Diverse Path Routing with Interference and

Mobile Netw Appl DOI 10.1007/s11036-011-0301-y

Diverse Path Routing with Interference and Reusability Consideration in Wireless Mesh Networks Farah Kandah · Weiyi Zhang · Chonggang Wang · Juan Li

© Springer Science+Business Media, LLC 2011

Abstract Multipath routing has been extensively employed in wireless mesh networks (WMNs) for providing network reliability and survivability, therefore, improves energy consumptions. To provide network survivability, each user should be protected against failures, either node or link failures. For each request, a primary path is set up for normal transmission, and an alternate path (protection path) should also be provided to protect the request in case of network failure. In this paper, we study how to provide survivability using multi-path scheme for dynamic network traffic, where users’ requests have random arrival times. Compared with previous work, our scheme considers interference and reusability factors when providing multiple paths for each request. By applying our scheme, the numerical results show that we can accommodate about 17% more requests than previous schemes. Meanwhile, the results show that our scheme not only accommodates more requests, but also takes less running time to find a solution for each request.

F. Kandah · W. Zhang (B) · J. Li Department of Computer Science, North Dakota State University, Fargo, ND 58105, USA e-mail: [email protected] F. Kandah e-mail: [email protected] J. Li e-mail: [email protected] C. Wang NEC Laboratories America, Princeton, NJ 08536, USA e-mail: [email protected]

Keywords wireless mesh network · multipath · network interference · reusability · primary path · protection path

1 Introduction Wireless Mesh Networks (WMNs) have attracted much research attention due to the capabilities including, fault tolerance, self configuration and scalability [1– 3]. A wireless mesh network [1, 2, 4, 5] is a multihop wireless network that consists of a large number of wireless devices, such as mesh routers which relay packets through wireless channels, mesh gateways which are connected with a wired network to the Internet and mesh end users. Wireless mesh networks have seen phenomenal growth due to their unique ability to self-heal and self-organize, while providing robust and reliable solutions for applications that require low data rate, long battery life and high reliability. One of the major concerns in ad hoc wireless networks is reducing node energy consumption. Recent studies provide designing schemes to reduce the operation expenditure or energy consumptions of mobile networks towards providing green mobile networks [6]. The limitation of energy availability has become one of the most critical issues in multihop wireless networks, and it motivates extensive research efforts towards power-efficient routing and topology control [7, 8]. Due to the large number of users and the emergence of real-time multimedia applications, providing reliability has become one of the critical issues in WMNs. Using multipath routing instead of a single path has been shown to be able to provide better reliability and quality of service (QoS) [9–11]. The idea of multipath

Mobile Netw Appl

routing is that instead of finding one path for a connection, we find several disjoint paths to reach destination [12]. Therefore, when any link or node failure happens on the primary path, all the information can still be transmitted using other paths. Due to the wireless nature, reaching a destination node located out of the coverage range of the sender node, requires a multihop communication strategy, where each node has to cooperate with the other ones to form a path and acts as relay for packet transmission. In this scenario, the instability of the topology due to link or node failures could result in disconnected routes. A set of links or nodes could be shared between many path and any failure occur could affect these paths, which might results in consuming user’s energy in sending packets without knowing the existence of any failure in his path. Thus, the existence of multiple paths (primary and protection path) provides a recovery for saving user energy, where user’s requests can be still carried by the use of the protection paths provided through the network. The ability of multipath routing schemes in providing a better QoS in transferring multimedia applications such as voice, video and data, has been proved in a number of previous studies, such as in [10, 11]. Chen et. al in [10], addressed the problem of real-time video streaming over a bandwidth and energy constrained in wireless sensor network. Due to these constraints, the authors proposed to divide a single video stream into multiple sub-streams, and use multiple disjoint paths to transmit these sub-streams in parallel. The authors presented a directional geographical routing (DGR) scheme which is a multipath routing scheme that allow the use of these parallel sub-stream in an efficient way that facilitate load balance, bandwidth aggregation as well as fast packet delivery. Through simulations they showed that their proposed scheme provides longer network life time as well as a better received video quality. Wu et al. in [11], presented a multipath routing scheme (Ad hoc on-demand multipath routing) that seeks a better quality of service in terms of bandwidth, hop count and end-to-end delay in mobile ad-hoc networks. Their proposed scheme provides an alternative path that will be used as a next primary path to continue data transmission without initiating a route discovery when the main primary path breaks due to node mobility. Through simulations they showed that their multipath routing scheme provides QoS support with high reliability and low overhead. The network performance when using diverse path routing in wireless networks has been studied in a number of previous works, such that, in [13] they showed

