WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. 2016; 16:1352–1362 Published online 22 June 2016 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.2694

SPECIAL ISSUE PAPER

A novel social contact graph-based routing strategy for workload and throughput fairness in delay tolerant networks Tuan Le* , Haik Kalantarian and Mario Gerla Department of Computer Science, UCLA, Los Angeles, CA 90095, U.S.A.

ABSTRACT Delay-tolerant networks are sparse mobile ad hoc networks in which there is typically no complete path between the source and destination. Although many routing schemes for delay-tolerant networks have been proposed, they do not address fairness issues in terms of the workload/traffic handled at each node and the share of throughput among different destination nodes. In this paper, we propose a socially aware routing strategy that optimizes both fairness and throughput. A relay node is selected based on the multi-hop delivery probability and its queue length. The effect of queue length control is to divert traffic away from highly connected nodes and allows nodes to explore less-congested paths to the destination. This helps balance the network loads, thus achieving workload fairness. Furthermore, to achieve throughput fairness, we sort arriving messages into different destination-based queues. Messages are then scheduled following a two-level forwarding strategy that optimizes throughput fairness using round-robin and delivery ratio using priority scheduling. Extensive real-tracedriven simulation results show that our scheme outperforms existing algorithms in terms of the delivery ratio. Furthermore, our scheme achieves a high throughput fairness, while distributing the network loads more evenly, with the top 10% of network nodes handling only 22% of the forwardings. Copyright © 2016 John Wiley & Sons, Ltd. KEYWORDS delay tolerant networks; relay selection; message scheduling; load balancing; fairness; throughput *Correspondence Tuan Le, Department of Computer Science, UCLA, Los Angeles, CA 90095, U.S.A. E-mail: [email protected]

1. INTRODUCTION Delay tolerant networks (DTNs) [1] are characterized as sparsely connected, highly partitioned, and intermittently connected ad hoc networks. In these challenging environments, end-to-end communication paths between node pairs are rarely available. There are many practical applications of DTNs, including wildlife tracking sensor networks [2], PeopleNet [3], ocean sensor networks [4], military networks [5], and vehicular ad hoc networks [6]. To handle the sporadic connectivity of mobile nodes in DTNs, the store-carry-and-forward method is used. That is, messages are temporarily stored and carried by a node until an appropriate communication opportunity with the next relay hop arises. Routing for DTNs has been widely studied in the past. To select the best relay node, a variety of network information, including dynamic network information (e.g., location information, traffic information, and encounter information), and static network knowledge (e.g., social 1352

relations among nodes) are utilized. Compared with dynamic information, social ties and behaviors between nodes tend to be stable over time and can be more reliably exploited to facilitate message transmission. Recently, a large number of routing protocols [7–11], which adopt social relations among nodes to determine when and where to forward messages, have been proposed. These protocols are commonly known as socially aware or socially based routing protocols. Although these works achieve a high throughput (or delivery ratio), they often ignore fairness issues in terms of the workload handled at each node and the share of throughput among different destination nodes. Achieving fairness is critically important in cooperative networks. First, workload fairness eliminates network bottlenecks and a single point of failure and thus makes the network resilient to targeted attacks [12]. Second, throughput fairness encourages nodes to stay in the network and to actively participate in forwarding and routing. These two fairness issues are largely governed by the relay selection and message-scheduling strategy, respectively. While Copyright © 2016 John Wiley & Sons, Ltd.

T. Le, H. Kalantarian and M. Gerla

an improper relay selection strategy can concentrate traffic at a few network nodes, an improper message scheduling policy can cause some destination nodes to receive disproportionately few messages. In DTNs, contact duration between nodes is usually short because of node movement and the limited range of peer-to-peer wireless communication. For example, when mobile devices communicate via Bluetooth, which supports a typical wireless range of about 10 m, the contact duration can last for only several seconds if the users are moving at walking speed [13]. Because of the short contact duration, not all messages can be exchanged between nodes in a single contact. Thus, determining which messages (intended for different destinations) to transmit first will have a profound impact on throughput fairness. In this paper, we propose to sort incoming messages into different destination-based queues at intermediate nodes. Messages are initially scheduled using round-robin for throughput fairness. In the event that the forwarding constraints are not met, we switch to priority scheduling to maintain a high delivery ratio. Regarding workload fairness, existing works tend to select the next hop node that is the most “popular” or has the highest delivery predictability with the destination [8,9,14]. In complex/social networks where connections among nodes follow a fat-tailed distribution (Figure 1), this strategy will guide messages toward a few highly connected nodes. Consequently, network load distribution becomes highly unbalanced, with very few nodes carrying the majority of traffic. Previously, we addressed the workload fairness issue for a single-copy DTN routing [15]. In this model, at any point in time, there is at most one copy of the message in the network. We proposed to select relay nodes based on the combination of social-tie (direct one-hop) delivery probability and queue length control (back pressure control). Messages are only forwarded to network nodes that have a higher delivery probability and a smaller or similar queue length. We showed that this strategy significantly reduces traffic at highly connected

