Performance Improvement of Delay-Tolerant Networks with Mobility Control under Group Mobility

Abstract

This paper considers mobility control to improve packet delivery in delay-tolerant networks (DTNs) under group mobility. Based on the group structure in group mobility, we propose two mobility control techniques; group formation enforcement and group purposeful movement. Both techniques can be used to increase the contact opportunities between groups by extending the group's reachability. In addition, they can be easily integrated into some existing DTN routing schemes under group mobility to effectively expedite the packet delivery. This paper is divided into 2 parts. First, we study how our proposed mobility control schemes reduce the packet delivery delay in DTNs by integrating them into one simple routing scheme called group-epidemic routing (G-ER). For each scheme, we analytically derive the cumulative density function of the packet delivery delay to show how it can effectively reduce the packet delivery delay. Then, based on our second proposed technique, the group purposeful movement, we design a new DTN routing scheme, called purposeful movement assisted routing (PMAR), to further reduce the packet delay. Extensive simulations in NS2 have been conducted to show the significant improvement of PMAR over G-ER under different practical network conditions.

1. Introduction

Delay-tolerant network (DTN) is a sparse or disconnected mobile ad hoc network where there is normally no connection or end-to-end path between any source and destination pair [1]. Hence, the traditional routing protocols designed for the connected network, such as Dynamic Source Routing (DSR) [2], fail to work in DTN [10]. In previous studies in DTN, two main approaches are proposed for the packet delivery, which are illustrated as follows.

The first approach is to increase the network connectivity by introducing more nodes to the network, thus decreasing or even avoiding the probability of the disconnection in the network [3-6]. In [3], these introduced nodes are randomly distributed in the network, whereas in [4-6] they are purposely placed to fill the gaps dynamically formed in the network or to keep the network connected most of time. However, the main drawbacks of introducing this kind of node with a special role in DTN lie in the potential failure of these special nodes and the centralized way to detect the disconnection and displace these special nodes.

The second approach, called store-carry-forward approach [7], is to make use of the movement of the node to deliver packets. Since there is no guarantee to set up a complete route between the source and destination pair in DTN, one feasible way for the packet delivery is to wait for any new contact opportunities arising in the changing of the network topology caused by the node movement. Therefore, to store and carry the packet becomes essential in this second approach. Most proposed routing schemes adopting this store-carry-forward approach can be further classified into the opportunistic routing and the mobility control based routing.

In the opportunistic routing, each node follows its initial planned movement and does not change its trajectory even though it cannot be connected to the destination(s) [8-15]; and it just passively waits for the chances to be connected to other nodes including the destination node(s) during its movement. Obviously, the problem of this strategy is that the packet delivery delay is unpredictable or very long in case that the destination node is out of contact from most of the nodes for long time. By contrast, in the mobility control based routing, the mobility of some nodes is controlled that they move purposely over the network area to assist in establishing a connection to the destination node(s) [16-19]. Thus, with mobility control in DTN, packets can be delivered faster. In [16,17], a special kind of node, called ferry node, is introduced to the network, and its mobility is controlled to assist other nodes in the packet delivery. Specifically, if a source node has packets to send to a destination node, the ferry node will firstly move towards the source node and carry its packets. Then, the ferry node helps deliver the packets to the destination node. Similar to [4-6], the drawback in [16,17] lies in the potential failure of the ferry node. Authors in [18] considers only adjusting the node speed for optimal packet delivery, whereas a more complicated solution is proposed in [19], where some intermediate nodes are employed to move to certain locations to help establish an end-to-end connection to the destination node. However, this solution suffers from its strict assumptions, e.g., how each node moves in the network should be known to each other in advance.

Hence, as seen from the previous DTN studies (e.g., [19]) above, mobility control is a promising approach to shorten the packet delivery delay in DTN, but the difficulty lies in its deployment. The reason for this difficulty is that most studies above target entity mobility [23], which assumes independence among nodes’ movement. However, the mobility control based routing requires some intermediate nodes to move in a cooperative way as shown in [19]. In fact, nodes in many real scenarios are required to move in a cooperative way due to some common mission or interest for them. For example, in the military field, soldiers or tanks for a common mission generally form a group and move forward close to each other. Thus, group mobility [20-22] is proposed to mimic this type of cooperative scenarios. In general, most of group mobility models proposed before [20-22] present the following two features. First, nodes in one group form a connected sub-network and there is a leader in each group to organize and manage its group. Thus, when the groups in the network are isolated, a disconnected network will be formed. Second, the cooperation can be well supported in each group. With these two features, it is obvious that the mobility control can be implemented under group mobility.

