RABP: Delay/disruption tolerant network routing and buffer management algorithm based on weight

Abstract

Delay/disruption tolerant network is a novel network architecture, which is mainly used to provide interoperability for many challenging networks such as wireless sensor network, ad hoc networks, and satellite networks. Delay/disruption tolerant network has extremely limited network resources, and there is typically no complete path between the source and destination. To increase the message delivery reliability, several multiple copy routing algorithms have been used. However, only a few can be applied efficiently when there is a resource constraint. In this article, a delay/disruption tolerant network routing and buffer management algorithm based on weight (RABP) is proposed. This algorithm estimates the message delay and hop count to the destination node in order to construct a weight function of the delay and hop count. A node with the least weight value will be selected as the relay node, and the algorithm implements buffer management based on the weight of the message carried by the node, for efficiently utilizing the limited network resources. Simulation results show that the RABP algorithm outperforms the Epidemic, Prophet, and Spray and wait routing algorithms in terms of the message delivery ratio, average delay, network overhead, and average hop count.

Keywords

delay/disruption tolerant network wireless sensor network routing algorithm buffer management weight function

Introduction

A delay/disruption tolerant network (DTN) was initially motivated by the idea of deploying an interplanetary Internet (IPN)¹ for deep space communication. Examples of DTN application in real life mainly include wildlife tracking sensor networks,² PeopleNet,³ ocean sensor networks,⁴ military networks,⁵ and vehicular ad hoc networks.⁶ Unlike traditional networks such as the transmission control protocol/Internet protocol (TCP/IP)-based Internet, the DTN is often subject to high latency caused by long propagation delay, intermittent connectivity, node resources that are extremely limited, and other characteristics.^7–20

Thus, a traditional “store-and-forward” network cannot complete its communication. It adopts a “storage-carry-forward” routing mode, and a node carries the message before locating a relay or destination node.¹ The message will be relayed from one node to another until the message arrives at the destination or is dropped when its time to live (TTL) equals 0.⁶ In order to increase the delivery ratio of the network, the DTN usually uses multiple copy routing protocols to forward the message; however, in a constrained-resource condition, the limited network resources are rapidly exhausted resulting in a sharp decline in network performance. Therefore, an efficient routing algorithm is crucial for improving the performance of a network in a constrained-resource condition.

With constrained resources, message delay and hop count are the two critical metrics for evaluating the performance of a DTN routing algorithm. Delay is the time required for a message to be transmitted from one end of the network to the other;²¹ it includes the transmission, propagation, processing, and queuing delays.²² The longer the delay, the longer the occupation of the network resource. Although delays are permitted in the DTN,²³ it is important to reduce them for a network in a constrained-resource condition.²⁴ Hop counts are the number of nodes that the message has experienced in the process of reaching the destination node. The channel will be occupied if the hop count of the message is incremented by one. Thus, when the number of channels/channel bandwidth is limited, reducing the message hop counts is also important to effectively utilize limited network resources.

To efficiently utilize limited network resources, we propose a DTN routing and buffer management algorithm based on weight (RABP). First, the algorithm estimates the message delay and hop count experienced by the message up to the destination node in order to construct a weight function of the delay and hop count. Furthermore, the RABP algorithm selects a node with the lowest weight value as the relay node and implements buffer management based on the weight of the message carried by the node, to efficiently utilize the limited network resources.

The rest of this article is organized as follows: section “Related works” presents the related works. In section “Network model,” the network model is described, and the RABP algorithm is presented in section “RABP algorithm.” Section “Simulation experiments and results” describes the simulation experiments and results. Finally, the conclusions are summarized in section “Conclusion.”

Related works

In this section, we review existing works on message delay and hop count. Currently, several routing algorithms are available for addressing delay; however, research on hop count is relatively limited.

Algorithms that address delay include the minimum expected delay (MED) algorithm proposed by Jain et al.,²¹ the minimum estimated expected delay (MEED) algorithm proposed by Jones et al.,²² and the expected delay (ED) algorithm proposed by Liu and Wu.²³ However, these three metrics compute the ED based on the MED among individual routes from the current node to the destination; they do not consider the aggregation of the EDs from multiple available routes. Thus, they do not effectively cope with unforeseeable changes in the node contact topology. Hence, Le et al.²⁴ proposed an expected minimum delay (EMD) algorithm with an alternative relay selection metric based on the EMD among all possible routes to the destination. This metric accounts for the expected gain in the meeting probability when multiple routes are available, and it estimates the actual delay more accurately. However, in this algorithm, in order to reduce the message delay up to the destination node, several relay nodes may be required to forward the message, thereby increasing the channel occupancy time. Therefore, to achieve near-optimal network performance in a constrained-resource condition on the premise of reducing the network delay, reducing the message hop count is also particularly important.

