci in T ðk þ rÞ. Assume that
the latest info message of the master node is in T ðkÞ, we have topiðk þ rÞ ¼ topiðkÞ þ r y;
bottomiðk þ rÞ ¼ bottomiðkÞ þ r y;
leftiðk þ rÞ ¼ leftiðkÞ þ r x;
rightiðk þ rÞ ¼ rightiðkÞ þ r x; where
hx; yi ¼the average of all AMi
!ðtsMotion
Start ; tsMotionEnd Þ in Ci
tsMotion
End tsMotionStart
:
Definition 5. Two allocation units Ci and Cj are said to be
cluster-wise connected in T ðkÞ if
1. BRiðkÞ and BRjðkÞ are overlapped or
2. there exists another allocation unit Cxso that BRiðkÞ
and BRjðkÞ are overlapped with BRxðkÞ, respectively.
Definition 6. Two allocation units Ci and Cj are said to be
potentially cluster-wise connected in T ðk þ rÞ if 1. BRiðk þ rÞ and BR
jðk þ rÞ are overlapped or
2. there exists a Cxso that BRiðk þ rÞ and BRjðk þ rÞ
are overlapped with BRxðk þ rÞ, respectively.
We observe that two allocation units Ci and Cj can be
merged into a new allocation unit if Ciand Cjare cluster-wise
connected in T ðkÞ and potentially cluster-wise connected in Tðk þ rÞ.
Example 9.Fig. 10 shows the bounding rectangles of cluster C1and C2in T ðkÞ and the estimated bounding rectangles
of C1and C2in T ðk þ rÞ. Although the moving behaviors
of C1 and C2 (i.e., GM!1ðkÞ and GM!2ðkÞ) are much
different, C1 and C2 are still cluster-wise connected in
TðkÞ and potentially cluster-wise connected in T ðk þ rÞ. As a result, they should be merged into an allocation unit in order to increase the data accessibility in C1and C2.
In replica allocation construction, each cluster master will broadcast a merge message containing the cluster master id, the current and estimated bounding rectangles. Note that the merge relation is an equivalence relation since it is reflective, symmetric and transitive. The cluster merge process can be performed by the following the procedure shown in Fig. 11.
3.3 Replica Allocation Phase
In order to compare to [11], the objective of replica allocation phase is to identify data items to be replicated, and the locations to replicate them for each allocation unit in order to maximize the data accessibility. The employed replica allocation algorithm is as follows: Let the allocation weight of data item Dj in allocation unit Cx in T ðkÞ
(denoted as wx
jðkÞ) be from now on, the expected number of
data access from all mobile nodes in Cx before the next
update of Dj. Suppose that the current time stamp is T ðkÞ,
wxjðkÞ can be obtained by the following equation: wxjðkÞ ¼ fx
j ðUj kÞ; where fjx¼
X
8 Mi2Cx
fij;
and Ujis the time-stamp of the next update of Dj. Since the
update of each data item is periodic, Ujcan be predicted in
advance.
All data items are allocated in Cx according to their
allocation weights in Cx in descendent order. Let the
allocation candidate set of Djin Cxbe a set of mobile hosts
in Cx where each mobile host in the set is of available
storage and with at least one path to the owner of Dj. If the
candidate set of Djin Cxis not empty, Dj will be allocated
to Mi, where fijis the largest among all mobile hosts in the
allocation candidate set of Dj. Otherwise, Dj will be
skipped. The allocation process completes if all mobile hosts in Cx is full. Each unit master then executes the
following replica allocation process as shown in Fig. 12. 3.4 Complexity Analysis
In algorithm ClusterVector, the complexity of clustering vectors by their time of the latest pause and motion periods is OðjVjÞ. In procedure ClusterByAngle, to calculate the number of neighbors in angle, these vectors are sorted according their angles and complexity of sorting is OðjVj log VjÞ, where jVj is the number of input vectors. After calculation, these vectors are sorted again by their number of neighbors. The clustering process (i.e., the loop in lines 3-6) requires one scan of these vectors. Therefore, the complexity of procedure ClusterByAngle is OðjVj log VjÞ. Similarly, the complexity of procedure ClusterByLength is also OðjVj log VjÞ. As a result, the complexity of algorithm VectorCluster is OðjVj log VjÞ.