that multi-path routing design can improve the reliability of packets delivery by providing many alternate loop-free paths to destination. Mohanoor et al. in [14] studied a way to improve the end-to-end throughput in wireless networks by the use of diverse paths with less interference. To improve route recovery and control the message overhead in wireless sensor networks for indoor environments, the authors in [15] proposed a routing scheme that used multiple node-disjoint paths. A number of multipath routing protocols have been proposed for WMNs. Tsai and Moors in [9] studied a multi-path routing design and focused on the concurrent use of multi-paths. Their scheme sends copies of data over different paths to improve the end-toend reliability. In their design the authors presented a heuristic for multipath selection that will exploit the frequency diversity offered in a multi-radio, multichannel network. In [16] the authors studied the use of multipath routing by using concurrent paths between two nodes to increase the effective throughput. Another study in [17] presented an interference-aware multi-radio routing protocol for detecting and resolving dynamic path deterioration in WMNs. This proposed protocol dynamically reconstructs a source-initiated path when radical link deterioration happens. Another approach for the multipath design was studied in [18]. They studied the problem of finding minimum energy disjoint paths in wireless ad-hoc network, in their work they concentrated with relatively static ad-hoc networks. They presented a heuristic algorithm to solve the problem of finding minimum energy disjoint paths. For each request, after finding a primary path, they used all the nodes along the primary path named the common nodes to find another path that shared these common nodes to form a disjoint path. Hu and Lee in [19] proposed a multipath routing protocol named AODV-DM, which aims to find multiple paths with less interference. After finding a primary path, an insulating region is formed around the primary path, which contains all the edges within the interference range of each node on the primary path. A protection path must be selected and established outside the insulating region to reduce potential network interference with the found primary path. However, most of the network links would be eliminated by the use of insulating region. Chen et al. in [10], proposed a directional geographical routing (DGR) which is a multipath routing scheme to address the problem of realtime video streaming over a bandwidth energy constrained wireless sensor network. Their proposed scheme facilitates load balancing, bandwidth aggregation and fast packet delivery.

Mobile Netw Appl

Through simulations the authors in [10] show that the proposed scheme provides lower delay, substantially longer network life time as well as better received video quality. We, in this work, aim to embrace the network interference for better protection performance. First of our observations is that any two primary paths should not use the interfered links because the interference will reduce bandwidths of both primary paths. Improving paths bandwidths by avoiding the use of interfered paths at the same time will allow the users to use their device’s energy in a more efficient way, where with a low bandwidth path, users might not be able to send or receive a large bandwidth request at once, they might need to split the request in multiple parts which will consume more energy from their devices through multiple sends. So in this work to provide an energy efficient multipath scheme, we try to avoid using the interfered paths at the same time, in other words, we will choose some links to be part of the primary path and the other links that interfere with them to be part of the protection path. Our second observation is that a primary path and its protection path will never transmit at the same time. Therefore, instead of using a link in an insulating region, we plan to use the links which are interfered with the links on a primary path for protection. This is the first work that considers using network interference to improve the connection accommodation in wireless mesh networks. Moreover, in this paper, we study routing in WMNs with dynamic traffic, i.e., users’ requests have random arrival times, which is different than the static network routing which was studied in [2, 5, 20], where all traffic demands were given in advance. For each coming request we need to provide two disjoint paths (one primary path and one protection path) to satisfy the request, i.e., by providing each request with two disjoint primary and protection paths, we can say that we had satisfied the request. Each primary path will be reserved for a specific user request. On the other hand, each protection path is reserved (not actively used) for a request in the case of failure in the primary path. Therefore, it is possible to use a same link to protect multiple primary paths if some criteria are satisfied. For example, if we assume single-link (single-node) failure in a network, then one link can be used to protect multiple active paths as long as they are link-disjoint (node-disjoint). We denote such ability to protect multiple paths as reusability of a protection link. To the best of our knowledge, this work is the first to discuss the reusability of protection links in wireless mesh networks. Reusability of a path to pro-

vide protection for multiple users’ requests, will reduce energy consumption in the network, where by using a single path multiple times, we will consume energy from a small number of nodes, compared to that when we assign each primary path a specific protection path. Moreover, reusability of protection paths, will increase the number of free links in the network, and since the nodes on those links are not active (not participating in any primary or protection paths) they can be put into a sleep mode for energy saving purposes. The rest of this paper is organized as follows. We describe the system model and formally define the problem in Section 2. Our diverse path routing scheme is presented in Section 3, which is followed by the numerical results in Section 4. We conclude the paper in Section 5.