Some literatures are available for addressing the message hop count issue. Wu et al.²⁵ proposed an algorithm for limiting the message hop count in edge router (ER) routing. This method can obtain a better performance by controlling the message hop count. You et al.²⁶ proposed a hop count–based multi-path forwarding (HCMF) algorithm. The main idea was to let the nodes decide whether or not to trigger the replication mechanism by comparing the average hop count value with the estimated one.

Thus, most available routing studies on message delay or hop count consider only a single performance metric; buffer management is rarely considered simultaneously. In this study, we simultaneously considered the message delay and hop count and proposed a DTN routing algorithm and a buffer management algorithm based on weight to achieve near-optimal network performance in a constrained-resource condition.

Network model

We model the DTN as a network composed of randomly moving nodes; these nodes and the connections between them are modeled as an undirected graph $G = (V, E)$ , where V is the node set and E is the edge set. Each edge $E (G)$ represents a connection between two nodes in the network, and $E (G)$ is a time-varying function. The DTN has a limited bandwidth when two nodes are connected, and a limited buffer size.

In this article, a message carried by a node in the network has a weight, wherein the weight quota of the message carried by the current node is $\sqrt[\frac{1}{u}]{\overset{u}{α (cdr)} + β \overset{u}{(coj)}}$ ; cdr and coj are the EMD and expected minimum hop count (EMJ), respectively, of the message carried by the node to the destination node and $α + β = 1$ . For the same node, the weight may vary in the process of carrying different messages. Let p represent a message. When a message p is generated at its source node, it is assigned a weight quota $Q_{src (p)}^{p}$ , where $src (p)$ is the source node of the message p. If each node $s \in V (G)$ has p’s copies in its buffer, then message p at node s has a weight quota $Q_{s}^{p}$ .

RABP algorithm

In this section, we first introduce the main idea of the RABP and then present the detailed design of the RABP algorithm in the following section.

This algorithm simultaneously estimates the message delay and hop count experienced by the message up to the destination node and constructs a weight function of the delay and hop count. A node with the least weight value will be selected as the relay node, that is, a node that arrives at the destination node of a message with less delay, and fewer hop counts will be selected as the next hop node.

Simultaneously, based on the weight of the message carried by the node, a buffer management mechanism is introduced. As the message arrives at the destination node with less delay and fewer hop counts, it is more likely to reach the destination node; thus, reducing the number of copies in the network is necessary.

The source node sets the number of copies of the message based on the weight of the message carried by the source node. During message forwarding, the number of copies assigned to the relay node depends on the weight of the message carried by it. For a lesser weight, more message copies are allocated. When the number of message copies allocated to the next hop is greater than zero, the message occupies the buffer space of one message only. When the node buffer overflows, the message with the least copies is first discarded; if the buffer continues to overflow, messages with the largest weight carried by the node will be discarded until the node has sufficient space for a new message.

Delay estimate

In this section, we introduce the EMD calculation. The EMD is calculated in the literature²⁴ as follows: Suppose a node s has a message p in its buffer intended for a destination node d; at each time slot t, s probes the environment to discover other mobile nodes in the vicinity. Each neighboring node v in turn advertises to s its $EMD (v, d)$ among all possible routes from v to d. Then, node s updates $EMD (s, d)$ as follows

EMD (s, d) = E [min (I_{s, i} + EMD (v_{i}, d))]

(1)

where $I_{s, i}$ is a random variable representing the inter-contact time between s and its neighbor v_i, $i \in {1, \dots, n}$ . $\forall i \in {1, \dots, n} : EMD (v_{i}, d) \leq {EMD}_{old} (s, d)$ , $\bar{dr} = \arg min_{i \in {1, \dots, n}} EMD (v_{i}, d)$ , and $EMD (d, d) = 0$ .

From the literature,²⁴ $EMD (s, d)$ is calculated as follows

\begin{array}{l} E M D = \sum_{i = 1}^{n - 1} {e^{- c i \cdot \bar{λ i} + \bar{c i}} (c i + \frac{1}{\bar{λ i}}) - e^{- c i + 1 \cdot \bar{λ i} + \bar{c i}} (c i + 1 + \frac{1}{\bar{λ i}})} \\ + e^{- c n \cdot \bar{λ n} + \bar{c n}} (c n + \frac{1}{\bar{λ} n}) \end{array}

(2)

where c_i is EMD(v_i,d), $I_{s, i} ~ Exp (λ_{i})$ , $\bar{λ_{i}} = \sum_{k = 1}^{i} λ_{k}$ , $λ_{i} = \frac{N}{\sum_{k = 1}^{N} T_{k}}$ , {T₁, T₂, …, T _N } are the inter-contact time samples, and $\bar{c_{i}} = \sum_{k = 1}^{i} λ_{k} c_{k}$ .