In procedure ReplicaAllocation, the calculation of alloca-tion weight for each data item requires one scan of fijfor each
data item Djand each mobile node Mi, and its complexity is
O m jCj
, wherem
jCj is the average number of mobile nodes in an
input cluster. The replica allocation process (i.e., the loop in lines 3-6) will traverse all data items once, and its complexity is OðnÞ. Finally, the complexity of procedure ReplicaAlloca-tion is O m
jCjþ n
. 3.5 Remarks
Li and Wang [20] proposed two pattern recognition-based algorithms to recognize mobility groups, and devised a service replication algorithm to provide continuous multi media streaming services. Different from this paper, the work in [20] is based on RVGM (Reference Velocity Group Mobility) which is a variation of RPGM. In addition, the mobility recognition algorithms proposed in [20] are centralized, and similarly to scheme E-DCG, will be prone for having much network traffic.
Yin and Cao [38] stated that, although being able to achieve high data accessibility, storage sharing among neighboring mobile nodes also increases query delay. Hence, Yin and Cao [38] proposed scheme RN to balance the tradeoffs between data accessibility and query delay based on the following two concepts:
1. Each mobile node shares only part of its storage with its neighbors.
2. A mobile node Mionly cooperates with its neighbors
which tend to be directly connected with Mi in the
future.
The work in [38] is indeed complementary to the work in this paper. When data accessibility and query delay are required to be considered together, it is easy to integrate the
Fig. 11. Procedure ClusterMerge(C).
above concepts into scheme DRAM to balance the tradeoffs between data accessibility and query delay.
4
P
ERFORMANCEE
VALUATION4.1 System Model
Although the notion of exploiting group mobility to data replication was mentioned in [13], the performance of scheme DRAM on several parameters was yet to be investigated. Consequently, we implemented an event-driven simulator in C++ with SIM [3] to evaluate the performance of scheme DRAM on various parameters. Scheme E-DCG is also implemented for comparison purposes. We assume that there are 120 mobile nodes in a 50m 50m flatland and each node owns 20 data items. The system parameters are shown in Table 2. Similar to [9], the access frequency for each data item, fij, is determined as a
positive value based on the normal distribution with mean 0:025ð1 þ 0:01iÞ and standard derivation 0:0025. For both schemes, the revised RPGM described in Section 2.2 is taken as the underlying group mobility model of the simulation. The simulation is run for 3,000 seconds.
Similar to [11] and [21], data accessibility is employed as the measurement of the performance of these schemes.
When one mobile node Miissues a data request, the request
is successful if the required data item is stored in Mi or in
another mobile node connected to Mi. Therefore, the data
accessibility is defined as below:
Accessibility¼Number of successful requests Number of issued requests : We also use the produced network traffic to evaluate the cost of the employed schemes. Similar to [9], traffic is defined as the total hop counts of message transmission (e.g., info messages, join messages . . . ) of all schemes. 4.2 The Effect of Relocation Period
In the first experiment, we investigate the effect of the varied relocation period in data accessibility and traffic of all schemes. Fig. 13 shows the effects of scheme E-DCG and DRAM with the relocation period ranging from 200 to 800. We observe from Fig. 13a that the data accessibility increases as the value of relocation period decreases. It can be explained that a shorter relocation period implies the more executions of relocation schemes and, therefore, makes both replica relocation schemes be able to quickly adapt to the mobility behavior of mobile nodes by frequently generating allocation units according to the network connectivity. We also observe that scheme DRAM outperforms scheme E-DCG in data accessibility. This result shows the importance of the consideration of group mobility. Since scheme E-DCG only considers the current network connectivity, the generated allocation units are unstable and may be partitioned soon. Hence, the effect of scheme E-DCG is limited. On the contrary, the generated allocation units of scheme DRAM are stable since the generated allocation units are formed with mobility groups. Therefore, the data accessibility of scheme DRAM is higher than that of scheme E-DCG. In addition, the performance gain of scheme DRAM over scheme E-DCG in data accessibility increases as the relocation period decreases. The reason is that each execution of scheme DRAM can obtain better replica allocations than that of scheme E-DCG and, hence, a short relocation period strengthens the advantage of scheme DRAM over scheme E-DCG.