2 Problem statement First in this section, we will describe our system model and notations. Then, formally we will define the optimization problem we are going to study. In this work the terms edge and link are interchangeable. Also the term diverse path and multipath are interchangeable. We use a similar network model as described in [2, 5, 20]. All nodes in any given network will use the same transmission range (R), where R > 0 and interference range (I R), which is typically 2 to 3 times of the transmission range (R) that associated with each node [20]. We use an undirected bi-connected graph G(V, E) to model the wireless mesh network where V is the set of n nodes and E is the set of m links in the network. For each pair of nodes (u, v), there exist a undirected edge e ∈ E if and only if d(u, v) ≤ R, where d(u, v) is the Euclidean distance between u and v. Each edge between any pair of nodes (u, v) in G corresponds to a potential wireless link between nodes u and v in the network. Definition 1 (Interference edge) Given any two edges (u, v) and (x, y) in G with a given channel assignment, if node x or node y is in the interference range of node u or node v (Lies within a distance I R from node u or node v), and they have been assigned the same channel k, then we can say that edge (x, y) is an interference edge of edge (u, v). Definition 2 For a coming request R(S, D, Br ), deciding the source (S), the destination (D) and the

Mobile Netw Appl

requested bandwidth (Br ), an edge e is said to be a primary link if it is used for a primary path. Similarly, if e is used for a protection path, it is a protection link. Otherwise, e is a free link. We state the DIverse Path ROuting (DIPRO) problem in the following: Definition 3 (DIPRO problem) Given the network G with assigned channels, for a coming dynamic request R(S, D, Br ), DIPRO problem seeks a pair of linkdisjoint paths (a primary path Pa and a link-disjoint protection path Pb ) consuming a minimum number of free links. By providing a pair of link-disjoint paths using our proposed scheme (DIPRO) for each coming request, we can guarantee that the user request will be satisfied even with any single link failure in the network.

3 Proposed solution for DIPRO Since the problem of finding disjoint paths with minimum energy has been proven to be NP-complete [18], we speculate the closely-related DIPRO problem is also NP-hard. Therefore, we present heuristic algorithms to solve the diverse path routing problem. Our scheme is based on two novel ideas which have not been well investigated in previous work. First, we consider to embrace interference to improve network resource (free links) usage. After a primary path is setup, there will be some links interfering with the links on the primary path. It is obvious that these links will not be preferred to be used for future primary paths. If we use these links for another primary path, interference will hurt both primary paths. Now we observe that we can use these links for the protection of the primary path. The reason lies in the fact that the primary and protection paths will never be used at the same time. Therefore, interference between a primary path and its protection path is not a problem. It will be resource efficient of using interfered links for protection. Second, we consider the reusability of each protection link. In other words, we try to use one protection link to protect as many primary paths as possible. Reusing existing protection links to protect a new primary path will save the free links for the future coming connection request, which will increase the network resource usage efficiency.

Our solution is listed in Algorithm 1. For each coming new connection request R, which is decided by source S, destination D and bandwidth request Br , we first remove the edges that does not have enough bandwidth to accommodate the request (Line 1–Line 5). Then Algorithm 2 and 3 will be used to find a primary and a protection path for the specified request. Note that, if we couldn’t find a primary path for the coming request using Algorithm 2 we drop the request, otherwise we search for a protection path using Algorithm 3. These steps are listed in Algorithm 1 (Line 6– Line 11).

Algorithm 1 DIPRO(G, R(S, D, Br )) 1: Given the coming request R(S, D, Br ) 2: for each link e in G do 3: if the residual bandwidth of e is less than Br then 4: Hide edge e; 5: end if 6: end for 7: Find a primary path Pa using Find-Primary 8: if Primary path found then 9: Find a protection path Pb using Find-Protection; 10: else 11: Drop the request R; 12: end if 13: Update the residual bandwidth of the edges on Pa and Pb ; 14: Restore all the hidden links in G;

Algorithm 2 Find-Primary(G, R(S, D, Br )) 1: for each edge e ∈ G do 2: if e has been used for primary or protection paths for existing connections then 3: Hide link e; 4: end if 5: end for 6: for each link e ∈ G do 7: Assign edge weight W1 (e) = B(e) on e; Br 8: end for 9: Find a shortest path p from S to D; 10: if p is found then 11: Restore all hidden links; 12: Return p as the primary path Pa for R; 13: else 14: Restore all hidden links; 15: Drop the connection request R; 16: end if