Figure 1. A social network graph with a fat-tailed degree distribution.

A novel social contact graph-based routing strategy

nodes and spreads traffic more evenly across the network. In this paper, we revise the relay selection strategy for a multi-copy DTN routing scenario. We also consider using the multi-hop delivery probability (instead of the direct one-hop) in the formulation of the relay selection metric. The paper makes the following contributions:  A revised relay selection strategy for a multi-copy routing scenario.  A message scheduling policy for throughput fairness.  A multi-hop delivery probability metric for relay selection.  An extensive evaluation of the fairness metric. The rest of the paper is organized as follows. Section 2 reviews the related work. Section 3 describes the design of the relay selection and message scheduling in detail. Section 4 presents the experimental results. Section 5 concludes the paper.

2. RELATED WORK Much work has been performed regarding network architectures and algorithms for routing and forwarding in DTNs. Research on message forwarding in DTNs originates from Epidemic routing [16], which floods the entire network. Spray and Wait [17] is another flooding scheme but with a limited number of copies. Recent studies develop relay selection techniques to approach the performance of Epidemic routing with a lower forwarding cost. Many schemes compute the delivery probability from the encounter node to the destination node before deciding whether to forward data. PROPHET [18] uses the past history of encounter events to predict the probability of future encounters. LeBrun et al. [19] use location information of nodes to forward data closer to the destination. Leguay et al. [20] observe that people who have similar mobility patterns are more likely to meet each other. Hence, they propose to forward data to nodes that have mobility patterns similar to the mobility pattern of the destination. Zhao et al. [21] take a different approach by utilizing a set of special nodes called message ferries (such as unmanned aerial vehicles or ground vehicles with short-range radios) to help provide communication service for other nodes through the controlled non-random movements of the ferries. Because node mobility patterns are highly volatile and hard to control, attempts at exploiting stable social network structure for data forwarding have emerged. In [7], nodes are ranked using weighted social information. Messages are forwarded to the most popular nodes (highly ranked nodes) given that popular nodes are more likely to meet other nodes in the network. The explicit friendships are used to build the social relationships based on their personal communications. SimBetTS [8] uses egocentric centrality and social similarity to forward messages toward the node with the highest centrality, to increase the possibility of finding the optimal carrier to the final destination.

Wirel. Commun. Mob. Comput. 2016; 16:1352–1362 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/wcm

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BubbleRap [9] combines the observed hierarchy of centrality and observed community structure with explicit labels to select the best forwarding nodes. In [22], social features of each node are extracted, and the node that has more similar social features with the destination is selected as a relay node. In [23], relay selection is based on the local social map constructed using the knowledge of surrounding social structure. The delivery probability is computed over the entire path from source to destination. However, these works do not address fairness issues. They either assume long contact duration in which all buffered messages are successfully forwarded to the relay node upon contact or schedule messages in decreasing order of the delivery probability. Consequently, most messages that are forwarded within a contact are intended for a few destination nodes, resulting in throughput unfairness. Furthermore, existing works tend to select relay nodes with the highest delivery probability. This causes the majority of traffic to flow into highly connected nodes, resulting in an unfair/unbalanced network load distribution. In this work, we introduce multi-queuing and a two-level message-scheduling strategy that optimizes both throughput fairness and delivery ratio. In addition, we combine queue length control with multi-hop delivery probability to achieve better load balancing (workload fairness).