Fig. 13b shows the produced network traffic of scheme DRAM and E-DCG with the relocation period varied. We
TABLE 2 System Parameters
observe that the produced network traffic increases as the relocation period decreases. The reason is that with the same time interval, a shorter relocation period implies more executions of the relocation schemes and, hence, implies more exchanged messages. It is also observed that the produced network traffic of scheme DRAM is smaller than that of scheme E-DCG. Due to the natural of blind flooding, the amount of network traffic produced by scheme E-DCG is rather large. On the contrary, scheme DRAM employs T T L to avoid blind flooding in the exchange of info messages and adopts a decentralized and hierarchical approach to form allocation units. Hence, the amount of network traffic produced by scheme DRAM is less sensitive on the number of mobile nodes than that produced by scheme E-DCG.
In addition, the increment of the produced network traffic of scheme DRAM is less than that of scheme E-DCG when the value of relocation period decreases. It is because that scheme DRAM adaptively maintains the mobility groups in the cluster maintenance step without requiring each mobile node to broadcast its information in each relocation period as scheme E-DCG. Therefore, the succes-sive executions of scheme DRAM will produce less network traffic than the first execution. Since a short relocation period implies frequent executions of relocation schemes, the network traffic reduction of scheme DRAM over scheme E-DCG increases as the value of relocation period decreases.
4.3 The Effect of the Number of Mobile Nodes This experiment investigates the effect of the number of mobile nodes. The data accessibility and produced traffic of both schemes with the the number of mobile nodes varied are shown in Fig. 14. The number of mobile nodes ranges from 40 to 200.
As observed in Fig. 14a, the data accessibility increases as the number of mobile nodes increases. It is because that with the same number of mobility groups, more mobile nodes imply that each mobility group is of more mobile nodes. Since the network connectivity of the mobile nodes within one mobility group is stable, more mobile nodes can share their storage by constructing large allocation units, and as a consequence, increase the data accessibility. It is also shown that scheme DRAM outperforms scheme E-DCG in data accessibility. It is because that scheme DRAM can take advantage of group mobility to obtain higher data accessi-bility than scheme E-DCG by constructing larger and more stable allocation units than scheme E-DCG.
As observed in Fig. 14b, the amounts of produced traffic of all schemes increase as the number of mobile nodes increase. In addition, the amount of produced traffic of scheme E-DCG increases drastically as the number of mobile nodes increases. This is due to the characteristic of blind flooding employed in scheme E-DCG that the amount of produced network traffic increases exponentially as the number of mobile nodes increases. On the other hand, the amount of produced traffic of scheme DRAM is less sensitive than that of scheme E-DCG. The reason is that the T T L in
Fig. 14. The effect of the number of mobile nodes. (a) Accessibility. (b) Traffic.
info messages can effectively reduce the number of ex-changed messages in the INITIAL state. In addition, the adaptive cluster maintenance in scheme DRAM is able to reduce the number of broadcast messages and, therefore, reduce the amount of produced network traffic. This result shows the scalability of scheme DRAM over scheme E-DCG. 4.4 The Effect of the Number of Mobility Groups We investigate in this experiment the performances of all schemes under cases with different degree of group mobility. The effects in the accessibility and traffic for both schemes with the the number of mobility groups varied are shown in Fig. 15. The number of mobility groups is setting from 1 to 120. In the case with 120 mobility groups, we set ¼ 0 so that this case degenerates to the case of waypoint mobility model.
We observe that the data accessibilities of all schemes are equal to 100 percent when the number of groups is set to one. In the case with one mobility group, the data accessibility is dependent on the initial network connectiv-ity and the effect of the maximal length of random vectors. In this experiment, since the initial network topology is connected and the maximal length of random vectors is relatively smaller than radio radius, the network topology will not be partitioned and all mobile nodes are connected throughout the simulation, thereby having complete data accessibilities for both schemes. When the number of groups is set to two, the data accessibilities are reduced to around 55 percent since each mobility group contains about half the mobile nodes and the network topology is highly likely to be separated into two equally sized partitions. These results show that the data accessibilities of scheme DRAM and scheme E-DCG are similar when the number of mobility groups is small.
