# On the Capacity of Hybrid Wireless Networks with Opportunistic Routing

- Tan Le
^{1}Email author and - Yong Liu
^{1}

**2010**:202197

https://doi.org/10.1155/2010/202197

© T. Le and Y. Liu. 2010

**Received: **26 August 2009

**Accepted: **21 September 2009

**Published: **10 November 2009

## Abstract

This paper studies the capacity of hybrid wireless networks with opportunistic routing (OR). We first extend the opportunistic routing algorithm to exploit high-speed data transmissions in infrastructure network through base stations. We then develop linear programming models to calculate the end-to-end throughput bounds from multiple source nodes to single as well as multiple destination nodes. The developed models are applied to study several hybrid wireless network examples. Through case studies, we investigate several factors that have significant impacts on the hybrid wireless network capacity under opportunistic routing, such as node transmission range, density and distribution pattern of base stations (BTs), and number of wireless channels on wireless nodes and base stations. Our numerical results demonstrate that opportunistic routing could achieve much higher throughput on both ad hoc and hybrid networks than traditional unicast routing (UR). Moreover, opportunistic routing can efficiently utilize base stations and achieve significantly higher throughput gains in hybrid wireless networks than in pure ad hoc networks especially with multiple-channel base stations.

## 1. Introduction

New portable devices, such as iPhone and PDAs, are increasingly equipped with strong communication and computation capabilities. They can host a wide range of applications, such as web browsing, audio/video streaming, and online gaming. Most devices have multiple radio interfaces and support different wireless protocols, such as Bluetooth, Wi-Fi, and 3G. It has become critical for such devices to efficiently utilize resources available in a hybrid wireless networking environment to achieve high data throughput and support bandwidth-intensive applications.

Recently, Opportunistic Routing (OR) was proposed to improve the throughput for ad-hoc networks. In this paper, we explore the gain of integrating OR with hybrid wireless networks that consist of ad hoc wireless nodes and base stations connected to a wireline infrastructure. We first extend the opportunistic routing algorithm to exploit high-speed data transmissions in infrastructure network through base stations. We then develop linear programming models to calculate the end-to-end throughput bounds from multiple source nodes to single as well as multiple destination nodes. The developed models are applied to study several hybrid wireless network examples. Through case studies, we investigate several factors that have significant impacts on the hybrid wireless network capacity under OR, such as density and distribution pattern of Base Stations, number of wireless channels on wireless nodes and BTs.

- (1)
We propose a simple method to extend OR to hybrid wireless networks. We develop new transmission cost metrics and forwarding priority rules to take into account candidate routes through BTs and infrastructure network.

- (2)
We develop linear programming models to calculate end-to-end throughput bounds from multiple source nodes to single as well as multiple destination nodes.

- (3)
We demonstrate through case studies that OR can efficiently utilize BTs and achieve significantly higher throughput gains in hybrid wireless networks than in pure ad-hoc networks. And the throughput gain of OR is also higher than that of UR in hybrid networks.

- (4)
We systematically evaluate several factors determining the throughput gains of OR in hybrid wireless networks.

The rest of the paper is organized as follows. We briefly review the related works in Section 2. In Section 3, we present the extension of OR to hybrid wireless networks and the LP models to characterize the throughput bounds from multiple sources to single destination and from multiple sources to multiple destinations. Case studies on several example hybrid wireless networks are presented in Section 4. The paper is concluded in Section 5.

## 2. Background and Related Work

## 3. Capacity of Hybrid Wireless Networks with OR

### 3.1. Network Model

- (i)
There are static wireless nodes randomly located in a square area. There are Wi-Fi Base Stations in the same area.

- (ii)
Wireless nodes are homogeneous. They have the same set of transmission rates and equivalent effective transmission ranges.

- (iii)
Assume that the coverage areas of BTs do not overlap with each other. Each wireless node could connect to at most one BT.

- (iv)
Source node transmits data with OR through relay nodes to destination. If the relay node is a wireless node, it uses OR to forward the packet to the next-hop node (relay or the final destination). If a relay node is a BT, it forwards the packet to the next-hop node through direct single-hop transmission.

- (v)
Through a separate control channel (e.g., 3G), every node knows the geographical locations of its neighbors, base stations, and the destination node. Nodes then could differentiate the transmissions in wireless domain and wireline domain when making route selection over hybrid wireless network.