In this paper, we consider the performance improvement of mobility control in DTN under group mobility [20-22]. Specifically, we propose two mobility control techniques under group mobility; the group formation enforcement and the group purposeful movement. The group formation enforcement requires some nodes in one group to be positioned strategically such that these nodes can help extend the reachability of the group. Thus, this technique can be used to increase the contact opportunities between groups. The group purposeful movement considers creating a new connection between two groups by letting some nodes in one group move purposely to approach the other group which is currently out of contact. The new created connection provides a way for one group to deliver packets to the other. Hence, with this second technique, one group can expand its reachability and create more contact opportunities with other groups. Importantly, both two proposed mobility control techniques can be easily integrated into some existing DTN routing scheme to effectively expedite the packet delivery or reduce the packet delivery delay. In this paper, we focus on the study of how each proposed technique reduces the packet delivery delay in DTN. To the best of our knowledge, none of the previous studies has considered the mobility control for the packet delivery in DTN under group mobility. The contribution of this paper is threefold.

The rest of this paper is organized as follows. In Section 2, we give a brief review of G-ER. Section 3 gives the stochastic analysis of how the two proposed mobility control techniques reduce the packet delivery delay, respectively. PMAR is illustrated in Section 4, followed by the simulation study in Section 5. Lastly, Section 6 concludes this paper.

 

2. Review of Group-Epidemic Routing

G-ER [21], which is designed based on a well-known DTN routing protocol, i.e., Epidemic Routing [10], is specifically proposed for group mobility. The key strategy in G-ER is to treat each group as one unit and disseminate one copy of each packet to one group only, and it works as follows.

If a packet is an intra-group packet (or if a packet has its source and destination in the same group), it will be routed to its destination by the intra-group routing, i.e., Destination Sequenced Distance Vector routing (DSDV). And if a packet is an inter-group packet (or if a packet is destined to another group), it will be firstly routed by the inter-group routing to any other group which does not have a copy of this packet. Finally, this inter-group packet will reach its destination group, and then will be delivered to its destination node by DSDV. Note that the destination node of a packet never delivers that packet to other groups. Here, we simply illustrate how the inter-group routing in G-ER works to deliver inter-group packets between groups.

First, when two groups meet each other, each group determines what packets the neighboring group has not received. For this determination, each node in one group maintains a table called Group Summary Vector (GSV), which is used to record the packets previously received by all of the nodes in its group. Thus, the two groups’ GSVs are firstly exchanged to let each node in the two groups obtain the neighboring group’s GSV, the details of which are shown in Fig. 1a. Second, after comparing the received GSV with the own maintained GSV, each node can send the packets the neighboring group does not have, as shown in Fig. 1b. Third, once a node receives some new packets from the neighboring group, it will inform other nodes in its group about these new received packets and let them update their GSVs.

Fig. 1.GSV exchange and broadcast inside the group (a) and data packet exchange between groups in G-ER (b)

Another important mechanism proposed in G-ER is the buffer sharing in each group. This mechanism states that the buffer resource of one node can be shared by all other nodes in its group. Thus, with buffer sharing, if one node detects its buffer is full upon receiving some inter-group packets, it can store them at other nodes in its group.

 

3. Analysis of the Two Mobility Control Techniques

In this Section, we firstly present the network model for our analysis. Then, based on this model, we give the stochastic analysis of how the two proposed mobility control techniques reduce the packet delivery delay of G-ER in DTN under group mobility, respectively.

3.1 Network Model

In this analysis, we suppose that there are a total of N+1 (N≥1) independent groups moving within a L×L (km2) network area, and that the radio transmission range of each node is r (in km). Other important assumptions related to the network model are stated as follows.