The weighing function F.x/ essentially reflects the influence of the recency and frequency of encounter events. In order to give more weight to more recent encounter events, F.x/ should be a monotonically non-increasing function. A function that satisfies this condition is F.x/ D . 21 /x , where 0    1. The control parameter  allows a tradeoff between recency and frequency in contributing to the social-tie value. As  approaches 0, frequency contributes more than recency. On the other hand, as  approaches 1, recency has higher weight than frequency. The social-tie value is solely determined by frequency when  D 0 and by recency when  D 1. In our experiments, the value of  is carefully tuned based on the analysis of the network characteristic and is set to e4 .

3. PROTOCOL DESIGN

3.2. Social knowledge formation

In this section, we first describe the social-tie metric and multi-hop delivery probability. We then present a relay selection strategy based on multi-hop delivery probability and queue length control. Lastly, a complete routing protocol is presented in detail.

In order to make an informed forwarding decision, a node needs to obtain network-wide knowledge of socialtie strength between any node pairs. This knowledge is contributed by both local observation and knowledge exchange.

3.1. Social-tie metric

3.2.1. Local observation. Upon each encounter event, a node records the encounter node ID and the timestamp of the encounter event and stores it in the encounter table. Periodically, social-tie values between the current node and its direct encounters are re-computed using Equation (1), where the input comes from the history of encounter events stored in the encounter table. In addition, each node maintains a social-tie-table, where each row has the following format:

In sociological terms, social tie describes an interpersonal connection by way of friendship or acquaintance. There are many tie strength indicators: frequency, intimacy/closeness, longevity, reciprocity, recency, multiple social context, and mutual confiding (trust) [8]. Among them, the most widely used heuristics in socially aware networking applications are the recency and frequency of encounters [24]. Two nodes are said to have a strong tie if they have met frequently in the recent past. We compute the social tie between two nodes using the history of encounter events. How much each encounter event contributes to the socialtie value is determined by a weighing function F.x/, where x is the time span from the encounter event to the current time. Assume that the system time is represented by an integer and is based on n encounter events of node i. Then, the social-tie value of node i’s relationship with node j at the current time tbase , denoted by Ri .j/, is computed as Ri .j/ D

n X kD1

1354

F.tbase  tjk /

(1)

where F.x/ is a weighing function, ftj1 , tj2 , : : : , tjn g are the encounter times when node i met node j, and tj1 < tj2 <    < tjn  tbase . As an example, suppose node i met node j at times 1, 3, and 5 and that the current time .tbase / is 10. Then, node i’s social-tie relationship with node j at tbase , denoted by Ri . j/, is computed as Ri .j/ D F.10  1/ C F.10  3/ C F.10  5/ D F.9/ C F.7/ C F.5/

hpeerX, peerY, social  tie  value, timestampi Through local observation, peerX is always the current node ID. PeerY is the encounter node ID. Timestamp is the time at which the social-tie value between peerX and peerY is computed. It is the tbase variable in Equation (1). As we will see next, timestamp plays an important role in knowledge exchange among nodes. 3.2.2. Knowledge exchange. Nodes, especially those that are not socially active, tend to have limited knowledge of the social network through local observation (i.e., through direct contacts with other

Wirel. Commun. Mob. Comput. 2016; 16:1352–1362 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/wcm

T. Le, H. Kalantarian and M. Gerla

A novel social contact graph-based routing strategy

nodes). To gain knowledge of nodes that have never met, during the encounter period, nodes can exchange and merge their local observations in the form of a social-tietable. In the event of a merge conflict (i.e., when there are two entries with the same peerIDs), we keep the entry with the latest timestamp. Through this process, a node can learn the social-tie values between different pairs of nodes in the network.

Pk .i, j/ D

Y

w.e/, 8e 2 PATHk .i, j/

(3)

e

One way to compute the delivery probability over the most probable path is to find all the paths between i and j, compute the delivery probability through each path, and then select the maximum value. Suppose that there are n paths between i and j. Then, the delivery probability through the most probable path Q.i, j/ can be computed as

3.3. Multi-hop delivery probability Q.i, j/ D max fPk .i, j/, 1  k  ng The delivery probability P.i, j/ represents the likelihood that a message buffered at node i will be delivered to node j, either through direct contact or through a sequence of two or more relays. We propose to compute the delivery probability based on the social contact graph constructed from the local social-tie table. In the social-tie table, each unique peerID represents a graph node, and each pair of peerIDs (or row) represents an undirected edge between two graph nodes. Assume that there are n entries in the social-tie table. Then, the edge weight wk .i, j/ of the kth entry is defined as the meeting probability between two nodes i and j relative to other pairs of nodes in the social-tie table and is computed as social  tie  valuerowk wk .i, j/ D Pn kD1 social  tie  valuerowk