When the number of mobility groups is larger than two, the data accessibilities of all schemes decrease as the number of mobility groups increases. It is because that with the same number of mobile nodes, the smaller number of mobile groups indicates that more mobile nodes are of similar moving behavior. Hence, more mobile nodes can share their storage by constructing large allocation units and, hence, increase the data accessibility. Moreover, as shown in Fig. 15a, scheme DRAM outperforms scheme E-DCG especially when the number of mobility groups is large (from four to 20 in this experiment). The larger number of mobility groups indicates that the movement
behavior of all mobile nodes are less regular. Therefore, the allocation units obtained by scheme E-DCG are more unstable and, hence, the data accessbility of scheme E-DCG degrades. On the other hand, scheme DRAM reduces the effect of the increment of the number of mobility groups by considering group mobility when constructing allocation units. As a result, the degradation in data accessibility of scheme DRAM is less significant than that of scheme E-DCG. This result shows that scheme DRAM outperforms scheme E-DCG when the number of mobility groups is medium. However, the performance gain of scheme DRAM over scheme E-DCG diminishes greatly when the number of mobility groups is large. Under these cases, since the network topology changes quickly and is highly likely to be partitioned into several disconnected partitions, the effect of replication diminishes significantly. As observed in Fig. 15b, the amount of traffic produced by all schemes increases as the number of mobility groups decreases. When the number of mobility groups is large, the MANET tends to be separated into many disconnected partitions since fewer mobile nodes are of similar moving behavior. Therefore, the amount of produced traffic of all schemes is small since many mobile nodes disconnect with others when the MANET is separated into several parti-tions. In addition, we also observe that scheme DRAM produces less network traffic than scheme E-DCG. Due to adaptive procedures of scheme DRAM, the successive executions of scheme DRAM are able to execute in an adaptive manner and, hence, produce less traffic than the first execution.
When the number of mobility groups is small, the MANET is often separated into several partitions, and each partition contains more mobile nodes than that in the case with many mobility groups. Due to the message exchange among adjacent mobile nodes, the produced traffic of all schemes are larger than that in the case with many mobility groups. With the employment of blind flooding, the amount traffic produced by scheme scheme E-DCG exponentially increases as the number of mobility groups increases. On the other hand, in scheme DRAM, due to the employment of T T L in info messages, the amount of message exchange in INITIAL state is greatly reduced. Therefore, the decrease of the number of mobility groups only slightly increases the amount of produced traffic.
4.5 The Effect of the Number of Replicas Per Node In this section, we investigate the effect of the number of replicas per node which is set from 5 to 120. Since the number of replicas per node does not affect the produced traffic of all schemes, only accessibility is shown in this experiment. Fig. 16a shows the effect of scheme E-DCG and DRAM in data accessibility. As shown in Fig. 16a, the data accessibility increases as the number of replicas per node increases. With a larger number of replicas per node, each mobile node has more space to store replicas, and each allocation unit has more shared storage. Moreover, the increment in data accessibility decreases when the number of replicas per node is large enough (i.e., 20 in this experiment) since data items with high access frequencies have mostly been replicated. Due to the consideration of group mobility, scheme DRAM utilizes the shared space better than scheme E-DCG by generating more stable allocation units and, hence, leads to better data accessibility than scheme E-DCG does.
4.6 The Effect of Update Period
In this section, we investigate the effect of update period which is set from 100 seconds to 500 seconds. The effect of scheme E-DCG and DRAM in data accessibility with the length of update period varied is shown in Fig. 16b. Similarly, only accessibility is shown in this section since the update period does not affect the traffic of all schemes. As observed in Fig. 16b, the data accessiblities of all schemes decrease as the update period decreases. It is because that a shorter update period implies frequent updates on data items. As a result, a short update period makes each replica invalid soon, thereby reducing the effect of replication. In addition, the improvement of scheme DRAM over scheme E-DCG decreases as the update period decreases. This can be explained by the fact that quick invalidations of replicas incurred by short update period will reduce the effect of data replication. As a consequence, although scheme DRAM is able to generate better replica allocation than scheme E-DCG, due to quick invalidation of replicas, the superiority of scheme DRAM over scheme E-DCG diminishes significantly as the update period decreases.