Mobile Netw Appl

Algorithm 3 Find-Protection(G, R, Pa ) 1: for each edge e ∈ G do 2: if e is a primary link then 3: Hide edge e; Continue 4: else 5: // Calculate its interference degree I(e) 6: for each edge l on Pa do 7: if l and e interfere with each other then 8: I(e) = I(e) + 1 9: end if 10: end for 11: end if 12: end for 13: for each link e do Br 1 1 14: W2 (e) = α · B(e) + β · I(e)+1 + γ · U(e)+1 15: end for 16: Find a shortest path p from S to D 17: if p is found then 18: for each e on p do 19: U(e) = U(e) + 1; 20: end for 21: Return path p as Pb for request R 22: else 23: Drop the request R 24: Release all the edges used by Pa 25: end if 26: Restore all the hidden links

Our scheme of finding a primary path for a given request is given in Algorithm 2. First, all the existing primary and protection paths must be reserved and cannot be used for future connection, including both protection and primary paths. Thus, all the links that have been used for other connections are hidden (Line 1–Line 5). Note that, in our discussion, we will use the term hide edge e to indicate that edge e will not be used further more in the path assigning process. Next, for each edge e in we assign a weight W1 (e) = B(e) Br the network in (Lines 6–8), where B(e) is the residual bandwidth of edge e, and Br is the bandwidth requested by request R. Using such an edge weight scheme, we want to make sure that we use the most matched links for the coming request R, i.e., by assigning weight W1 on each edge, we aim to save links with higher bandwidth to be used for the protection paths. After assigning weight for each edge, shortest path algorithm is used to find a primary path. If we cannot find a path p, request R will be dropped. Otherwise, we reserve it as the primary path for R, and then use Algorithm 3 to find its protection.

Interference within the network might lead to degradation in the network performance [21], where edges that had been assigned to the same channel will interfere with each other. In previous work [19], primary and protection paths are setup in a manner that they are not interfering with each other. However, we find that this actually is a overkill for protection. To find a protection path with minimum free link consumption, the first observation is that a primary path Pa and its protection path Pb will not be used at the same time. Pa is the first choice as the path for the request. And Pb will only be used when a single link failure occurred on the primary path. Therefore, in our proposed solution, we will use the interfered edges of a primary path Pa to provide protection. Therefore, the interference-free edges could be saved for future connections. In Algorithm 3, we prefer to use the edges that mostly interfere with the primary path Pa for protection. An interference degree I(e) is assigned for each edge e (Line 6–Line 11). For each edge e, its interference degree I(e) is the number of edges on the primary path that interfere with e. The second scheme to improve the network resource (links) usage is the reusability of a protection edge e, which is denoted by U(e). The basic idea is to re-use a protection edge to protect multiple primary paths. By reusing protection edges of existing connections for the new connection request, we can improve the efficiency of the network utilization. For each edge e, its reusability value U(e) indicates how many times this edges has been used as a protection edge. Between Line 19 and Line 21, for each link on a found protection path, its edge reusability value, U(e), is increased by one. Thus, these links will more likely be used for future connection protection. To choose the best protection path Pb for a coming request, we calculate a protection edge weight W2 (e) for each edge e (Line 15), this weight considers three different factors: bandwidth ratio, interference degree and edge reusability, for selecting protection links. To adjust the importance of different factors in the selection, we give each factor a weight α, β and γ , respectively. By adjusting the weights, we can make one factor more dominate than another in protection path selection. After assigning edge weights, a shortest path is found using the assigned edge weights. If a protection path p is found, we increase the edge reusability for all edge on p and return it as the protection path Pb for the request R. If there is no protection path available, we drop the request because we cannot satisfy it. To illustrate our algorithm, let us use an example in Fig. 1 for illustration. For simplicity, we assume that

Mobile Netw Appl S=A T=C Br = 0.5 Mbps

1.57

1.57

I

S=A T=E Br = 1.5 Mbps

I

1.8

5

1.

P1

P’

1

P’1

1

9 2.2

3

7

E

H

I

J I

P1’

G

A

P2

32

J

F

2.

83

H

P G

A

8

2.32

2

E

1.82

2.3

F

1.79

B

2.1

1.68

2.2

29

1.83

P1’ D

D

1.

1.5

1.0

2.3

1.5

2

C

B

2.2

J

(f) Pick primary path for request (A,E; 1.5)

2.32

2.

57

1.

A

1.2

3

1.8

7

2.2

C

D B

G

1.05

K

(e) Hide primary and protection edges

S=A T=E Br = 1.5 Mbps

1.57

E

I

K

(d) Hide primary edges and pick protection path for request (A,C; 0.5)

1.83

H 1.05

K

1.57

7

7

1.57

C

1.4

J

I

2

2.32

4

1.57

1.0

7 H

F

5

27 2.

3

7 2.2

2.2

J

G A

1.5

2 2.3

2.32

E

22 1.