(2)

P where i and j are unique peerIDs and nkD1 wk D 1. Note that we normalize the social-tie values between 0 and 1 by dividing each social-tie value by the summation of all the values in the table. The normalized social-tie values represent the edge weights in the social contact graph. As an example, Figure 2 shows the social-tie table of node S after meeting and merging node A’s social-tie table and the resulting social contact graph with the edge weights properly computed using Equation (2). For simplicity, the fourth column for the timestamp is not shown, and the social-tie values are in the form of integers. In a graph, two nodes can be connected by many different paths. However, as we describe in Subsection 3.5, intermediate nodes use a single-copy routing strategy to reduce the replication cost. Therefore, only the path with the highest delivery probability will be selected. Thus, we are interested in computing the delivery probability through the most probable path. Given a PATHk .i, j/ between two nodes i and j, the delivery probability over the kth path can be computed as

Figure 2. An example of node S’s social-tie table and its corresponding social contact graph.

(4)

However, this approach is computationally infeasible as finding all the paths between two nodes on an undirected graph is NP-hard. This can be proven as follows: It is shown in [25] that finding the longest path between two graph nodes in an undirected graph is NP-hard. Suppose that we could find all the paths between two nodes in polynomial time. Then, by sorting the results in polynomial time, we could find the longest path, also in polynomial time. This contradiction shows that finding all the paths between two graph nodes is NP-hard. Alternatively, we propose to transform the problem of finding a path where the product of edge weights is maximized into the problem of finding a path where the sum of edge weights is minimized. Note that the two problems are equivalent as shown in the following: arg max Pk .i, j/  arg max log.Pk .i, j// PATHk

PATHk

D arg min log PATHk

D arg min PATHk

X

Y

! w.e/ , 8e 2 PATHk

e

log.w.e//, 8e 2 PATHk

e

A polynomial-time algorithm such as Dijkstra’s algorithm can then be used to find the least cost path (which is the most probable path) and the corresponding delivery probability over that path. Note that the edge weights need to be transformed by negating the log values of the current edge weights. As an example, consider again the contact graph in Figure 2. Suppose that S’s objective is to deliver a message to E. Thus, upon meeting A, S is interested in computing the delivery probability from A to E. S, in turn, runs Dijkstra’s algorithm using the log-transformed edge weights (not shown on the graph). The resulting least cost path is PATHA!D!E with the cost (summation of logs) D . log 2=15/ C . log 3=15/ D 1.574. Note that the cost of PATHA!B!D!E is . log 1=15/ C . log 4=15/ C . log 3=15/ D 2.449. The delivery probability is the product of non-transformed edge weights on PATHA!D!E , which is 2=15  3=15 D 0.0267. For comparison, the product of non-transformed edge weights on PATHA!B!D!E is 1=15  4=15  3=15 D 0.0036 < 0.0267. This confirms that our approach correctly identifies the most probable path and computes the delivery probability over that path.

Wirel. Commun. Mob. Comput. 2016; 16:1352–1362 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/wcm

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3.4. Relay selection strategy Relay selection is the main factor that determines the workload fairness. Relay selection based on multi-hop delivery probability follows a simple strategy: a message carrier node i will select an encountered node j as a next relay hop if and only if j has a higher delivery probability to destination k than i. That is, the following condition must hold: P. j, k/ > P.i, k/

(5)