4.7 Effect of the Precision of Location Information In this section, we investigate the effect of the precision of location information on accessibility, and the experimental
result is shown in Fig. 17a. We assume that a GPS is likely to produce random errors in location information, and the error of location information is defined as the maximal distance between the actual location of a mobile node and the location reported by the GPS device of the mobile node. Intuitively, the smaller the error is, the more precise the location information is. Since scheme E-DCG does not rely on location information, its performance is not affected by precision of location information. On the other hand, the performance of scheme DRAM degrades as the error of information information increases since scheme DRAM relies on location information to form stable allocation units. However, as shown in Fig. 17a, the performance degrada-tion of scheme DRAM is limited even the error is up to three meters. This phenomenon results from the effect of precision lists. Since a precision list stores multiple locations of the corresponding mobile node in the latest motion period, according to Lemma 1, the expectation of the motion vectors in the position list is equal to the actual motion vector of the mobile node. Therefore, the aggregated location information stored in the precision list is close to the corresponding actual motion vector. As a consequence, the motion vectors in info messages are close to the actual motion vectors and, hence, the performance degradation of DRAM caused by the error of location information is limited.
4.8 Effect of Packet Loss Rate
Since the wireless communication is prone to packet errors, packet loss is common in MANETs. We investigate in this section the effect of packet loss rate on data accessibility. Packet loss rate is setting from 0 percent to 20 percent and the corresponding experimental result is shown in Fig. 17b. It is intuitive that data accessibilities of both schemes degrade as packet loss rate increases. In addition, as shown in Fig. 17b, the superiority of scheme DRAM over scheme E-DCG diminishes when the pack loss rate is high. Since scheme DRAM relies on the exchange of location information among neighboring mobile nodes, in the case of high packet loss rate, one node may miss some location information of its neighbors and, therefore, recognize some connected nodes as unconnected. Such situation results in smaller allocation units which lead to lower degree of storage sharing and lower data accessibility. The experimental result shows that both schemes are vulnerable on packet loss. The degradation of accessibility caused by packet loss can be reduced by some
techniques such as acknowledge and retransmission which enable reliable transmission at the cost of increasing produced network traffic.
4.9 The Effect of the Value of Time-to-Live
Fig. 18 shows the experimental results with the values of time-to-live (T T L) and simulation time varied. The values of T T L and simulation time are set from five meters to 20 meters and from 600 seconds to 3,000 seconds, respectively. We use “DRAM-n” to indicate the scheme DRAM with T T L ¼ n. It is obvious that the values of T T L only slightly affect data accessibilties. Although the smaller T T L value indicates that some mobility groups may be partitioned into several clusters, they are likely to be merged into the same allocation unit in the procedure of cluster merge. Therefore, the value of T T L does not significantly affect the accessbilities.
Fig. 18b shows the produced network traffics of all schemes with simulation time varied. Due to the employ-ment of blind flooding, scheme E-DCG produces more traffic than all other schemes. We also observe that DRAM-based schemes with smaller T T L values produce less traffic than that with larger T T L values in the 600th second. It is because that when the relocation period is set to 600 sec-onds, most mobile nodes are in INITIAL states before the 600th second and, hence, the produced traffic before the 600th second is mainly caused by the broadcasting of infomessages. Since the value of T T L indicates the ranges of the info message broadcasting in INITIAL states, and as a result, DRAM-based schemes with smaller T T L values produce less traffic than that with larger T T L values. After the 600th second, most mobile nodes are in CLUSTER-MASTER and CLUSTER-MEMBER states. Therefore, most mobile nodes perform the procedure of cluster maintenance instead of info message broadcasting in each relocation period. DRAM-based schemes with smaller values of T T L indicate smaller clusters and, therefore, in the procedure of cluster maintenance, they produce more traffic (i.e., transmission of status messages) than DRAM-based schemes with larger values of T T L. As a result, DRAM-based schemes with smaller T T L produce less traffic in the first relocation period, and produce more traffic in the successive relocation periods than DRAM-based schemes with larger T T L. As shown in Fig. 18b, the traffic produced
by DRAM-based schemes with smaller T T L is smaller than that produced by DRAM-based schemes with larger T T L, and they are getting more and more close when the time approaches the 3000th second.