First, we illustrate how each group in the network is formed. As mentioned earlier, each group is organized by a leader, so we assume that the leader locates at the center of the group and all of its members move randomly around it. Moreover, we further assume that each member is within the radio transmission range of the leader, r, for simplicity. Thus, each group assumed here has a circular coverage with a radius of d (d≤r) (in km), as shown in Fig. 2a. Actually, our group structure is similar to the widely used group mobility model called Reference Point Group Mobility (RPGM) [22], of which details are omitted here.

Fig. 2.The assumed group structure (a) and illustration of the group movement (b)

Second, we present how each group moves in the network area. The movement of each group conforms to the Random Waypoint Mobility Model (RWMM) [24]. Specifically, before a group starts to move, its leader randomly selects a destination point in the network area, and each member also randomly selects a point near the leader’s point within a distance of d. Then, the leader chooses a velocity, v, uniformly in [vmin,vmax] (in km/h), and each member chooses a velocity around v. Note that this velocity selection for the group member is used to keep each group connected most of time. Later, once all nodes reach their destination points, they can pause for time tp. After the pause time, the group repeats the above procedure to continue moving. Fig. 2b roughly illustrates how one group moves within the network area.

Third, similar to [25], we assume a simple traffic model for this analysis: among the N+1 groups, only one group, say group x, generates one data packet P1 to send to another group, say group y. Note that this data packet can be generated by any node in group x.

Fourth, we further assume that (1) each group is capable of storing one data packet; and (2) if two groups meet (i.e., if any two nodes from two groups meet), the contact duration is long enough to allow any node in one group to send a data packet to the other group. Thus, if group x meets an intermediate group, say group z, which previously has not received P1, then group z can also obtain P1 after this meeting.

3.2 Cumulative Density Function of the Packet Delivery Delay in G-ER

With the abovementioned assumptions and the group behavior defined in G-ER in Section II, we firstly derive the lower bound and the upper bound of the cumulative density function (CDF) of the packet delivery delay, TGE, under G-ER when tp=0 and r≪L. We denote FTGE as the CDF of TGE, and we let LB(FTGE) and UB(FTGE)represent the lower bound and the upper bound of FTGE, respectively. These two bounds will be considered as the benchmark in our paper. To derive the two bounds, we start with the computation of the following three parameters when tp=0 and r≪L.

Fig. 3.Maximal distance in a connection between two leaders

Now, we employ Ordinary Differential Equations (ODEs) [26,27] to derive LB(FTGE). With the fourth assumption above, we can see that actually determines how fast the data packet is spread over groups in the network. This is to say, if two groups meet frequently (i.e., if is small), then P1 will be spread quickly. Thus, due to < as shown above, we can derive LB(FTGE) by assuming conforms to the known distribution of or by assuming d=0. Suppose the packet delivery delay in G-ER is T′GE under the assumption of d=0, then we have LB(FTGE)=FT′GE. To derive FT′GE, two steps are involved.

Step 1: Calculation of X(t). Suppose X(t) is dedicatedly used to count the number of groups (excluding the destination group) which have received P1 at time t. Then, X(t) can be treated as a Markov chain with the transition rate, R(t), expressed as follows

For (3), we can use the following differential equation to solve it [25,26]

The differential equation (4) above is separable and can be solved with the initial condition X(0)=1, i.e., only the source group x owns P1 at time 0. Consequently, X(t) is expressed as follows, of which the derivation is omitted here.

Step 2: Derivation of FT′GE. Suppose at time t the destination group y has not received P1. Then, let us consider P(t

Due to FT′GE(t)=P(T′GE≤t) andFT′GE(t+δt)=P(T′GE≤+t+δt), we have the following differential equation for FT′GE(t) from (6):

The differential equation (7) is also separable and can be solved with the initial condition FT′GE(0)=0. Finally, we obtain FT′GE(t) or LB(FTGE)as shown in the following expression, of which the derivation is omitted here.

Next, we proceed to derive UB(FTGE). Similarly, due to > , we can derive UB(FTGE)by assuming conforms to the known distribution of . Particularly, the steps to derive UB(FTGE)are the same as those to derive LB(FTGE) shown above. More specifically, we only need to replace with in (8) to obtain UB(FTGE), which is given by the following equation.

