# Flow Oriented Channel Assignment for Multi-radio Wireless Mesh Networks

- Fei Ye
^{1}Email author, - Sumit Roy
^{1}and - Zhisheng Niu
^{2}

**2010**:930414

https://doi.org/10.1155/2010/930414

© Fei Ye et al. 2010

**Received: **1 November 2009

**Accepted: **21 February 2010

**Published: **13 April 2010

## Abstract

We investigate channel assignment for a multichannel wireless mesh network backbone, where each router is equipped with multiple interfaces. Of particular interest is the development of channel assignment heuristics for multiple flows. We present an optimization formulation and then propose two iterative flow oriented heuristics for the conflict-free and interference-aware cases, respectively. To maximize the aggregate useful end-to-end flow rates, both algorithms identify and resolve congestion at instantaneous bottleneck link in each iteration. Then the link rate is optimally allocated among contending flows that share this link by solving a linear programming (LP) problem. A thorough performance evaluation is undertaken as a function of the number of channels and interfaces/node and the number of contending flows. The performance of our algorithm is shown to be significantly superior to best known algorithm in its class in multichannel limited radio scenarios.

## Keywords

## 1. Introduction

The success of such WMNs largely hinges on their potential for scaling backbone throughput with increasing client density while preserving network coverage. As has already been noted in [3–5], a crucial element in throughput scaling is more effective utilization of available multiple (nonoverlapping) channels. We propose to achieve this by having multiple interfaces per node at incremental hardware cost; for example, note the availability of integrated 802.11 a/b/g transceivers on the same network interface card (NIC). In the future, such integration of multiple transceivers (such as different generations of a successful technology such as 802.11) on a single device will be commonplace, and our work is thus well aligned with this trend.

Channel assignment (CA) is a resource management challenge in such a multiradio multichannel paradigm, whereby a particular channel is now assigned to a specific *link and network interface pair*. This is a largely underexplored domain with the potential of boosting network throughput as it can mitigate both intra- and interflow interference. Optimal channel assignment would simultaneously involve the choices of routing metric, rate control, power control, and medium access control (MAC). Such an integrated global approach is ambitious and results in very complex systems optimization; typically, only a partial subset of all available resources are used to obtain insight, and our work is no exception.

Various channel assignment algorithms [6–16] which are studied in literature can be classified into *packet level, link level* and *flow level* based on their granularity. *Packet level* algorithms are highly dynamic, where channels are assigned for every packet [6] or every few packets [7]. Channel switching overhead [17] is the major drawback of these algorithms. In *flow level* algorithms, channels are assigned to several successive links which compose a flow or a set of intersecting flows. In [18], channels are assigned to flows along with the route establishment in a single-radio multichannel network. In [19], links from intersecting flows are assigned the same channels. Flow level algorithms are free of channel switching and are aware of traffic flows however, at the cost of spatial reuse, especially in a dense network. *Link level* algorithms belong to the most popular category, in which channels are assigned at the granularity of a link. Some optimize link-based metrics, for example, minimizing accumulated interference among links [8, 9] and maximizing weighted sum of simultaneously active links [10]. In networks with stable topology and traffic flows, *end-to-end* metrics have been shown to be a better suit [13–16]. The performance metric in [13] is the cross-section goodput which is defined as the sum of all useful bandwidth between traffic aggregation nodes and gateway nodes. In [14], the minimum throughput that can be routed from a node to the Internet is maximized. End-to-end throughput optimizations are studied in [15], however, without concrete protocol design. In [16], the authors assume that all links reside in a single collision domain and formulate channel assignment as a game, where players (links) compete for the same pool of channels. Links from a multihop flow form a coalition, and their payoff is the end-to-end flow rate.

- (i)
A generalized optimization model for flow oriented channel assignment in a multiradio multichannel mesh backbone,

- (ii)
A flow oriented graph coloring (FOGC) algorithm that maximizes the aggregate useful flow rates for conflict-free channel assignment problem,

- (iii)
A centralized flow oriented channel assignment (FOCA) heuristic for interference-aware cases. It maximizes the aggregate useful flow rates by utilizing cross-layer routing and network topology information.