5
C
ONCLUSIONWe explored in this paper the problem of replica allocation in a MANET with group mobility. We first analyzed the employ group mobility model and derived several theore-tical result. In light of these results, we proposed a replica allocation scheme DRAM to allocate replicas by considering group mobility. To evaluate the performance of the proposed schemes, several experiments were conducted. The experimental results showed that scheme DRAM cannot only obtain higher data accessibility, but also produce less traffic than prior schemes.
R
EFERENCES[1] D. Barbara, “Mobile Computing and Databases—A Survey,” IEEE Trans. Knowledge and Database Eng., vol. 11, no. 1, pp. 108-117, Jan./ Feb. 1999.
[2] K. Blakely and B. Lowekamp, “A Structured Group Mobility Model for the Simulation of Mobile Ad-Hoc Networks,” Proc. ACM Int’l Workshop Mobility Management and Wireless Access, Sept.-Oct. 2004.
[3] D. Bolier and A. Elie¨ns, “SIM: A C++ Library for Discrete Event Simulation,” http://www.cs.vu.nl/~eliens/sim/, Oct. 1995. [4] A. Bria, F. Gessler, O. Queseth, R. Stridh, M. Unbehaun, J. Wu, and
J. Zander, “4th-Generation Wireless Infrastructures: Scenarios and Research Chanllenges,” IEEE Personal Comm., vol. 8, no. 6, pp. 25-31, Dec. 2001.
[5] T. Camp, J. Boleng, and V. Davies, “A Survey of Mobility Models for Ad Hoc Network Research,” Wireless Comm. and Mobile Computing, vol. 2, no. 5, pp. 483-502, 2002.
[6] R. Friedman, M. Gradinariu, and G. Simon, “Locating Cache Proxies in MANETs,” Proc. Fifth ACM Int’l Symp. Mobile Ad Hoc Networking and Computing, May 2004.
[7] M. Gerla and J. Tsai, “Multicluster, Mobile, Multimedia Radio Network,” ACM/Baltzer Wireless Networks, vol. 1, no. 3, pp. 255-265, 1995.
[8] J.C. Haartsen, “The Bluetooth Radio System,” IEEE Personal Comm., vol. 7, no. 1, pp. 28-36, Feb. 2000.
[9] T. Hara, “Effective Replica Allocation in Ad Hoc Networks for Improving Data Accessibility,” Proc. IEEE INFOCOM Conf., Apr. 2001.
[10] T. Hara, “Cooperative Caching by Mobile Clients in Push-based Information Systems,” Proc. 12th ACM Int’l Conf. Information and Knowledge Management, Nov. 2002.
[11] T. Hara, “Replica Allocation Methods in Ad Hoc Networks with Data Update,” ACM/Kluwer Mobile Networks and Applications, vol. 8, no. 4, Aug. 2003.
[12] X. Hong, M. Gerla, G. Pei, and C.-C. Chiang, “A Group Mobility Model for Ad Hoc Wireless Networks,” Proc. Second ACM Int’l Workshop Modeling Analysis and Simulation of Wireless and Mobile Systems, Aug. 1999.
[13] J.-L. Huang, M.-S. Chen, and W.-C. Peng, “Exploring Group Mobility for Replica Allocation in a Mobile Ad-Hoc Network,” Proc. 12th ACM Int’l Conf. Information and Knowledge Management, Nov. 2003.
[14] S. Jamin, C. Jin, A.R. Kurc, D. Raz, and Y. Shavitt, “Constrained Mirror Placement on the Internet,” Proc. IEEE INFOCOM Conf., Apr. 2001.