However, this heuristic still biases toward highly connected nodes and thus does not address the load balancing (workload fairness) problem. To spread the traffic across different nodes in order to eliminate buffer congestion that causes frequent message drops, we propose a queue length control mechanism such that nodes can only forward messages to nodes of similar or smaller queue length. That is, a congested node is allowed to forward messages to a lesscongested node, but not the other way around. The intuition behind this scheme is as follows: The queue length reflects a node’s connectivity. A highly connected node tends to receive lots of messages, and thus, its queue length grows larger than others. By requiring nodes to forward messages only to nodes of similar or smaller queue length, we can effectively divert traffic away from congested nodes, while allowing nodes to explore alternative, less-congested paths. Over time, as messages flow out of congested nodes, their queue length becomes smaller, and the control mechanism will dynamically enable the traffic to flow into these nodes again. As we will show in Section 4, this queue length controls strategy results in a more balanced load distribution without compromising the delivery ratio. With queue length control, node i will forward a message intended for k to j if the following condition is met:   (6) .P. j, k/ > P.i, k// ^ Qj  Qi where Qi and Qj are the queue lengths of nodes i and j, respectively. 3.5. Routing protocol In this section, we develop a reliable routing protocol, namely, social contact graph-based routing (SCGR), that achieves both workload and throughput fairness without compromising the delivery ratio. The protocol consists of controlled multi-copy routing at the source node and single-copy routing at intermediate nodes. Figure 3 depicts our general framework, where the source node S “sprays” a few data copies into the network and then routes each copy independently using single-copy routing toward the destination.

Figure 3. Node S sprays three copies of message D1 (destined to D) into the network. Node A, B, E, and F can make at most one replication each and forwards it to a node that has a higher delivery probability to D than itself. All relaying nodes, including S, retain a copy of the message until the wait timer (the duration a message is cached at a node) expires and can perform direct transmission upon contacting D.

number of replications mean higher delivery rate, replicating a message in an uncontrolled fashion causes network congestion and wastes resources. In order to increase the utility of each replication and prevent replicating to lessbeneficial nodes, we propose to perform replication only if contact nodes meet the following constraints: 8 < numberOfReplica < ı P.encounter, dst/ > bestDeliveryProbdst : Qencounter  Qcurrent

(7)

The first constraint ensures that we do not replicate endlessly and flood the network. In our experiments, we set the threshold ı D 4. The second constraint attempts to improve the delivery likelihood of extra replications by relaying data to a node that has a better delivery probability than previous relay nodes. The third constraint aims to balance the network loads among nodes. Initially, bestDeliveryProbdst , which is the best-so-far delivery probability to destination dst, is set to be equal to P.current, dst/. Each time a message is successfully forwarded to an encounter node subject to the aforementioned constraints, bestDeliveryProbdst is updated to P.encounter, dst/. Pseudocode 1 summarizes our source node’s routing strategy.

3.5.1. Source node’s multi-copy routing. The source node is responsible for creating and injecting multiple replications into the network. While a larger 1356

Wirel. Commun. Mob. Comput. 2016; 16:1352–1362 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/wcm

T. Le, H. Kalantarian and M. Gerla

3.5.2. Intermediate node’s single-copy routing. To reduce the replication cost, intermediate nodes are allowed to make at most one replication subject to the same constraints as for the source node, but with ı D 1. It is possible for an intermediate node to hold messages destined to different nodes. Because of the short contact duration, it may not be possible to forward all buffered messages to an encounter node within a single contact. Thus, an intermediate node needs to implement a forwarding policy that ensures throughput fairness, while retaining a high delivery ratio. A simple first-come first-served (FCFS) strategy is not sufficient because, for example, due to node movements, the fact that message D1 arrives at the current node before message D2 does not necessarily mean that D1 is generated and injected into the network before D2 . Thus, it may be unfair to select a message to forward next simply based on its arrival time. Instead, we ensure throughput fairness by providing buffered messages (destined to different destinations) with an equal chance of being selected to be forwarded next. This can be performed by first sorting arriving messages into different queues based on their destinations. We then schedule one message per queue at a time following a round-robin order. Within the candidate queue, FCFS is employed as all messages within the queue are destined to the same destination. Figure 4 demonstrates the data selection process. However, a selected queue in the round-robin order (first-level scheduling) may not satisfy the forwarding constraints. For example, the encounter node may have a larger queue length or a lower delivery probability than the current node. If the former constraint is violated, the scheduling for the current contact is aborted in order to maintain the workload fairness. On the other hand, if the latter constraint is violated, we switch to the second-level scheduler that implements priority scheduling. Here, the priority is defined in terms of the delivery probability to any known destination passing through an encounter node. Therefore, the queue with the highest delivery probability will be selected. Similar to the first-level scheduler, FCFS is used to select a message within the candidate queue. After the message has been forwarded, round-robin is resumed at the next queue following the “failed" queue. In both levels of scheduling, an already forwarded message is removed out of the queue, but remains in a node’s caching buffer, waiting for a direct transmission opportunity with the final destination, until a wait timer expires. Note that the wait timer is used to prevent messages from being held up for too long at the source or any intermediate

Figure 4. Round-robin scheduler for data selection.