The remaining of this paper is organized as follows. System model and problem formulation are presented in Section 2. We first introduce and evaluate FOGC algorithm for conflict-free cases in Sections 3 and 4. Then this algorithm is extended to FOCA algorithm in Section 5. Simulation of FOCA is presented in Section 6, followed by concluding remarks in Section 7.

## 2. System Model and Problem Formulation

We model a wireless mesh backbone consisting of wireless routers (nodes), active links, and multihop flows. The connection between mobile clients and wireless access points is out of the scope of this paper. The sets of wireless routers, links, channels, and flows are indexed as , , and , respectively. Notations , , are used for the th link, the th flow, and the th channel, respectively. For convenience, all notations are summarized in Table 1 with additional explanations as follows.

- (i)
- (ii)
- (iii)
- (iv)
*Interference Matrix.*, for all , representing the binary symmetric conflicts among links. Entries in are determined using a binary two-hop interference model that is widely used in graph modeling of wireless networks [10, 14, 20] (whereby links within two hops of each other deemed to be mutually interfering). - (v)
*Clique Matrix.*for all . A clique is a maximum subset of links such that all distinct pairs in this subset would potentially conflict with each other [21]. Assume the total number of cliques is ; each row of , thus represents one of these cliques. Clearly, depends on network topology, and links within one clique must time share a channel if they are assigned the same one: - (vi)
*Channel Reward.*for all . Reward is the maximum supportable data rate of link when it exclusively uses channel . - (vii)
*Achievable Link Rate Vector.*. A rate (for all ) is the achievable data rate of under a given channel assignment decision:where diag( ) returns a column vector formed from all the diagonal elements.

- (viii)
- (ix)
*Link Rate Allocation Matrix.*. A flow is allowed to use up to of a link 's rate. If does not traverse ( ), is set to 0. Equation (4) is then expressed in a component-wise way:Both and are hidden variables in the formulation (7) that we will present soon; however, they will act as important roles in both heuristic algorithms.

- (x)
*Network Interface Constraint.*The total number of channels assigned to links incident to a node cannot exceed the node's NIC number. Channels are assigned to links while NIC constraint resides on nodes. We introduce a network topology-dependent matrix to solve such contradiction. The entry denotes that node is one end of link . By mapping the channel assignment results to each wireless router, the NIC constraint is given by:where the cardinality function Card( ) counts the number of nonzero entries in each column; hence Card( ) is the number of NICs needed at wireless routers.

- (xi)
*Flow Oriented Metric.*is a continuously differentiable, increasing, and concave utility function of end-to-end flow rates, that is, the aggregated flow rate .

Notations in system model and problem formulation.

Notations | Description |
---|---|

The set of the wireless routers. | |

The set of the wireless links. | |

The set of the wireless channels. | |

The set of the multihop flows. | |

The channel assignment matrix. | |

The routing matrix. | |

The interference matrix. | |

The clique matrix. | |

The channel reward matrix. | |

The topology matrix. | |

The vector that stores the number of network interface cards on each node. | |

The achievable data rate vector. | |

The supportable flow rate vector. | |

The link rate allocation matrix. | |

The vector that stores bottleneck links. |

The optimization variables are channel assignment decisions and supportable flow rates . The routing matrices is the required cross-layer routing information, while matrix and are computed from the topology information. Channel reward is considered to be a known parameter. If there always exist sufficient NICs per mesh router, the only cardinality (nonconvex) constraint is eliminated, making (7) a convex problem.

## 3. Flow Oriented Graph Coloring Algorithm (FOGC)

*conflict-free*channel assignment is required. Then assigning each channel becomes a binary decision:

When there is no NIC limitation and is linear, (10) is further reduced to an integer linear programming (ILP) problem by removing the last constraint. Optimal solution for ILP problems can be obtained numerically.

Several past work have demonstrated the effectiveness of greedy graph coloring algorithms in solving conflict-free resource assignment problems. A greedy solution, *Progressive Minimum Neighbor First* (PMNF), is proposed in [22] for the unified time/frequency/code domain channel assignment problem. The PMNF is extended to *Color-Sensitive Graph Coloring* (CSGC) in [20] to solve the channel assignment problem in a multichannel scenario. In the color-sensitive contention graph, vertices are connected via multiple colored edges that represent multiple channels, and colors may have different rewards on different vertices.