3.3 The Group Formation Enforcement

In previous sub-section, we have shown the lower bound and the upper bound of FTGE. In fact, it is highly impossible to achieve the upper bound of FTGE because of the random mobility of the group members around the leader in each group. Here, we propose a simple mobility control technique called the group formation enforcement to approach the upper bound of FTGE. The group formation enforcement imposes a constraint on the mobility of some members in each group such that a certain structure or formation appears in each group. Suppose each group leader leads at least four members, then the formation enforcement works as follows.

Fig. 4.The extended reachability of the group (a) and the connection between two leaders under the formation enforcement (b)

Obviously, with this formation enforcement technique, the reachability of each group will be extended. More specifically, if we fix the four selected members above at the four boundary positions, then, any node within a distance of d+r to the leader is very likely to be connected to the leader, as shown in Fig. 4a. Thus, as shown in Fig. 4b, it is also very likely that two leaders within a distance of 2d+r can be connected, which indicates that ≈ or ≈. Consequently, with the group formation enforcement in G-ER, the upper bound of FTGE given by (9) can be approximated.

Note that for the CDF derivation above, we assume that each group is connected or all members in a group are within the radio transmission range of the leader. In fact, observing from Fig. 4 that we only need four members to execute the group formation enforcement, we could keep UB(FTGE)still being approximated by the group formation enforcement even if we allow other members to leave freely from the group.

To show how the upper bound of FTGE is approximated under the formation enforcement, we run simulation in NS2 to show the CDF of TGE in the case of d≈r. As a comparison, we also conduct simulations by deactivating the formation enforcement or allowing all members to move freely around the leader. We emphasize that all simulation results shown here are collected in the ideal case that the contact duration between two meeting groups is long enough to allow one data packet to be sent from one group to the other. Table 1 shows the main simulation parameters.

Table 1.Simulation parameters in the formation enforcement

Before showing the simulation results of FTGE, we firstly determine UB(FTGE) and LB(FTGE) shown in (9) and (8), respectively. It can be seen from (8) and (9) that we only need to determine and under the setting shown in Table 1 for LB(FTGE) and UB(FTGE), respectively. In [24] it has shown that E[V∗]=8.7km/h under RWMM when tp=0 and [vmin,vmax]=[4,10]. Thus, we get ≈0.148 from (1) and =0.444 from (2). Accordingly, LB(FTGE) and UB(FTGE) are already determined under our simulation setting, as shown in Fig. 5.

Fig. 5.Comparison between simulation results and analytical results for FTGE

After hundreds of simulation times, the collected simulation results of FTGE are shown in Fig. 5. It can be observed that 1) with the group formation enforcement, G-ER delivers packets faster than that without mobility control, and 2) the group formation enforcement is an effective technique to improve G-ER to approach UB(FTGE).

3.4 The Group Purposeful Movement

Besides the technique of the group formation enforcement, we here introduce another mobility control technique called the group Purposeful Movement (PM). Due to the cooperative nature of each group mentioned earlier, the leader can command some of its members (e.g., robots or unmanned aerial vehicles in the military field, and hereafter called PM members) to move towards some other group to create a new connection between them when this other group is not far away but currently out of connection. For example, as shown in Fig. 6, when the leader X detects that group Y is currently three hops away, it can let two members, nodes I and J, to move fast to approach group Y. Obviously, if a connection can be created between group X and group Y, it can expedite the packet delivery. This is the motivation for this second mobility control technique in this paper.

Fig. 6.Connection creation in the purposeful movement of a group

In this sub-section, we integrate this PM into G-ER to form a new scheme called G-ER+ and analytically study how this PM reduces the packet delivery delay of G-ER. For simplicity, we have the following three assumptions for this study.

With the three assumptions above, we now proceed to derive the CDF of the packet delivery delay, TPM, in G-ER+. We denote FTPM as the CDF of TPM. Similarly, the derivation of FTPM also involves two steps as shown below.