A novel social contact graph-based routing strategy

node. Pseudocode 2 summarizes our intermediate node’s routing strategy.

Lastly, note that a node can hold its self-owned data and data arriving from other nodes. That is, a node can serve the role of a source node and an intermediate node simultaneously. In this case, regarding data selection, we give higher priority to self-owned data. Upon contacting a node, the current node will first pick self-owned data to forward next, subject to the source node’s forwarding constraints. If the forwarding constraints are not met, the current node will select data items (arriving from other nodes) following intermediate node’s single-copy routing strategy.

4. PERFORMANCE EVALUATION In this section, we evaluate the performance of our proposed SCGR scheme in a packet-level simulation, using a real-world mobility trace. We first describe the simulation setup, followed by the metrics used and the results. 4.1. Simulation setup We implement the proposed routing protocol using the NS3.19 network simulator. We adopt the IEEE 802.11g wireless channel model and the PHY/MAC parameters as listed in Table I. To obtain meaningful results, we use the reallife mobility trace of San Francisco’s taxi cabs [26]. This data set consists of global positioning system coordinates of 483 cabs, collected over a period of three consecutive weeks. For our studies, we select an NS-3-compatible trace file from downtown San Francisco (area dimensions: 5700  6600 m) with 116 cabs, tracked over a period of 1 h [27]. Vehicles advertise Hello messages every 100 ms [28]. The broadcast range of each vehicle is fixed to 300 m, which is typical in a vehicular ad hoc network setting [29]. In our experiments, each node sends a unique message of the same size (1 MB) to a random destination in the network after 1000 s of the warming-up period. For statistical convergence, the results reported in this section

Wirel. Commun. Mob. Comput. 2016; 16:1352–1362 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/wcm

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 Load distribution: the distribution of the total number of forwardings across all network nodes.  Throughput fairness: the share of throughput among destination nodes. It is evaluated using Jain’s fairness index [30], which will be discussed in detail in Subsection 4.4.

Table I. Simulation parameters. Parameter RxNoiseFigure TxPowerLevels TxPowerStart/TxPowerEnd m_channelStartingFrequency TxGain/RxGain EnergyDetectionThreshold CcaModelThreshold RTSThreshold CWMin CWMax ShortEntryLimit LongEntryLimit SlotTime SIFS

Value 7 1 12.5 dBm 2407 MHz 1.0 74.5 dBm 77.5 dBm 0B 15 1023 7 7 20 s 20 s

4.3. Comparative results

are averaged from 20 simulation runs. We evaluate the performance of SCGR against the following schemes:  Epidemic routing [16] is a flooding-based multicopy routing algorithm. It is optimal in terms of delivery ratio but is very inefficient in terms of cost (the number of forwardings). Furthermore, Epidemic routing is expected to distribute the network load quite well as it does not apply any heuristic to guide the forwarding. Recall from previous sections that heuristics that select the relay with the highest delivery probability to the destination will bias toward highly connected nodes, causing congestion and unbalanced load distribution.  PROPHET [18] is a utility-based routing protocol that uses the past history of encounter events to forward data to nodes with higher delivery predictability to the destination. In our simulations, we use the same parameters as specified by the authors in [18]. That is, fPinit , ˇ,  g D f0.75, 0.25, 0.98g.  BubbleRap [9] is a community-based algorithm that routes data based on rankings calculated from the social centrality. A message is first bubbled up using the global ranking until it reaches a node in the same community as the destination. Then the local ranking is used to bubble up the message until the destination is reached or the message expires. 4.2. Evaluation metrics We use the following metrics for evaluation:  Delivery ratio: the proportion of messages that have been delivered out of the total messages created.  Average delay: the average interval of time for each message to be delivered from the source to destination.  Cost: the total number of forwardings in the network. 1358