Following this color-sensitive graph coloring approach, we present a flow oriented graph coloring (FOGC) algorithm that heuristically solves (10) with the objective function , where is the requested end-to-end rate of flow . FOGC is an iterative algorithm that resolves instantaneous congestion. In each iteration, FOGC first identifies bottleneck links and assigns a new channel to the most critical one. This heuristic process is carefully designed so that the conflict constraint (the 4th constraint) and the NIC constraint (the 5th constraint) in (10) are satisfied. Therefore, the remaining process prior to next iteration is an LP problem that optimally allocat the rate of each link to contending flows that share the link. This iterative algorithm is of low complexity, based on local optimality for each additional assignment.

We use a symbol—vector
—to store the instantaneous bottleneck links^{1} of all
flows. If the end-to-end traffic demand of a flow has already been satisfied, there is no bottleneck for that flow. The superscript on all notations denote the current iteration, that is,
is
's value in the
th iteration.

Step 1 (identify bottleneck Links).

where
is the requested rate of
. The set of bottleneck links,
, are labeled and sorted in descending order according to their *unsatisfied* traffic demand. An all-zero vector indicates the end of the algorithm, otherwise the link with the largest label is selected. Future steps may set a label value to zero if the rate of that particular link can not be improved by assigning a new channel.

Step 2 (channel assignment strategy (update
*to*
)).

Assume that link connecting nodes and is the critical bottleneck selected in Step 1. The channel assignment decision varies according to the number of available NICs on and .

- (1)
If and both have free NICs and at least one available channel in common, assign the most beneficial

^{2}available channel in common to link . Eliminate from the available channel list of all 's and 's conflicting neighbors. - (2)
Otherwise, redirect to Step 1, set the label value of to zero, and reselect a link with the largest label.

Step 3 (link rate allocation (solve )).

Thus far, we have a new link rate allocation matrix . Returning to Step 1, we can determine a new set of bottleneck links for next iteration. This algorithm terminates when an all-zero label vector appears in Step 1.

Since the 4th and 5th constraints in (10) are satisfied in the heuristical process in FOGC, the optimal result from (13) is not necessarily an optimal solution for (10). The following proposition shows that FOGC achieves optimality in a simple single flow case.

Proposition 1.

In the single flow case, FOGC is the optimal channel assignment when channels have identical reward.

Proof.

Assume that is an optimal channel assignment that assigns a channel to link at its th operation. It is easy to verify that exchange the sequence of terms in does not affect its optimality. Let be the assignment from FOGC algorithm which has exactly the same first assignments as . Here we will show that either agrees with the optimal assignment on its first assignments or has already achieved optimality on the th assignment. If and , swap and in . Then has the same first assignments as . If and , then the flow rate will never increase after the th assignment in , because is an instantaneous bottleneck which is never treated again in . Then achieves optimality at its th operation.

In the simplest case, FOGC's locally optimal strategy leads to global optimality. In general, FOGC's performance in more complicated scenarios is evaluated through simulation in the following section.

## 4. Simulation Results of FOGC

*Link-Based Graph Coloring*(LBGC) algorithm which seeks to maximize the overall link rates without routing knowledge. The upper bound is the optimal channel assignment

^{3}(OPT) obtained by exhaustive search. In LBGC, the flows traversing a common link share this link's rate fairly.

## 5. Flow Oriented Channel Assignment Algorithm (FOCA)

Due to the broadcast nature of wireless communication, the conflict-free assumption is rarely true in practice and should be viewed as a model approximation. The a forementioned graph coloring algorithm FOGC is extended to a general flow oriented channel assignment (FOCA) algorithm to heuristically solve (7). Conflicting links are allowed to time-share the same channel, and in each iteration, apart from assigning a new channel, channel switching mechanism and channel switching propagation are designed to adjust existing assignment decisions.

FOCA has a similar iteration process as FOGC. It first identifies the bottleneck links, then assigns a new channel, or adjusts existing channel assignment to resolve congestion, and prior to entering the next iteration, optimal allocation of link rate to contending flows that share this link is computed by solving an LP problem.

Step 0.

Same as FOGC.

Step 1.

Same as FOGC.

Step 2 (channel assignment strategy (update
*to*
)).

Assume that link connecting nodes and is the critical bottleneck selected by Step 1. The channel assignment decision varies according to the number of available NICs on and .

