# Adaptive Allocation Algorithm for Multi-Radio Multi-Channel Wireless Mesh Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Mathematical Formulation of Adaptive Channel Allocation Problem

#### 3.1. Assumptions

#### 3.2. Notations

#### 3.3. Network Mathematical Model

- The total number of NICs over the network should not exceed $M={\displaystyle \sum _{i}^{N}}{m}_{i}$.
- The output number of assigned NICs for $A{P}_{i}$ should be at least one. Suppose it will be ${n}_{i}$; therefore, $1<{n}_{i}<{m}_{i}$ where $i\in \{1,2,\cdots ,N\}$.
- Each link ${l}_{ij}$ should be assigned to a channel $c{h}_{ij}$, where $c{h}_{ij}\in \{{c}_{1},{c}_{2},\cdots ,{c}_{k}\}$.
- The maximum number of assigned channels is k.
- The chosen channel for the link ${l}_{i}j$ at both APs’ NIC must be the same $c{h}_{ij}=c{h}_{ji}$.
- The number of channels assigned to the links adjacent to $A{P}_{i}$ must be ${n}_{i}$ or less.

#### 3.4. The Outputs

- The number of NICs assigned to $A{P}_{i}$, ${n}_{i}$.
- The channel between the two APs $A{P}_{i}$ and $A{P}_{j}$, $c{h}_{ij}$.

#### 3.5. The Problem Formalization

## 4. Adaptive Channel Allocation Algorithm

#### 4.1. The Initial Channel Allocation

#### 4.1.1. NIC Deploying Stage

**NIC Initialization**- (i)
- Compute the load per AP from link traffic ${t}_{ij}$:$$\begin{array}{cc}\hfill {t}_{i}^{AP}& =\sum _{j\in {G}_{i}}({t}_{ij}+{t}_{ji}).\hfill \end{array}$$
- (ii)
- Allocate one NIC to every AP: ${n}_{i}=1$ as a default.
- (iii)
- Assign the traffic for each NIC by:$${t}_{i}^{NIC}=\frac{{t}_{i}^{AP}}{{n}_{i}}.$$
- (iv)
- Set the number the allocated NICs: AN = N.

**NIC Deployment**- (i)
- Add one NIC to an AP (suppose $A{P}_{s}$) where ${t}_{s}^{NIC}$ reaches the maximum load while maintaining ${m}_{s}<{n}_{s}$. After that, ${n}_{s}++$ and $AN++$.
- (ii)
- Stop the phase if $AN=M$ or the physical constraint (${n}_{s}={m}_{s}$) is reached for every AP.
- (iii)
- Recalculate the traffic:$${t}_{s}^{NIC}=\frac{{t}_{s}^{AP}}{{n}_{s}}.$$
- (iv)
- Return to step (i).

#### 4.1.2. The Fixed Channel Allocation

- Compute the collision for the traffic:$$co{l}_{ij}={t}_{ij}\xb7\sum _{p=1}^{N}\sum _{q=p+1}^{N}{t}_{pq}\xb7{f}_{ijpq}.$$
- Arrange the links according to the collision in a descending order.
- Allocate ${c}_{1}\in NOC$ to the most crowded link, let ${l}_{ij}$ be the first link, and assign ${c}_{1}$ to both $A{P}_{i}$’s first NIC and $A{P}_{j}$’s first NIC.
- Allocate the links’ channel according to the following filtration steps:
- (a)
- Mandatory channel allocation:
- (i)
- Allocate ${c}_{p}\in NOC$ to link ${l}_{ij}$ if both $A{P}_{i}$ and $A{P}_{j}$ have NICs allocated to ${c}_{p}$. If there are two or more such ${c}_{p}$ for both $A{P}_{i}$ and $A{P}_{j}$, select the channel that minimizes $Flink$ without consideration to un-allocated links.
- (ii)
- If $A{P}_{i}$ has only one NIC allocated with ${c}_{p}\in NOC$, and $A{P}_{j}$ has no channel, then the link ${l}_{ij}$ is allocated ${c}_{p}$ and one $A{P}_{j}$’s NIC allocates to the same channel.