Figure 5(a) compares the delivery ratio among the schemes. As expected, Epidemic has the highest delivery ratio of around 65% after 1 h of simulation. SCGR and PROPHET deliver 49.7% and 45.2% of the messages, respectively. BubbleRap has a slightly worse performance with a delivery ratio of 41.5%. This is perhaps because BubbleRap is impacted by the weak community structure in the San Francisco cab trace. Recall that BubbleRap is a community-based algorithm, in which forwarding decisions are made based on the community structure of the network. Figure 5(b) depicts the average delay. Again, Epidemic has the best delivery delay, followed by BubbleRap. BubbleRap successfully delivers messages by 5% and 12% less time than SCGR and PROPHET, respectively. SCGR does not have the best average delay because it may take a longer path for message delivery to achieve load balancing. In terms of cost, as shown in Figure 5(c), Epidemic and PROPHET require 136 and 1.14 times more forwardings than SCGR. Although the cost of SCGR is 1.2 times higher than BubbleRap, SCGR has a better load distribution and delivery ratio than BubbleRap. Lastly, the load distribution is compared in Figure 5(d). SCGR has the best load distribution with the top 10% of network nodes handling 22% of message forwardings. This is significantly better than 37% for Epidemic, 44% for PROPHET, and 49% for BubbleRap. Note that Epidemic routing has a better load distribution than PROPHET and BubbleRap because it does not use any heuristic to guide message forwarding. BubbleRap has the worst load distribution because its forwardings are directed toward a few most popular nodes (highly connected nodes) for the final direct message delivery. 4.4. Throughput fairness performance In this subsection, we evaluate the throughput fairness performance of various message scheduling policies. As stated earlier, throughput fairness measures the share of throughput among destination nodes and is evaluated using Jain’s fairness index [30], which has the following form: Pn J .x1 , x2 , : : : , xn / D

iD1 xi

n

Pn

2

2 iD1 xi

(8)

Jain’s equation rates the fairness of a set of values when there are n destinations, and xi is the throughput of destination i. The result ranges from 1=n (worst case) to 1 (best

Wirel. Commun. Mob. Comput. 2016; 16:1352–1362 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/wcm

T. Le, H. Kalantarian and M. Gerla

A novel social contact graph-based routing strategy

Figure 5. Performance comparison of various routing strategies on the San Francisco cab trace.

case), and it is maximum when all destinations receive the same throughput allocation. As an example, suppose that there are six messages created and intended for each of destinations d1 , d2 , and d3 . Suppose further that at the end of the simulation, the number of messages successfully received by d1 , d2 , and d3 are 1, 3, and 5, respectively. Then, their corresponding throughput are x1 D 1=6, x2 D 3=6, and x3 D 5=6. Using Equation (8), we obtain the following Jain’s fairness index for the given set of throughput: J



1 3 5 , , 6 6 6

and thus has the best Jain’s value of 1. This shows that Jain’s fairness index can be a good indicator for throughput fairness performance [31]. Next, we compare the delivery ratio and throughput fairness of the following message scheduling policies:  RR-Priority-FCFS is a two-level message scheduler that uses RoundRobin+FCFS at the first level and Priority+FCFS at the second level. Performance results for SCGR in Subsection 4.3 assume the use of this scheduler.  RR-FCFS follows a round-robin order for queue selection but then aborts further transmission if the selected queue does not meet the forwarding constraints. Round-robin resumes at the “failed" queue in the next contact.  Priority-FCFS schedules messages with the highest delivery predictability first, following FCFS order.

  0.77

As we can see, the Jain’s fairness index value is not close to 1, which indicates that the destinations do not have the fair share of throughput. Destination d1 receives disproportionately fewer messages than d2 and d3 . Consider another scenario where each destination d1 , d2 , and d3 receives three messages. The resulting Jain’s value is   3 3 3 , , D1 J 6 6 6 Although the total number of messages received in both scenarios is the same (nine messages), the second scenario has a perfect share of throughput for each destination

We implement these policies on top of SCGR, using the same simulation setup as in the previous subsection. The results are shown in Figure 6. RR-FCFS and Priority-FCFS are on the two opposite extremes. Whereas RR-FCFS has the lowest delivery ratio and highest throughput fairness, Priority-FCFS has the highest delivery ratio and lowest throughput fairness. The two-level scheduler RR-

Wirel. Commun. Mob. Comput. 2016; 16:1352–1362 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/wcm

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1 0.9

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Figure 6. Delivery ratio versus throughput fairness for different message scheduling policies.