- (1)
At least one free NIC on both and : assign a locally least occupied channel to a free NIC on and , respectively.

- (2)
No free NIC on at least one free NIC on (or vice versa): choose locally least occupied channel from 's channel usage list and have one free NIC of tuned to that channel to communicate with .

- (3)Neither nor has any free NIC:
- (a)
and have at least one common channel

^{4}: communicate on a least occupied common channel utilizing the NICs already tuned to that channel. - (b)
and have no common channel, and the connectivity between and has already been satisfied: return to Step 1 to set the label of link to zero.

- (c)
and have no common channel in use, and the connectivity between and is not satisfied:

*channel switching*and*channel switching propagation*are needed. A least occupied channel is selected from 's and 's channel usage list, respectively. Assume they are and , and carries a lower traffic load. As Figure 6 shows, 's NIC that originally works on is switched to to communicate with . To preserve 's connection with its own neighbors on , this switching is propagated to those neighbors, and then to neighbors of those neighbors, and so on.

- (a)

Step 3.

Same LP optimization as in FOGC.

## 6. Simulation Results of FOCA

^{5}. First, we generate random topologies, multiple source-destination pairs, and one least hop-count path for each pair. This routing information is stored to assist future channel assignments. Then channel assignment algorithm is performed in a centralized manner before data transmission. All results are averaged over multiple runs on multiple random topologies. The FOCA is compared to a unified one-to-one channel assignment, which assigns the th channel to the th NIC. The unified algorithm is of zero complexity and performs well when the number of NICs matches with the number of channels. It generates a much better baseline than any random assignment, which is unfortunately always used as an inaccurate benchmark. Another contrast is an empirical traffic load-aware channel assignment (LACA). In [13], LACA, a routing algorithm, as well as the control loop between them are designed. Assumeing a precalculated routing and fixed injected traffic load, the LACA assigns channel resources to links in the decreasing order of the expected link load. The original evaluation metric "cross-section bandwidth" is similar to the end-to-end flow rate in this paper.

*multichannel limited-radio*scenario performance is the key criteria in evaluating channel assignment algorithms. We first simulate three 5-hop flows in random networks, where each node has only 2 NICs, and vary the number of channels. Similar to the conclusion from Figure 5, in Figure 8, FOCA's throughput saturates at approximately 9 channels and outperforms LACA approximated 50% in the saturated case. Once saturation is reached, increasing the number of channels causes only jitter but not significant increment in flow rate, because now the limitation is insufficient NICs on some bottleneck links. A good channel assignment algorithm will efficiently utilize as many channels as possible with very few NICs by diversifying traffic over as many channels as possible to avoid intra- and inter flow interference. Hence, the saturation point (in terms of the number of channels) and the saturation flow rate in the multichannel limited-radio scenario are of particular interest to system designers.

## 7. Conclusion

The fast deployment of WMNs places stringent requirements on end-to-end rates of the underlying multihop mesh backbone, especially in large scale and dense scenarios. This paper studies the channel assignment problem for a multichannel multiradio mesh backbone. We first presented a general optimization formulation, which is nonconvex due to practical constraints. Then a flow oriented graph coloring (FOGC) greedy algorithm was designed for the conflict-free case, and it was extended to a flow oriented channel assignment (FOCA) heuristic for the general case where interference is considered. Both algorithms identify instantaneous bottlenecks at each additional assignment iteration using routing and network topology information and try to resolve congestion by (i) assigning a new channel, (ii) channel switching (FOCA only), and (iii) optimally allocating link rate to contending flows by solving an LP problem. Simulation not only demonstrated the effectiveness of addressing bottlenecks at each additional iteration but also showed that both FOCA and FOGC can efficiently exploit multiple channels with very limited number of NICs.

Although both heuristics are for a static network, their low complexity as well as the relatively high stability of traffic flows in mesh backbone allow the channel assignment decision to be adapted periodically or once the accumulated changes exceed a certain threshold. While the proposed algorithms pursue local optimality at each additional assignment, this does not lead to global optimality. An option is to extend this heuristic (at cost of additional complexity) by looking several steps ahead, that is, considering more than one critical bottleneck link at each iteration. This framework can be applied towards other utility functions as well.

## Authors’ Affiliations

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### Endnotes

## Copyright

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