[15] A. Jardosh, E. Belding-Royer, K. Almeroth, and S. Sun, “Towards Realistic Mobility Models for Mobile Ad Hoc Networks,” Proc. Ninth ACM Int’l Conf. Mobile Computing and Networking, Sept. 2003. [16] D.B. Johnson and D.A. Maltz, Dynamic Source Routing in Ad Hoc
Wireless Networks. Kluwer Academic Publishers, 1996.
[17] S. Kapp, “802.11: Leaving the Wire Behind,” IEEE Internet Computing, vol. 6, no. 1, Feb. 2002.
[18] D.L. Lee, B. Zheng, and W.-C. Lee, “Data Management in Location-Dependent Information Services,” IEEE Pervasive Com-puting, vol. 1, no. 3, pp. 65-72, July-Sept. 2002.
[19] B. Li, “On Increasing Service Accessibility and Efficiency in Wireless Ad-Hoc Networks with Group Mobility,” Wireless Personal Comm., vol. 21, no. 1, pp. 105-123, Apr. 2002.
[20] B. Li and K.H. Wang, “NonStop: Continuous Multimedia Streaming in Wireless Ad Hoc Networks with Node Mobility,” IEEE J. Selected Areas in Comm., vol. 21, no. 10, pp. 1627-1641, Dec. 2003.
[21] S. Lim, W.-C. Lee, G. Cao, and C.R. Das, “A Novel Caching Scheme for Internet Based Mobile Ad Hoc Networks,” Proc. 12th Int’l Conf. Computer Comm. and Networks, Oct. 2003.
[22] M. Mauve, J. Widmer, and H. Hartenstein, “A Survey on Position-Based Routing in Mobile Ad Hoc Networks,” IEEE Network, vol. 15, no. 6, Nov./Dec. 2001.
[23] D. Niculescu and B. Nath, “Ad Hoc Positioning System (APS),” Proc. IEEE GLOBECOM Conf., Nov. 2001.
[24] D. Niculescu and B. Nath, “Error Characteristics of Ad Hoc Positioning Systems (APS),” Proc. Fifth ACM Int’l Symp. Mobile Ad Hoc Networking and Computing, May 2004.
[25] P. Nuggehalli, V. Srinivasan, and C.-F. Chiasserini, “Energy-Efficient Caching Strategies in Ad Hoc Wireless Networks,” Proc. Fourth ACM Int’l Symp. Mobile Ad Hoc Networking and Computing, June 2003.
[26] G. Pei, M. Gerla, and X. Hong, “LANMAR: Landmark Routing for Large Scale Wireless Ad Hoc Networks with Group Mobility,” Proc. First ACM Ann. Workshop Mobile Ad Hoc Networking and Computing, Aug. 2000.
[27] G. Pei, M. Gerla, X. Hong, and C.-C. Chiang, “A Wireless Hierarchical Routing Protocol with Group Mobility,” Proc. IEEE Wireless Comm. and Networking Conf., Sept. 1999.
[28] W.-C. Peng and M.-S. Chen, “Developing Data Allocation Schemes by Incremental Mining of User Moving Patterns in a Mobile Computing System,” IEEE Trans. Knowledge and Data Eng., vol. 15, no. 1, Feb. 2003.
[29] L. Qiu, V.N. Padmanabhan, and G.M. Voelker, “On the Placement of Web Server Replicas,” Proc. IEEE INFOCOM Conf., Apr. 2001. [30] E.M. Royer and C. Toh, “A Review of Current Routing Protocols for Ad-Hoc Mobile Wireless Networks,” IEEE Personal Comm., vol. 6, no. 2, pp. 46-55, Apr. 1999.
[31] M. Satyanarayanan, “Pervasive Computing: Vision and Chal-lenges,” IEEE Personal Comm., vol. 8, no. 4, pp. 10-17, Aug. 2001. [32] T.M. Siep, I.C. Gifford, R.C. Braley, and R.F. Heile, “Paving the
Way for Personal Area Network Standards: An Overview of the IEEE P802.15 Working Group for Wireless Personal Area Net-works,” IEEE Personal Comm., pp. 6-13, Feb. 2000.
[33] K.H. Wang and B. Li, “Efficient and Guaranteed Service Coverage in Paritionable Mobile Ad-Hoc Networks,” Proc. IEEE INFOCOM Conf., June 2002.