H

F

7

1.22

2

G A

1.4

1.2

E

1.83

1.

2.27

F

D B

2.2

1.8

1.56

6

83 1.

6

3.1

D B

1.5

27 2.

1.5

C

05 1.

G

4.4

S=A T=E Br = 1.5 Mbps

57 1.

32 2. 2.32

(c) Pick primary path for request (A,C; 0.5)

C

D B

A

7

K

(b) Bandwidth assignment

2.32

2.27

4. 4

7

7

(a) Original network with channel assigned C

J

3.6

K

K

S=A T=C Br = 0.5 Mbps

3.14

I

3.14

3 1.8

3

2

H

I

1.57

1.5

3

4.4

J

E 3. 67

H

J

3.67

F

22

3

3.67

G

3.1 4

2.2

2

H

A

3

2

1

3.14

E

67 3.

2

1.83

F 83 1.

3

1.83

G 1.5 7

A

4.4

3.6

1.57

E

1.8

F

1. 83

2

G

A

2.2

2.2

B

2.2

14 3.

2

3

D

B

1

1

57 1.

1

3.14

D

D B 3

C

4.4

F

E

P’2

P’2

P2’

P2

H

P

2

C

2.2

1

J

P

Cap = 11 Mbps B(e) = Cap / IN(e)

3

83

C

I

2.2

2.3 2

3

1.8

1.5

9

7

2

K

(g) Hide primary and restore protection edges

K

(h) Pick protection path for request (A,E; 1.5)

K

(i) Final paths assigned

Fig. 1 Diverse Path Routing (DIPRO)

all the links are in the same interference range in this example. Figure 1a shows the original network, with channels assigned on the edges. Channel assignment is beyond the scope of this paper. With this channel assignment, we calculate the bandwidth on each link e denoted as B(e) in the figures as the channel capacity Cap divided by the number of interfere edges of e, I N(e). In short, B(e) equals to ICap . Note that this is the best case estimation N(e) for the network in terms of bandwidth allocation fairness. The network with edge bandwidth is shown in Fig. 1b. After calculating link bandwidths, let us consider for example that a request came with node A as the source

node (S), node C as the destination node (T) and a requested bandwidth (Br ) of 0.5 Mbps. To pick a primary path for this specified request, first we assigned W1 (e) for each edge e as specified in Algorithm 2 (Line 7) and then a shortest path is selected as the primary path for this request, it can be seen in Fig. 1c that the path ((A, B), (B, C)) which is shown by the blue solid arrow lines has been picked as the primary path for the request R(A, C, 0.5). After finding the primary path, we need to find a link-disjoint protection path for the request. In Fig. 1d, according to Algorithm 3, we first hide all the edges which previously picked to be primary edges, then we assign W2 (e) defined in Algorithm 3 (Line 15) on each link e in the network. After assigning

Mobile Netw Appl

edges weights we run the shortest path algorithm and found the path ((A, G), (G, F), (F, D), (D, C)) to be the shortest path which we assigned to form a protection path for the request (A, C, 0.5). The protection path for request (A, C, 0.5) is marked by the red dashed arrow lines in Fig. 1d. Note that on the protection path, we use the links that interfere with the primary path. Since these links cannot be used for other primary paths due to the conflict with the selected primary path, using them for the protection clearly improves the network resource utilization. After accommodating request R(A, C, 0.5), another request with a source node A, a destination node E with Br = 1.5 Mbps comes. First we need to hide all the previously used edges (the primary and the protection edges) and not use them for new coming requests. Edges that can be used as a part of the primary path for the (A, E, 1.5) request after hiding previously used edges are shown in Fig. 1e. Similarly to provide the specified coming request with a primary path, as specified in Algorithm 2, the wight W1 (e) is assigned for each link e in the network (Line 7). After the weights have been assigned on the edges, a shortest path from A to E is picked to form a primary path for the specified request. The path ((A, H), (H, I), (I, J), (J, E)), marked by the bold blue solid arrow lines shown in Fig. 1f, is picked to be the primary path for the request (A, E, 1.5). To satisfy the request R(A, E, 1.5) we refer to Algorithm 3 to find a linkdisjoint protection path. First we hide all edges that have been used previously to form primary paths as in lines 1–3 in Algorithm 3. Note that, all edges that have been assigned for protection paths can be reused to protect multiple request. The available edges which could be used as a part of a protection path for request R(A, E, 1.5) is shown in Fig. 1g. Previously protection edges are marked by the dashed lines. These edges will more likely be used for future connection protection, due to the fact that the primary and the protection paths will never be used at the same time. Picking the protection path for request R(A, E, 1.5) is shown in Fig. 1h, where we assigned weights on each edge as specified in (Line 15) of Algorithm 3, and then the shortest path (A, G, F, E) has been picked to form a protection path for request R(A, E, 1.5). Using path ((A, G), (G, F), (F, E)) for protection, our scheme reuses links (A, G) and (G, F) for the protection of both requests, where this improves the network resource (link) utilization. The final paths assignment for both coming requests R(A, C, 0.5) and R(A, E, 1.5) is shown in Fig. 1i, where the primary path’s edges are indicated by P, and the protection path’s edges are indicated by P , while the numbers