Priority-FCFS obtains the best compromise between the two extremes. It has a delivery rate of 49.7% and a Jain’s value of 0.81. 4.5. Discussion In this subsection, we discuss extreme scenarios where attempting to obtain workload fairness can be detrimental to routing performance (e.g., the delivery delay). As mentioned earlier, SCGR considers the queue length factor when making a forwarding/replicating decision. Thus, in cases in which there are very few paths between multiple sources to a destination, SCGR can suffer from a very long delay. Figure (7) shows an example where there exists a single opportunistic routing path from node A, B, C, to D passing through an intermediate node E. Suppose the buffers of A, B, and C have a single message destined to D. The buffers of D and E are initially empty. In addition, suppose E encounters A, B, and C before D. Based on the queue length forwarding constraint in Equation (7), nodes A and B are allowed to replicate their messages to E. However, node C has to wait (even though there is no alternative path) until E relieves its buffer by delivering messages of A and B to D. This simple example raises an important question: How long should a node wait for an alternative path, which may or may not ever exist? If node C decided to replicate its

Figure 7. A social contact graph with a single path from multiple sources (A, B, C) to destination D.

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message to E during their first encounter, the delivery delay would have been significantly shortened. One solution is that because node C has a complete contact topology (Subsection 3.2), node C can easily determine if the path to D through E is the only path available by running depth first search (DFS) twice. For example, the first DFS is run on the original graph. The second DFS is run on a modified graph, in which the edge between the starting node and its first-hop node on the first path (e.g., edge C-E) is removed. If there exists exactly one path to D passing through the current encounter node E, node C can replicate its buffered messages to E, ignoring the queue length condition. For the second case, where more than one path exists, we can use pair-wise inter-contact times (edge costs) to estimate the delay of each path. A node can then decide whether it is worthwhile to continue waiting for an alternative path. We plan to investigate this issue further in our future work.

5. CONCLUSION In this paper, we proposed a novel social contact graphbased routing strategy that optimizes workload fairness, throughput fairness, and delivery ratio. Our relay selection strategy is based on the multi-hop delivery probability and queue length of the relay node. The effect of queue length control is to divert traffic away from congested nodes and allow nodes to explore alternative, less-congested paths to the final destination, thus achieving workload fairness. Furthermore, we proposed destination-based multi-queuing for message storing and a two-level message scheduler that uses round-robin at the first level to maintain throughput fairness and priority scheduling at the second level to optimize delivery ratio. Experimental results show that our proposed scheme SCGR achieves a delivery rate of up to 8.2% higher than existing schemes, while maintaining a high throughput fairness with a Jain’s value of 0.81. Furthermore, our scheme achieves much better workload fairness with the top 10% of network nodes handling 22% of the forwardings, compared with 37% for Epidemic routing, 44% for PROPHET, and 49% for BubbleRap.

Wirel. Commun. Mob. Comput. 2016; 16:1352–1362 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/wcm

T. Le, H. Kalantarian and M. Gerla

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AUTHORS’ BIOGRAPHIES Tuan Le received his BA degree in Computer Science in 2011 from the University of California, Berkeley. In 2014, he received his MS degree in Computer Science from the University of California, Los Angeles. Currently, he is a PhD candidate in Computer Science at

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UCLA. His research interests include routing protocol design, security, trust, and reputation management in mobile social networks and mobile information-centric networks.

Haik Kalantarian received his BS degree in Electrical Engineering in 2011 from the University of Washington. In 2013, he received his MS degree in Electrical Engineering from the University of California, Los Angeles. Currently, he is a PhD candidate in Computer Science at UCLA. His research interests include wireless health and embedded systems.

Mario Gerla is a professor in Computer Science Department at University of California, Los Angeles. He holds an Engineering degree from Politecnico di Milano, Italy, and a PhD degree from UCLA. He became IEEE fellow in 2002. At UCLA, he was part of the team that developed the early ARPANET protocols under the guidance of Professor Leonard Kleinrock. He joined the UCLA faculty in 1976. At UCLA, he has designed network protocols including ad hoc wireless clustering, multicast (ODMRP and CODECast), and Internet transport (TCP Westwood).

Wirel. Commun. Mob. Comput. 2016; 16:1352–1362 © 2016 John Wiley & Sons, Ltd. DOI: 10.1002/wcm