Step 1: Calculation of X(t) in G-ER+. Here, X(t) is defined the same as before. Because there is no PM between any two of the groups counted by X(t) in G-ER+, the derived X(t) in G-ER+ is very close to that in G-ER in the condition of d≈0. Thus, X(t) in G-ER+ can be given by (5) approximately.

Step 2: Derivation of FTPM. Similar to the derivation of FT′GE shown above, we need to firstly determine the rate of group y receiving P1 at time t. Since at time t there are X(t) groups owning P1, including the source group, the total rate of group y receiving P1 is given by (M+1)+(X(t)−1), where the first term is contributed by the source group and the rest is contributed by all intermediate groups, of which each owns the packet P1. Consequently, we obtain the following equation

Thus, from (10) we obtain the differential equation (11) as follows

The differential equation (11) is also separable and can be solved with the initial condition FTPM(0)=0. We omit the details of the derivation and show FTPM as follows.

Note that to have FTPM(t) in (12), we only need several members in one group to stay close to the leader to execute PM. Thus, in the group purposeful movement, we also do not require all members to stay close to the leader. We now present the following three observations based on (12).

First, to achieve the packet delivery delay TPM within some certain value of t at a given probability, we can set a minimal M, Mmin, properly. For example, under the network setting shown in Table 1 but with d≈0, Table 2 shows several small values of Mmin for achieving different values of t with FTPM(t)≥0.8. A larger Mmin not shown in Table 2 is actually not practical because we expect that it is not possible to create a connection between two groups far apart due to the group mobility.

Table 2.Mmin under network setting shown in Table 1 but with d≈0

Second, the proposed PM technique works more effectively in a DTN with small N. That is, when N is small, the average packet delivery delay of G-ER will be reduced more by the PM technique. We use one example as shown in Fig. 7 to show this observation. The results, i.e., the delay reduction of G-ER+ over G-ER, in Fig. 7 are obtained based on (8) and (12) at different N. It can be seen that the average packet delivery delay of G-ER is reduced more by the PM technique when N is small. The main reason for this observation is that when N is small, the network is more disconnected and thus, it is more likely that the packet highly relies on PM technique to be delivered to the destination. Third, given fixed M and N, the delay reduction of G-ER+ over G-ER does not vary with . This actually can be derived from (8) and (12). However, for simplicity, we also use one example to show this observation. Fig. 8 shows the delay reduction of G-ER+ over G-ER at different but with fixed M and N. Obviously, it can be seen that for any given M and N, the delay reduction keeps constant regardless of . Thus, the analysis here shows that the effectiveness of the PM technique is mainly determined by M and N.

Fig. 7.The delay reduction of G-ER+ over G-ER at different N

Fig. 8.The delay reduction of G-ER+ over G-ER at different

 

4. Purposeful Movement Assisted Routing

From the previous Section, we can see that the group formation enforcement is just a mobility control technique and it works independently of the DTN routing. However, the PM technique, as shown in Fig. 6, further requires some specific mechanisms to initiate the purposeful movement of a group and deliver packets effectively along the newly established connection. Hence, in this Section we propose a new routing scheme called purposeful movement assisted routing (PMAR) to implement the PM technique. Then, by integrating PMAR into G-ER, we can study how it improves G-ER by simulation under different practical conditions.

First, we present the following two assumptions in PMAR: (1) each group member and each leader in the network is equipped with Global Positioning System (GPS); and (2) each leader is able to increase its transmission power to have a longer transmission range, R, in addition to the normal transmission range, r. Second, we present the two major objectives that PMAR needs to achieve; to establish a new connection between two disconnected groups if necessary and to deliver packets along the new established connection.

Now we proceed to introduce how PMAR is executed in a cooperative way in a group. There are eight major steps in PMAR as listed below: the first five steps are executed for the first objective, and the steps six and seven are executed for the second objective.

The first five steps used to create a new connection between groups are as follows.

After the five steps above, a new connection could be established provided that the destination group does not go too far away. Subsequently, the packet delivery along this new connection (i.e., the second objective in PMAR) follows.