(1 and 2) refereed to request R(A, C, 0.5) and request R(A, E, 1.5) respectively.

4 Numerical results In this section, to illustrate the performance of our scheme, we implemented our solution (denoted by DIPRO in the figures), and compared it with previous schemes in [18] (denoted by DPR in the figures) and in [19] (denoted by AODV-DM in the figures). As in [19], we considered static wireless mesh networks with n nodes uniformly distributed in a square playing field. Each node has a fixed transmission rage of 250 m (m) and interference range of 500 m [20]. We assign the values α = 0.25, β = 0.25 and γ = 0.5, to be used in calculating W2 (e) in finding the protection paths. The results shown are the average of 5 test runs for various scenarios. All the requests in the experiments were generated randomly, where each one specified the source node, the destination node and the requested bandwidth. The first metric used for performance evaluation is the satisf ied ratio. By providing a pair of link-disjoint paths for each dynamic request, it is said that the request is satisfied. Satisf ied ratio can be calculated as the number of satisfied request divided by the total dynamic requests. The second performance metric is the running time, which is the time that the scheme takes to satisfy a request. We tested the performance with different network density, where density is the number of nodes in one square unit. In our simulation we tested two scenarios. In the first scenario, we randomly distributed different number of nodes (100, 150, 200, 250 and 300) in a 1,000 m by 1,000 m fixed playing area. In the second scenario, we fixed the number of nodes as 300 nodes, and change the network density by changing the area size. The corresponding results for the first scenario (Fixed Area Size) are presented in Fig. 2, which shows the satisfied ratio versus different number of nodes, in where we tested with 500, 1,000 and 1,500 coming requests. The results in Fig. 2a shows that, with 500 coming requests by using our proposed scheme (DIPRO), we can satisfy more requests compared to that when we used DPR or AODV-DM schemes. In our DIPRO scheme, since we are considering to embrace interference and protection links reusability, we can satisfy more requests than that in DPR and AODVDM. The results also showed that because AODV-DM hide all the edges that interfere with the primary or the protection path, it might hide most of the links in the network, so it can be seen from the figure that

Mobile Netw Appl 0.9

0.6

0.6 0.5 0.4 0.3

AODV-DM DPR DIPRO

0.6 0.5

0.5

Satisfied Ratio

Satisfied Ratio

Satisfied Ratio

0.7

AODV-DM DPR DIPRO

0.7

AODV-DM DPR DIPRO

0.8

0.4 0.3

0.4 0.3 0.2

0.2 0.2

0.1

0.1

0.1 0

100

150

200

250

0

300

100

150

200

250

0

300

100

150

200

250

Number of Node

Number of Node

Number of Nodes

(a) 500 Requests

(b) 1000 Requests

(c) 1500 Requests

300

Fig. 2 Satisfied ratio—multiple requests within a fixed area size

AODV-DM (100 Sec) DPR (Sec) DIPRO (Sec)

0.08

0.03

Running Time

Running Time

0.035

0.025 0.02 0.015 0.01 0.005 0 100

150

200

250

0.16 0.14

0.07 0.06 0.05 0.04

0.12 0.1 0.08

0.03

0.06

0.02

0.04

0.01

0.02

0 100

300

AODV-DM (100 Sec) DPR (Sec) DIPRO (Sec)

0.18

AODV-DM (100 Sec) DPR (Sec) DIPRO (Sec)

0.09

Running Time

0.04

150

200

Number of Nodes

250

0 100

300

150

Number of Nodes

(a) 500 Requests

200

250

300

Number of Nodes

(b) 1000 Requests

(c) 1500 Requests

Fig. 3 Running time—multiple requests within a fixed area size

AODV-DM DPR DIPRO

Satisfied Ratio

Satisfied Ratio

0.6 0.5 0.4 0.3

0.5 0.4 0.3

0.2

0.2

0.1

0.1

0

1000

1500

2000

AODV-DM DPR DIPRO

0.6

0

2500

Area Size (m x m)