- (vi)We study two different models for data transmissions in hybrid wireless networks:
- (1)
*Single-Channel Model.*In this model, all BT nodes and wireless nodes are equipped with a single radio interface. They use the same frequency spectrum to communicate with each other. In other words, infrastructure and ad-hoc transmissions share the same wireless channel. Wireless nodes use OR and BTs use UR to forward packets toward their destinations. Since every BT node only has a single wireless channel, it could communicate with no more than one wireless node at any given time. - (2)
*Multiple-Channel Model.*In this model, infrastructure and ad-hoc transmissions operate at nonoverlapping frequency ranges. Wireless nodes in the coverage of a BT can simultaneously communicate with the BT using infrastructure mode and other wireless nodes using ad-hoc mode. Moreover, every BT node has multiple wireless channels, and so it can communicate with multiple wireless nodes simultaneously. Wireless nodes use OR and BTs use UR to forward packets. If the Candidate Relay Set (CRS) of a wireless node consists of a BT and some wireless nodes, the wireless node simultaneously employs infrastructure and ad-hoc transmissions to push the same packet to the BT and wireless nodes, respectively.

- (1)

### 3.2. Concurrent Transmitter Sets

The biggest challenge of studying the capacity of wireless networks is to model the conflicts between wireless links. The concept of Concurrent Transmitter Sets (CTSs) was proposed in [14] to calculate the end-to-end throughput in ad-hoc networks with OR. We extend the CTS concept to study the capacity of hybrid wireless networks.

With OR, a transmitter has multiple forwarding candidates in its Candidate Relay Set (CRS). Let all links from a transmitter to nodes in its CRS be links associated with that transmitter. In a hybrid wireless network, Conservative CTS (CCTS) is a set of transmitters (including the BTs) that when all of them are transmitting simultaneously, all links associated with them are still usable (no interfere with any other link [14]). However, such a requirement is too restrictive. Data from a transmitter can be forwarded to the next hop as long as one forwarding candidate in its CRS receives the data. To account for this, Greedy CTS (GCTS) is a set of transmitters (including the BTs) that when all of them are transmitting data simultaneously, at least one link associated with each transmitter is usable. This leads to the maximum end-to-end throughput. A maximal CCTS (GCTS) is a CCTS (GCTS) that is not a true subset of any another CCTS (GCTS).

- (1)
*Single-Channel Model.*Pairs of nodes , , and could not be included in the same CCTS. The reason is that two sets of links associated with each pair of nodes are not interference free. Also the pairs of of nodes and could not be included in the same CCTS because their links to node are not interference free. So the maximal Conservative CTSs in this case are , , and . The maximal Greedy CTSs in this case are exactly the same as the above maximal CCTSs. When all nodes in each of these GCTSs is transmitting simultaneously, usable links associated with each node are and . - (2)
*MultiChannels Model.*For Conservative CTSs, pairs of nodes , and could not be included in the same CCTS. So the maximal CCTSs in this case are , , and . On the other hand, for GCTSs, there are only pairs of nodes and that could not be included in the same GCTS. It is because the only link associated with node will be not usable whenever nodes or activated to transmit data. So the maximal Greedy CTSs in this case are and . When all nodes in each of these GCTSs is transmitting simultaneously, usable links associated with each node are and .

### 3.3. Opportunistic Routing Model

In OR, a transmitter selects neighbors "closer", that is, with lower transmission cost, to the destination as candidate forwarders in CRS. Forwarders in CRS are ranked based on their "closeness" to the destination. Since there is no preset route to a destination with OR, it is impossible to determine the accurate transmission cost from a node to a destination. In a pure ad-hoc network, one can use the geographic distance between a node and destination node to measure the packet transmission cost from to through ad-hoc network. For hybrid wireless networks, we propose a new metric that takes into account the low transmission cost through the infrastructure network. We assume that costs of the infrastructure transmissions between BTs are negligible. Then the cheapest transmission from to through infrastructure network is for to transmit a packet destined to first to its closest BT, Then transmits the packet to a BT that is the closest to node Finally, sends the packet to If is directly covered by we use geographic distance between and to estimate the transmission cost from to . If is not in the coverage of , we choose a node in 's coverage that is the closest to as a relay node. All packets from to will be first sent to using the ad-hoc mode, then be relayed to using the infrastructure mode. Consequently, the transmission cost is estimated as . Similarly, the transmission cost from to can be estimated as . The total transmission cost through the infrastructure network is then estimated as . The effective transmission cost from to in the hybrid wireless network is the minimum of the cost of pure ad-hoc transmission and that of transmission through infrastructure:

In OR, a forwarding candidate is utilized to transmit a packet if and only if it receives the packet and all other candidates with higher priority in the CRS do not receive the packet. To study the capacity of OR, we need to calculate the*effective forwarding rate* of a link between a transmitter
to each of its forwarding candidate
. Let
send data to its forwarding candidate set with rate
. Let
be the candidate forwarding set for
, and let
. The priority order to forward packets from
is
. Let
be the Packet Reception Ratio (PRR) between
and
theoretically depends on distance between
and
end node density around the position of nodes
and
and the MAC scheduling scheme. Then the effective forwarding rate
on link
is

### 3.4. Throughput Bound to Single Destination

Notation on Linear Programming Formulations.

Assume that there are maximal CTSs . At any time, when a CTS is scheduled to transmit, nodes in the scheduled CTS could transmit packets simultaneously. Let be the time fraction that CTS is scheduled. We need to calculate the effective forwarding rate for each link under each CTS . If a CCTS is scheduled and , all links associated with are usable, and therefore , for all , which is calculated in (3); if , . If a GCTS is scheduled and node , some links associated with maybe not usable. Let be a binary variable for the usability of link under a GCTS , then we have , for all .

Let be the sending rate from source toward the destination . We have the following LP optimization formulation to characterize the throughput bound with single destination:

Equation (4) is to find the maximum amount of traffic sent out from all the source nodes to the destination. Constraint (5) specifies that the traffic on all links are none negative and there are no traffic from one node to its neighbor nodes that are not in its forwarding candidate set. Constraint (6) specifies flow conservation on all relay nodes. Constraint (7) specifies the flow conservations on all source nodes . Constraint (8) states that no outgoing traffic from destination node . Constraint (9) preserves that only one CTS could be activated to transmit at any given time and the traffic assigned on each link is no more than the aggregate effective forwarding rate of that link during all active phases of CTSs. Depending on what types of CTSs we used as the input of the above formulation, we will get different bounds. Conservative CTS (CCTS) leads to conservative upper bound; Greedy CTS (GCTS) leads to optimistic upper bound of the end-to-end throughput.

### 3.5. Throughput Bound to Multiple Destinations

Since CTS is also defined based on forwarding sets for all nodes, we need to include destination information into the definition of CTS. More specifically, a Conservative CTS (CCTS) is a set of transmitter-destination pairs , such that all links are usable when all transmitters in CCTS are active. Similarly, a Greedy CTS (GCTS) is a set of transmitter-destination pairs such that for each transmitter in GCTS, there exists at least one link , that is usable when other transmitters in GCTS are active.

Similar to the single destination case, we need to calculate the effective forwarding rate on each link for destination under each CTS . If a CCTS is scheduled and , all links from to nodes in are usable, therefore , which is calculated in (10); if , . If a GCTS is scheduled and , some links associated with maybe not usable. Let be a binary variable for the usability of link under a GCTS , then we have .

Let be the sending rate from source to the destination , and let be the traffic on link destined to . We have the following LP optimization formulation to characterize the aggregate throughput bound:

Similar to the single destination case, constraints (12), (13), (14), and (15) specify legitimate per-destination traffic flow on all links, relay nodes, source nodes, and destinations. Constraint (16) preserves that one CTS can be activated to transmit at any time; for each destination, the traffic assigned on each link is no more than total amount of traffic that could be delivered on that link during all active phases of CTSs.

## 4. Performance Evaluation

In this section, we apply models developed in the previous section to study the throughput bound and capacity of hybrid wireless networks with OR in three different cases: Single Source to Single Destination, Multiple Sources to Single Destination, and Multiple Sources to Multiple Destinations.