Hop count estimate

In this section, we introduce the EMJ calculation. The EMJ can be calculated as follows: When a connection is built between two nodes, one hop count is added. Therefore, we estimate the hop count of the message for reaching the destination node as per the ratio of the delay to the average interval contact time. Then, $EMJ (s, d)$ can be calculated as given below. The average interval contact time $E (u)$ is given in equation (3), and the message hop count is presented in equation (4), where n is the number of neighbor nodes of node s

E (u) = \frac{\frac{1}{λ_{1}} + \frac{1}{λ_{2}} + \dots + \frac{1}{λ_{n}}}{n}

(3)

EMJ (s, d) = \frac{EMD (s, d)}{E (u)}

(4)

Relay node selection

In this section, we first introduce the weight of the message carried by the relay node and then present the relay node selection. Suppose a node s has a message p in its buffer intended for a destination node d; at each time slot t, s probes the environment to discover other mobile nodes in the vicinity. $\forall m$ belongs to the set of neighbors of node s.The minimum EMD of the neighbor of node s that forwards message p to its destination node is $\bar{dr}$ , and the minimum value of the EMJ is $\bar{oj}$ . The EMD and the EMJ of node m are mdr and moj, respectively; the weight of the message carried by node m is

Q_{m}^{p} = {[α {(mdr)}^{u} + β {(moj)}^{u}]}^{\frac{1}{u}}

(5)

In order to maximize the performances of these two metrics simultaneously, node s replicates message p to m subject to the following constraint

m = \arg \max i \in {1, \dots, n} (Q_{s}^{p} - Q_{v i}^{p})

(6)

where $v_{i}$ is the neighbor node of node s and $i \in {1, \dots, n}$ . The weight of message p carried by node s is $Q_{s}^{p} = \sqrt[\frac{1}{u}]{\overset{u}{α (sdr)} + \overset{u}{β (soj)}}$ . It is a fixed value; hence, node m having the least weight value will be selected as the relay node. The smaller the weight value, the closer mdr and moj are to $\bar{dr}$ and $\bar{oj}$ , respectively.

Buffer management

For efficient utilization of the node buffer resources, we introduce a buffer management mechanism to efficiently allocate the number of message copies based on the weight of the message carried by a node. As the message arrives at the destination node with less delay and fewer hop counts, it is more likely to reach its destination node; thus, reducing the number of copies in a network is necessary. When the source node generates a message p, it sets the number of message copies to ${num}_{src (p)}^{p}$ based on the weight of the message carried by the source node, as depicted in equation (7)

{num}_{src (p)}^{p} = Q_{src (p)}^{p} \times δ

(7)

where $δ$ is the adjustment factor and $Q_{src (p)}^{p}$ is the weight of message p carried by its source node.

Suppose that the relay node of s is m. During the forwarding of message p, the number of copies assigned to the relay node m depends on the weight of message p carried by it. The lesser the weight, the more the number of message copies allocated. The copies of message p allocated to relay node m is $allocate (mp)$ , as depicted in equation (8). When $allocate (mp)$ is greater than zero, the message occupies the buffer space of one message only

allocate (mp) = ⌈ \frac{Q_{s}^{p} + Q_{m}^{p}}{Q_{m}^{p}} \times {num}_{s}^{p} \times χ ⌉

(8)

where $χ$ is the adjustment factor and $Q_{m}^{p}$ is the weight of node m that carries message p.

When ${num}_{s}^{p} = 1$ , it directly transmits message p to the next hop node m and does not store message p further. When the node buffer overflows, the message with the least number of copies in the buffer is first discarded. If the buffer continues to overflow, messages with the largest weight, which are carried by the node will be discarded until the node has sufficient space for a new message.

RABP algorithm implementation

Based on the above, we present the concrete realization of the RABP algorithm in this section. The RABP algorithm is implemented, as presented in Table 1.

Table 1.

RABP algorithm.