(a) 500 Requests

AODV-DM DPR DIPRO

0.6 0.5

Satisfied Ratio

0.7

0.4 0.3 0.2 0.1

1000

1500

2000

0

2500

1000

1500

2000

Area Size (m x m)

Area Size (m x m)

(b) 1000 Requests

(c) 1500 Requests

2500

Fig. 4 Satisfied ratio—multiple requests with fixed number of nodes

0.045

0.1

AODV-DM (100 Sec) DPR (Sec) DIPRO (Sec)

0.2 0.18

AODV-DM (100 Sec) DPR (Sec) DIPRO (Sec)

0.16

0.03 0.025 0.02 0.015

Running Time

Running Time

0.035

0.12 AODV-DM (100 Sec) DPR (Sec) DIPRO (Sec)

Running Time

0.04

0.08 0.06 0.04

0.14 0.12 0.1 0.08 0.06

0.01

0.04

0.02 0.005 0 1000

0.02 1500

2000

2500

0 1000

1500

2000

2500

0 1000

1500

2000

Area Size (m x m)

Area Size (m x m)

Area Size (m x m)

(a) 500 Requests

(b) 1000 Requests

(c) 1500 Requests

Fig. 5 Running time—multiple requests with fixed number of nodes

2500

Mobile Netw Appl

AODV-DM can satisfy less number of requests. And also by increasing the number of nodes within the same area size, using AODV-DM scheme will lead to a drop in the satisfied ratio, by hiding more number of interfered edges in the graph. In DPR scheme, finding the protection path works by finding paths between common nodes along the primary path. Since these links within the paths are not reused for other primary or protection paths, we might use most of the links in the network, which leads to small satisfied ratio. These results can be seen in Fig. 2a. From Fig. 2a, it can be seen that using DIPRO scheme with 200 nodes had increased the number of satisfied requests by 27.6% compared with DPR. We also tested our solution with 1,000 and 1,500 random requests, shown in Fig. 2b and c respectively. Similar results are observed in these figures. The results for the running time metric are shown in Fig. 3. From the results we can see that DIPRO in most cases can satisfy the coming requests faster compared to DPR and AODV-DM schemes. In most cases AODV-DM was the most time consuming scheme, which is shown using a different unit (100 s), due to taking much time in forming the insulating region around the primary path and hide all the edges that interfere with the primary path edges. The difference in time can be seen more clear by having more number of coming requests. In Fig. 3b with 1,000 requests, we can see that the average time to satisfy a request increases while the network become more dense (having more number of nodes). Similar results are observed in the case of having 1,500 requests in In Fig. 3c. The second scenario is shown in Fig. 4, where we adjust the network density by distributing 300 nodes in an area with size range from 1,000 to 2,500 square meters. The results shows that the number of satisfied requests will drop as the network density decreases. We tested this scenario with different number, (500, 1,000 and 1,500), of random requests. Our results showed that our proposed DIPRO scheme satisfied more number of requests than the other two schemes. Figure 4a showed the case with 500 requests in 1,000 m by 1,000 m area size, DIPRO scheme satisfied 217 more requests than DPR scheme did, and 232 more requests than AODV-DM scheme did. With 1,000 requests, DIPRO satisfied 42.5% of the total dynamic requests in a 1,500 m by 1,500 m area, which is better that DPR and AODV-DM schemes. These results are shown in Fig. 4b. The AODV-DM scheme has the lowest satisfied ratio due to hiding most of the edges that lied within the insulating region of the primary path. On the other hand, the DPR scheme has a lower satisfied ratio compared to that of the DIPRO scheme

because using the common nodes concept made it hard to find many disjoint paths. Increasing the area size while having the same number of nodes will decrease the number of edges in a graph, this can affect the performance of the tested schemes where in Fig. 4c it can be seen that, by having less number of edges, due to the increase in the area size, we can satisfy less number of requests. For example, with our proposed DIPRO scheme in an area of size 1.000 m by 1,000 m we satisfied 303 request, while in a 2,500 m by 2,500 m area size we can satisfy 53 requests. Also these results are better compared with the results of DPR and AODVDM schemes. For the fixed number of nodes scenario, the running time metric is shown in Fig. 5. The results for 500, 1,000 and 1,500 requests in are shown in Fig. 5a–c, respectively. These results show that, in average, our schemes consume less time to satisfy a coming request than DPR and AODV-DM schemes in most cases, where the AODVDM scheme consumes much time forming the insulating region, while the DPR scheme consumes much time finding multiple path using the set of common nodes.