[34] K.H. Wang and B. Li, “Group Mobility and Partition Prediction on Wireless Ad-Hoc Networks,” Proc. IEEE Int’l Conf. Comm., pp. 1017-1021, Apr. 2002.
[35] H.-K. Wu, M.-H. Jin, J.-T. Horng, and C.-Y. Ke, “Personal Paging Area Design Based on Mobile’s Moving Behaviors,” Proc. IEEE INFOCOM Conf., Apr. 2001.
[36] B. Xu, O. Wolfson, S. Chamberlain, and N. Rishe, “Cost Based Data Dissemination in Broadcast Networks,” Proc. Eighth Int’l Conf. Database Theory, Jan. 2001.
[37] B. Xu, O. Wolfson, S. Chamberlain, and N. Rishe, “Cost Based Data Dissemination in Satellite Networks,” ACM/Kluwer Mobile Networks and Applications, vol. 7, no. 1, Jan. 2002.
[38] L. Yin and G. Cao, “Balancing the Tradeoffs between Data Accessibility and Query Delay in Ad Hoc Networks,” Proc. 23rd IEEE Symp. Reliable Distributed Systems, Oct. 2004.
[39] L. Yin and G. Cao, “Supporting Cooperative Caching in Ad Hoc Networks,” Proc. IEEE INFOCOM Conf., Mar. 2004.
Jiun-Long Huang received the BS and MS degrees from the Department of Computer Science and Information Engineering at Na-tional Chiao Tung University in 1997 and 1999, respectively, and the PhD degree from the Department of Electrical Engineering at National Taiwan University in 2003. Currently, he is an assistant professor in the Depart-ment of Computer Science at National Chiao Tung University. His research interests in-clude: mobile computing, mobile data management, wireless net-works, and Internet technology.
Ming-Syan Chen received the BS degree in electrical engineering from National Taiwan University, Taipei, Taiwan, and the MS and PhD degrees in computer, information, and control engineering from The University of Michigan, Ann Arbor, in 1985 and 1988, respec-tively. Dr. Chen is currently a professor and the chairman of the Graduate Institute of Commu-nication Engineering, and a professor in the EE Department and also the CSIE Department at National Taiwan University, Taipei, Taiwan. He was a research staff member at IBM Thomas J. Watson Research Center, Yorktown Heights, New York, from 1988 to 1996. His research interests include database systems, data mining, mobile computing systems, and multimedia networking, and he has published more than 200 papers in his research areas. Dr. Chen served as an associate editor of the IEEE Transactions on Knowledge and Data Engineering (TKDE) from 1997 to 2001, is currently on the editorial board of the Very Large Data Base (VLDB) Journal, the Knowledge and Information Systems (KAIS) Journal, the Journal of Information Science and Engineering, and the International Journal of Electrical Engineering, and is a Distinguished Visitor of the IEEE Computer Society for Asia-Pacific from 1998 to 2000. He served as the program chair of PAKDD-02 (Pacific Area Knowledge Discovery and Data Mining), International Vice Chair of INFOCOM 2005, and program vice chair of IEEE ICDCS 2005, ICPP 2003, and VLDB-2002. He was a keynote speaker on Web data mining at the International Computer Congress in Hong Kong, 1999, a tutorial speaker on Web data mining at DASFAA-1999 and on parallel databases in the 11th IEEE ICDE in 1995 and also a guest coeditor for the IEEE Transactions on Knowledge and Data Engineering on a special issue for data mining in December 1996. He holds, or has applied for, 18 US patents and seven ROC patents in the areas of data mining, Web applications, interactive video playout, video server design, and concurrency and coherency control protocols. He is a recipient of the NSC (National Science Council) Distinguished Research Award, Pan-Wen Yuan Outstanding Research Award, and K.-T. Li Research Penetration Award for his research work, and also the Outstanding Innovation Award from IBM Corporate for his contribution to a major database product. He also received numerous awards for his research, teaching, inventions, and patent applications. Dr. Chen is a fellow of the IEEE and a member of the ACM.
. For more information on this or any other computing topic, please visit our Digital Library at www.computer.org/publications/dlib.