Algorithm RABP:
Input: the set of nodes: node the set of messages: $p, p_{1}, \dots, p_{n}$ Output: 1: for $\forall s, m \in node$ ; \\ “node” is the set of nodes in the network; 2: while $(p, s - d)$ \\ s has message p required to be forwarded to d 3: s traverses $V_{1}$ ; \\ node s traverses its neighbor nodes; 4: if ( $d \in V_{1}$ ) \\” $V_{1}$ “ is the neighbor set of node s; 5: s forwards message p to d; 6: end if 7: else if 8: $\forall m \in V_{1}$ ; 9: calculate $EMD (m, d)$ ; \\ evaluate delay; 10: calculate $EMJ (m, d)$ ; \\ evaluate hop count; 11: calculate $Q_{m}^{p}$ ; \\ $Q_{m}^{p}$ is the weight of m that carries p; 12: calculate $Q_{s}^{p} - Q_{m}^{p}$ ; 13: select m: $max (Q_{s}^{p} - Q_{m}^{p})$ as the relay node; \\ node m with the least weight is selected; 14: end if 15: execute buffer management; 16: end while 17: end for

Algorithm RABP:

Input:
the set of nodes: node
the set of messages:

p, p_{1}, \dots, p_{n}

Output:
1: for

\forall s, m \in node

; \\ “node” is the set of nodes in the network;
2: while

(p, s - d)

\\ s has message p required to be forwarded to d
3: s traverses

V_{1}

; \\ node s traverses its neighbor nodes;
4: if (

d \in V_{1}

) \\”

V_{1}

“ is the neighbor set of node s;
5: s forwards message p to d;
6: end if
7: else if
8:

\forall m \in V_{1}

;
9: calculate

EMD (m, d)

; \\ evaluate delay;
10: calculate

EMJ (m, d)

; \\ evaluate hop count;
11: calculate

Q_{m}^{p}

; \\

Q_{m}^{p}

is the weight of m that carries p;
12: calculate

Q_{s}^{p} - Q_{m}^{p}

;
13: select m:

max (Q_{s}^{p} - Q_{m}^{p})

as the relay node; \\ node m with the least weight is selected;
14: end if
15: execute buffer management;
16: end while
17: end for

At a time slot t, a node s has a message p in its buffer intended for a destination node d. s probes the environment to discover other mobile nodes in the vicinity; if d belongs to the set of neighbors of node s, s forwards message p directly to d; otherwise, node s selects a node with the lowest weight as the relay node and implements buffer management.

Simulation experiments and results

In this section, we evaluate the performance of the RABP with the widely used simulator Opportunistic Networking (ONE)²⁷ and compare it to the following three multiple copy routing protocols: the Epidemic,²⁸ the Prophet,²⁹ and the Spray and wait (SAW).³⁰

Simulation settings

In the simulation, the nodes consist of pedestrians, taxis, and trams; the movement model of the nodes is the “ShortestPathMapBasedMovement.” The initial values of adjustment factors are $α = 0.5$ , $β = 0.5$ , $δ = 5$ , and $χ = 0.1$ ; these values can be changed in different simulation scenarios. The speed of pedestrians is [0.5, 1.5] m/s, the speed of taxis is [2.7, 13.9] m/s, and the speed of trams is [7, 10] m/s; the transmission radius of pedestrians is [3, 6] m, whereas those of taxis and trams are [15, 20] m and [22, 30] m, respectively. In order to sufficiently simulate real-life scenarios, we set up schools, cinemas, parks, and other public places in the simulation map. The specific environmental parameters are presented in Table 2.

Table 2.

Simulation parameters.

Parameters	Setting
Simulation scenario	Helsinki
Node types	pedestrians, taxis, trams
Number of nodes	150
Simulation scenario size	8000 m × 6000 m
Message TTL	180 min
Buffer size	5–50 M
Simulation time	100 h
Node wait time	0–120
Message size	500 kb–2 Mb

TTL: time to live.

Simulation results comparison

Delivery ratio

The delivery ratio is the ratio of the successfully delivered to the generated messages within a given time period.³¹

Figure 1(a) illustrates the changes in the message delivery ratio when the buffer size is varied from 8 to 40 M; with the increase in the node buffer size, the message delivery ratios of all the four algorithms increase. Among these four algorithms, the delivery ratio of the RABP algorithm is the highest, whereas that of the Prophet algorithm is the least. Figure 1(b) depicts the changes in the message delivery ratio when the simulation time is varied from 60 to 300 h; the delivery ratios of all the four algorithms are relatively stable during the period 60–300 h. The delivery ratios of the Epidemic and Prophet algorithms are closely matched, while the delivery ratio of the RABP algorithm is the highest. Overall, the delivery ratio of the RABP algorithm is the highest. This is mainly because the algorithm can select an appropriate node as one of the relay nodes. Thus, the delivery ratio of the message is increased.

Figure 1.

Delivery ratio on varying the buffer size and simulation time: (a) illustrates the changes in the message delivery ratio when the buffer size is varied and (b) depicts the changes in the message delivery ratio when the simulation time is varied.