5 Conclusion In this paper, we define the DIverse Path ROuting (DIPRO) problem, and present an effective heuristic which seeks a pair of link-disjoint paths for each dynamic requests in case of any single link failure in the network. Simulation results showed that our solution performs well in terms of satisf ied ratio and running time. Since the protection path will not be used until a failure occurred in the primary path, we embraced the interference, by using the most interfered links with the primary path to form a protection path. Also by considering the reusability of each protection link, i.e, each link that used in a protection path could be used to protect another user request. By considering the interference embracement and the links reusability, we have shown that we can improve the network resource (links) usage, by satisfied more dynamic users’ requests. Acknowledgements The research developed in this paper is supported by North Dakota State EPSCoR Infrastructure Improvement Program FAR0015846 and National Science Foundation grants CNS-0845776 and NSF CNS-0721880.

References 1. Bononi L, Felice MD, Molinaro A, Pizzi S (2009) Joint channel assignment and multi-path routing for multi-radio

Mobile Netw Appl

2.

3.

4.

5.

6.

7.

8.

9.

10.

wireless mesh networks. In: Proceedings of the 2009 29th IEEE international conference on distributed computing systems workshops (ICDCSW). Washington, D, pp 476– 481 Tang J, Xue G, Zhang W (2005) Interference-aware topology control and QoS routing in multi-channel wireless mesh networks. In: Proceedings of the 6th ACM international symposium on mobile ad hoc networking and computing (MobiHoc, pp 68–77 Waharte S, Ishibashi B, Boutaba R, Meddour D (2009) Design and performance evaluation of IAR: interference-aware routing metric for wireless mesh networks. Mobile Netw Appl 14:649–660 Akyildiz IF, Wang X, Wang W (2005) Wireless mesh networks: a survey. Elsevier Journal of Computer Networks 47(4):445–487 Raniwala A, Gopalan K, Chiueh T (2004) Centralized channel assignment and routing algorithms for multi-channel wireless mesh networks. ACM Mobile Computing and Communications Review 8:50–65 Yamada A, Imai S, Kakemizu M (2010) A path-based traffic control method for green networks. 8th Asia-Pacific symposium on information and telecommunication technologies (APSITT) 2010, pp 1–5 Runser KJ, Comaniciu C (2008) A probabilistic interference and energy aware gradient broadcasting algorithm for wireless sensor networks. ISWPC 2008 Tang J, Xue G, Chandler C, Zhang W (2005) Interferenceaware routing in multihop wireless networks using directional antennas. INFOCOM 2005 Tsai JW, Moors T (2007) Interference-aware multipath selection for reliable routing in wireless mesh networks. In: MeshTech. IEEE Chen M, Leung V, Mao S, Yuan Y (2007) Directional geographical routing for real-time video communications in wireless sensor networks. Comput Commun 30(17):3368– 3383

11. Wu C, Zhang F, Yang H (2010) A novel QoS multipath path routing in MANET. International Journal of Digital Content Technology and its Applications 4(3):132–136 12. Nelakuditi S, Zhang Z (2001) On selection of paths for multipath routing. In: Proceedings of the 9th international workshop on quality of service, vol 2092. Springer-Verlag, London, pp 170–186 13. Mosko M, Garcia-Luna-Aceves JJ (2005) Multipath routing in wireless mesh networks. First IEEE workshop on wireless mesh networks (WiMesh 2005). Santa Clara, CA 14. Mohanoor A, Radhakrishnan S, Sarangan V (2008) Interference aware multi-path routing in wireless networks. IEEE MASS 2008. Atlanta, Georgia, pp 516–518 15. Huang P, Tian H, Zhang M, Zhang P (2007) Robust multipath routing for dynamic topology in wireless sensor networks. J China Univ Post Telecommun 14(1):1–5 16. Sheriff I, Belding-Royer E (2006) Multipath selection in multi-radio mesh networks. Broadband communications, networks and systems (BROADNETS). San Jose, Broadnets 17. Shin B, Ko Y, An J, Lee D (2009) Interference-aware routing protocol in multi-radio wireless mesh networks. In: Proceedings of the 4th international conference on future internet technologies 18. Srinivas A, Modiano E (2003) Minimum energy disjoint path routing in wireless ad-hoc networks. In: Proceedings of the 9th annual international conference on mobile computing and networking (MobiCom). San Diego, CA, pp 122–133 19. Hu X, Lee MJ (2007) An efficient multipath structure for concurrent data transport in wireless mesh networks. Comput. Commun. 30(17):3358–3367 20. Raniwala A, Chiueh T (2005) Architecture and algorithms for an IEEE 802.11-based multi-channel wireless mesh network. INFOCOM 2005 21. Gupta P, Kumar PR (2000) The capacity of wireless networks. IEEE Trans Inf Theory 46:388–404