Fig. 9.Connection notification in PMAR

The overhead in terms of the energy consumption in PMAR is actually very limited. It can be seen that the overhead in PMAR refers to the transmissions of PMreply, PMsearch, and other control packets. The lengths of these control packets are similar, but the transmissions of PMreply and PMsearch require a radio with longer transmission range, thus consuming most of the energy in PMAR. Nevertheless, both PMreply and PMsearch are very short messages (only several bytes) as compared to the data packet, and later we will see from the simulation study that the number of PMreply and PMsearch transmitted in total is very low. Hence, the energy consumption in PMAR is very limited.

Now we illustrate how the proposed PMAR is integrated into G-ER to cooperate for the packet delivery. First, each group member in G-ER is required to report its buffer state to its leader: whenever a member is ready to broadcast its periodic DSDV routing update in G-ER, its current buffer state is collected and carried in the routing update packet. This member buffer state mainly states the number of inter-group packets destined to each other group. Again, only the information of the inter-group packet generated by the group itself is collected in this report, because one group is not responsible for carrying out the PM for other groups. Second, with this member buffer state information, a group leader can determine whether to initiate PMAR as introduced in Step 1). If PMAR is not triggered in one group, then, that group will follow the procedures in G-ER to exchange packets with other groups. Hence, from the interaction between PMAR and G-ER, we can see that PMAR can be treated as an independent module to boost the performance of G-ER.

 

5. Simulation Study and Results

5.1 Simulation Model

The simulation study in this Section is conducted in NS2 to show how PMAR improves G-ER under different practical network conditions, namely under different searching range, R, different group speed, and different group buffer size. First, for the searching range, R, two values are selected; 2r and 3r. Second, we select the speed range [vmin,vmax] from three non-overlapped ranges as will be shown later. Third, we vary the total buffer space in each group (i.e., the group buffer size) from an inadequate value to an adequate value. The “inadequate” (“adequate”) means the group buffer size is less (larger) than the total number of the data packet generated at the source nodes. We would like to study how these three factors interactively affect the effectiveness of PMAR in improving G-ER. The main performance metric in this simulation study is the average packet delivery delay, td.

There are five groups in a 1km×1km network area with 9 members in each group, and each group moves conforming to RWMM. The normal radio transmission range, r, for each node is 0.1km. For the traffic model, we let only one group among the five groups be the source group to generate traffic to another group for simplicity. The source group will generate a total of 400 packets: five members in the source group will take turn to generate packets every 50 seconds from the beginning of the simulation; and each member will generate 80 packets at a rate of 1 packet per second. Here, we assume the buffer space of the source group is fixed and it is capable to store all generated packets. Thus, all data packets can be successfully delivered to the destinations in all routing schemes in our simulation. Table 3 shows other main default simulation parameters, among which the PM member speed, Spm, is set at a relatively high value, i.e., 15m/s, as compared to the group speed. For each setting in the simulation, it is run for at least sixteen times to make the result within 90% confidence interval ±5%.

Table 3.Default simulation parameters in PMAR

5.2 PMAR at Different Group Buffer Size and Searching Range

In this sub-section, we study how PMAR improves G-ER under the default parameters shown in Table 3 by changing the group buffer size, b, and the searching range, R.

Fig. 10 shows the packet delivery delay, td, of G-ER and G-ER with PMAR at different b and R. Two observations can be made from Fig. 10. First, it can be seen that PMAR reduces td of G-ER at all b and R. Particularly, we see that td of G-ER is significantly reduced by PMAR with a longer R (=3r). This is because with a longer R, the destination group could be found earlier and thus, the packet can be delivered earlier. Table 4 shows the performances in terms of the packet delivery ratio, rpmar, and the packet delivery delay, dpmar, of PMAR at different b and R. Obviously, it can be seen that dpmar at R = 300m is much shorter than that at R = 200m. Actually, we will find later that this longer R takes effect only when the group moves at a low speed or when the new connection established in PMAR stays for adequately long time. Second, for each R, as the group buffer size increases, the delay of G-ER is less reduced by PMAR. For example, when R = 300m, td of G-ER is reduced by about 35% at b = 100 whereas it is reduced by about 20% at b = 700. There are two reasons for this observation. On one hand, with larger b of each group, G-ER itself delivers packets faster, thus reducing td as shown in Fig. 10. On the other hand, with larger b, the ability of each intermediate group in forwarding the packets of the source group is intensified. As a result, the packet number delivered by PMAR decreases. By comparing the percentage of the packet delivered by PMAR, rpmar, at different b in Table 4, we see that rpmar decreases to some extent at large b, especially at R = 300m. Consequently, the effectiveness of PMAR gradually diminishes as b increases.