### 4.1. Methodology

We set up the case studies with different network sizes and different characteristics of the network in order to get the most accurate conclusions about the hybrid wireless network capacity. Based on the transmission range of transmitters, we developed a C++ program to calculate CTSs. Given node locations, the program calculates CTSs for both single-channel and multiple-channel models. The proposed LP method could be used for any type of packet loss model. For demonstration, we use a simple packet loss model on link : , where is the distance between and , and is the maximum transmission range. The node transmission rate is fixed at 10 packets/timeslot. We then calculate the effective forwarding rate on each link for each CTS. Then we use AMPL-CPLEX to solve the LP Problem to find the maximum throughput in each case. For each case study, we conduct multiple simulation runs and report the average of all runs.

To understand the gain of OR in hybrid wireless networks, we also compare the performance of OR with that of hybrid unicast routing in the same network setting. To calculate the throughput bound of UR, we first build up the link conflict graph out of the original graph. In the conflict graph, each vertex corresponds to a link in the original graph. There is a link between two vertexes in the conflict graph if two corresponding links in the original graph interfere with each other. By finding all maximal independent sets of vertexes in the conflict graph, we can find the maximal sets of links in the original graph that can be activated at the same time. Assume that there are maximal independent sets . At any time, one set can be scheduled to transmit and all links in the scheduled set can transmit simultaneously. Let be the time fraction that is scheduled. The forwarding rate on link is

Then, we can reuse the LP formulation from (4) to (9) and from (11) to (16) to calculate the capacity of hybrid wireless networks under either OR or UR routing method.

### 4.2. Single Source to Single Destination

When wireless nodes use UR to forward data, throughput gets through a single path from the source node to the destination node. The throughput bound on each case is Case 1: 0.3 packets/TS; Case 2: 0.3 packets/TS; Case 3: 0.47 packets/TS; Case 4: 1.06 packets/TS; Case 5: 4.09 packets/TS; Case 6: 5.14 packets/TS. Throughput bound of the network with OR will be higher than that with UR when the optimal solution uses more than one path to forward data toward the destination node. Therefore in cases 2, 3, 4, and 5, throughput gain with OR is higher than that with UR. But both routing methods get the same throughput bound for the cases 1 and 6. From the above results, we can see that infrastructure network could significantly increase the end-to-end throughput of ad-hoc network with OR. The numbers and locations of BTs are important and could significantly impact the end-to-end throughput. OR will outperform UR for the cases of using multipaths to get to the destination.

### 4.3. Multiple Sources to Single Destination

For the case of multiple sources and single destination, we studied two different settings. The first setting is to calculate the throughput bound with random demands, random nodes, and BTs positions. The second setting is to study the impact of BT distribution patterns on the throughput bound of the network. For each setting, we make comparisons between two different node models and between OR and UR.

There are 35 nodes randomly located in an area of We randomly select 10 nodes as source nodes and one node as destination node. The radio range of nodes is 150 m. Source nodes and relay nodes send data with rate 10 packets/TS. We start with pure ad-hoc network and then add BTs randomly to the network. For the multiple-channel model, we assume that BTs have 4 wireless channels to communicate with wireless nodes.

### 4.4. Multiple Sources to Multiple Destinations

## 5. Conclusion

In this paper, we studied the throughput gain of OR routing schemes in hybrid wireless networks. We first extended OR to exploit the high-throughput routes over infrastructure network. We then developed linear programming models to characterize the capacity of hybrid wireless networks with OR. Our models calculate the end-to-end throughput bounds from multiple source nodes to single as well as multiple destination nodes. Through case studies on example hybrid wireless networks, we demonstrated the throughput gain of OR in hybrid wireless networking environment. The impacts of several factors on OR performance, such as the radio range of nodes, the density, and distribution pattern of BTs, were evaluated in the case studies. We also demonstrated that OR got higher throughput gain than UR in both ad-hoc and hybrid wireless networks, and single-channel and multiple-channel models. The current solving assumes simplified packet loss model. As a work for future direction, we will study the capacity of hybrid wireless networks with more realistic packet loss models. We used maximal CTS to calculate the throughput bounds. However it is time consuming to identify maximal CTS for large networks. We will study more efficient ways to model the conflicts between hybrid wireless links and characterize network capacity. We also plan to verify our capacity results using packet level simulations.

## Authors’ Affiliations

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