Average delay

Average delay is the average time between message generation and successful reception at a destination node.

Figure 2(a) illustrates the changes in the delay when the buffer size is varied from 8 to 40 M; on increasing the node buffer size, the message delays of all the four algorithms increase. Among the four algorithms, the delays of the Epidemic and Prophet algorithms are closely matched. The delay of the RABP is considerably lower compared to the other three compared algorithms. Figure 2(b) displays the changes in the message delay when the simulation time is varied from 60 to 300 h; the delays of all the four algorithms are relatively stable during the period 60–300 h. Among these four algorithms, the delay of the Prophet algorithm is the highest, whereas that of the RABP algorithm is the least. Overall, the delay of the RABP algorithm is the lowest. This is mainly because the algorithm can select a node with the least weight as one of the relay nodes. Thus, the average delay of the network is reduced.

Figure 2.

Delay on varying the buffer size and simulation time: (a) illustrates the changes in the delay when the buffer size is varied and (b) displays the changes in the message delay when the simulation time is varied.

Overhead ratio

Overhead ratio is the ratio of the number of messages that are not successfully delivered to the destination node to the number of messages that are successfully delivered to the destination node.

Figure 3(a) illustrates the changes in the network overhead when the buffer size is varied from 8 to 40 M; when the buffer size increases from 8 to 40 M, the overheads of the Epidemic and Prophet algorithms decrease; the overhead of the Epidemic algorithm is the largest, whereas that of the RABP algorithm is the least. Figure 3(b) depicts the changes in the overhead when the simulation time is varied from 60 to 300 h. During the simulation period 60–300 h, the changes in the network overhead of all the four algorithms are relatively less; the overhead of the Epidemic algorithm is the largest, whereas that of the RABP algorithm is the least. Overall, the overhead of the RABP algorithm is the least. This is mainly because the RABP algorithm implements buffer management based on the weight of the message carried by the node such that the number of message copies is limited. Thus, the overheads are reduced.

Figure 3.

Overhead on varying the buffer size and simulation time: (a) illustrates the changes in the network overhead when the buffer size is varied and (b) depicts the changes in the overhead when the simulation time is varied.

Average hop count

The value of the average hop is calculated using equation (9)³²

H_{i} = C \times \frac{1}{m_{i}} \sum_{j = 1}^{m_{i}} H_{ij}

(9)

where m_i is the number of messages in the buffer of node i and H_ij represents the hop count of message j in node i; the H_i of node i can be counted only after successful delivery. C is the hop count constant, which is equal to unity.

Figure 4(a) illustrates the changes in the message hop count when the buffer size is varied from 8 to 40 M. In Figure 4(a), when the buffer size increases from 8 to 40 M, the hop counts of the Epidemic and Prophet algorithms decrease, whereas the changes in the message hop counts of the SAW and the RABP algorithms are relatively less. The message hop counts of the RABP algorithm are lesser compared to those of the other three compared algorithms. Figure 4(b) depicts the changes in the message hop count when the simulation time is varied from 60 to 300 h. During the simulation period 60–300 h, the changes in the message hop counts of all the four algorithms are relatively less. The message hop count of the Epidemic algorithm is the largest, whereas that of the RABP algorithm is the least. Overall, the hop count of the RABP algorithm is the least. This is mainly because the algorithm can select a node with the least weight as one of the relay nodes. Thus, the message hop counts are reduced.

Figure 4.

Hop count on varying the buffer size and simulation time: (a) illustrates the changes in the message hop count when the buffer size is varied and (b) depicts the changes in the message hop count when the simulation time is varied.

Conclusion

In this article, we proposed an RABP algorithm to solve relay node selection and buffer management issues with constrained network resources. The RABP estimates the delay and hop count of the message carried by the node to the destination and constructs a weight function of the delay and hop count. The node with the least weight value is selected as one of the relay nodes such that the message delay and hop count from the relay node to the destination are near optimal. Simultaneously, based on the weight, the number of message copies is limited. Thus, the limited network resources are efficiently utilized. Simulation results show that the RABP algorithm outperforms the Epidemic, Prophet, and SAW routing in terms of the message delivery ratio, average delay, network overhead, and average hop count.

Footnotes

Handling Editor: Carlos Calafate

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (nos 61502118, 61402127, and 61370212), the National Science and Technology Major Project of the Ministry of Science and Technology of China under Grant (no. 2016ZX03001023-005), the Natural Science Foundation of Heilongjiang Province in China (nos F2016028, F2016009, and F2015029), and the Natural Science Foundation of Zhejiang Province in China (no. LY17F020030).

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