Fig. 10.The average packet delivery delay, td

Table 4.Performance of PMAR

Note that the cost or overhead in achieving the benefit of PMAR above is limited. That is, we find in the simulation that the total number of the transmitted PMsearch and PMreply is only about 40 at R = 300m and Wt = 15s. Besides, we also find that decreasing Wt increases the total cost, but cannot attain more benefit from PMAR. However, at a longer Wt, e.g., 30 s, the total cost decreases, but the benefit of PMAR is reduced. Hence, obviously, a proper Wt should be determined by the group mobility model to balance the benefit of PMAR and the energy consumption in PMAR: with a large Wt, the source group is likely to miss the opportunity to find the destination group nearby, and a small Wt is unnecessary and increases the energy consumption.

5.3 PMAR at Different Group Speed

In this sub-section, we proceed to study how PMAR improves G-ER at different group speeds, s. In addition to the default speed range shown in Table 3, i.e., [1,4] (m/s), we set two higher speed ranges for this study; [4,7] (m/s) and [7,10] (m/s). The simulation here is conducted at a relative high b = 500 with other default parameters listed in Table 3.

Table 5 shows the performance, in terms of td, between G-ER and G-ER with PMAR at different ranges of s. Obviously, as s increases, the improvement of G-ER with PMAR over G-ER descreases regarding the packet delivery delay. For example, as s increases to [7,10] (m/s), the delay reduction at R=300 even vanishes. There are two reasons for this observation. First, G-ER itself performs more effectively by delivering packets much faster as the group speed increases, as shown in Table 5. This is because there are more contact opportunities between any two groups at higher group speed, which allows the packet to be spread to groups faster. Second, the contribution (i.e., the delivered packet number) of PMAR is reduced at high s. One reason is due to the unstable connection established by PMAR at high s. In order to see this instability, we define the following two parameters for the connection stability:

Table 5.Performance of G-ER with PMAR at different node speed

Table 6 shows Pbpmar and rpmar at different s when R=300. Overall speaking, it shows that Pbpmar and rpmar decreases with s. The trend of these two parameters shows that a less stable connection in PMAR is established at a higher group speed. Hence, as the contribution of PMAR diminishes at high s, the improvement of PMAR made to G-ER almost diminishes.

Table 6.Connection parameters in PMAR at different node speed when R = 300

 

6. Conclusions

In this paper, we propose two mobility control techniques for delay-tolerant networks (DTN) under group mobility by making use of unique properties of the group structure. The two techniques are the group formation enforcement and the group purposeful movement. Both two techniques are simple, but effective in extending the reachability of the group, and they can be integrated into some existing DTN routing scheme under group mobility to expedite the packet delivery. We integrate them into a simple replication based routing scheme called group-epidemic routing (G-ER) and analytically show that 1) with the group formation enforcement, the upper bound of the cumulative density function of the packet delivery delay in G-ER can be approached; and 2) with the group purposeful movement, the packet delivery delay in G-ER can be greatly reduced in the scenario where a limited number of groups exist.

In particular, we put emphasis on the performance study of the second technique, i.e., the group purposeful movement, under different network conditions. Specifically, we firstly design a new routing scheme called purposeful movement assisted routing (PMAR) to implement this second technique. Then, we conduct simulations in different network conditions to evaluate the effectiveness of PMAR in improving G-ER. The simulation results show that PMAR works effectively when the group buffer size is small and the group speed is low.

Based on the simulation results in this paper, we believe that we can still improve PMAR by maintaining a stable connection to the destination group in PMAR at relatively high group speed. In addition, given a group mobility model, how to find an optimal scanning interval Wt for energy saving in PMAR is also our focus in the future. We leave them as our future work.