- (b)
- Variety channel allocation:
- (i)
- For each link ${l}_{ij}$, $A{P}_{i}$ and $A{P}_{j}$ have both un-allocated NICs, then select ${c}_{p}\in NOC$ that minimizes $Flink$ without consideration to un-allocated links.
- (ii)
- if $A{P}_{i}$ and $A{P}_{j}$ have two or more NICs in allocated channels $NO{C}_{g}\subseteq NOC$, then the link ${l}_{i}j$ is allocated ${c}_{p}\in NO{C}_{g}$ to minimize $Flink$ without consideration to un-allocated links.

- (c)
- Priority channel allocation change: If $A{P}_{i}$ and $A{P}_{j}$ are allocated to ${c}_{p}$ and ${c}_{q}$ sequentially and ${c}_{p}\ne {c}_{q}$ and ${l}_{i}j$ is not an allocated channel, then the channel allocation priority for that link is increased. Return to step 2 after multiplying $co{l}_{ij}$ by a constant number greater than one.
- (d)
- Manage un-utilized NICs: After the completion of channel allocation for every link in the network, if there are unused NICs, these NICs are switched to other APs with the maintenance of the constraints, and then return to step 2.

#### 4.2. The Adaptive Channel Allocation

#### Decision Function

- Step (1)
- We begin by calculating the traffic of GW’s links, where these links are assigned the same channel p, $TG{W}_{p}$:$$TG{W}_{p}=\sum _{{l}_{gi}\in \phantom{\rule{3.33333pt}{0ex}}GWL,c{h}_{gi}=p}{t}_{gi},$$
- Step (2)
- We compute the decision factor:$$\underset{p,q}{max}|\frac{TG{W}_{p}}{TG{W}_{q}}-1|\ge \lambda ,$$

## 5. Simulation Module Implementation

#### 5.1. Modified NS-2 Simulator for IEEE802.11n

#### 5.2. Simulation Instances

#### 5.3. Network Topology 1 Simulation Results

#### 5.3.1. Case 1

#### 5.3.2. Case 2

#### 5.4. Network Topology 2 Simulation Results

#### 5.4.1. Case 1

#### 5.4.2. Case 2

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

FCA | Fixed Channel Allocation |

ACA | Adaptive Channel Allocation |

GW | Gateway |

NIC | Network Interface Card |

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**Figure 2.**Patterns of numbers of the associate hosts, supposing that the maximum number of associated hosts is n.

**Figure 4.**The network topology 1 results, the number of channel reassignments, and the overall throughput with the maximum two NICs, (

**a**) throughput comparisons and (

**b**) channel reassignment comparisons.

**Figure 5.**The network topology 1 results, the number of channel reassignments, and the overall throughput with the maximum three NICs, (

**a**) throughput comparisons and (

**b**) channel reassignment comparisons.

**Figure 6.**The network topology 2 results, the number of channel reassignments, and the overall throughput with the maximum two NICs, (

**a**) throughput comparisons and (

**b**) channel reassignment comparisons.

**Figure 7.**The network topology 2 results, the number of channel reassignments, and the overall throughput with the maximum three NICs, (

**a**) throughput comparisons and (

**b**) channel reassignment comparisons.

Symbol | Definition |
---|---|

${l}_{ij}$ | link between the access point (AP) $A{P}_{i}$ and $A{P}_{j}$ |

NOC | non-overlapped channels |

F | interference matrix between links |

${t}_{ij}$ | expected throughput between $A{P}_{i}$ and $A{P}_{j}$ |

C | the matrix of interfered channels |

${m}_{i}$ | the maximum number of network interface cards (NICs) that can be allowed to $A{P}_{i}$ |

${n}_{i}$ | the output assigned number of NICs to $A{P}_{i}$ |

$c{h}_{ij}$ | the assigned channel to ${l}_{ij}$ |

$FNIC$ | maximum number of hosts per one NIC |

$Flink$ | total interference of gateway (GW) adjacent links |

$FStop$ | number of channel re-allocations |

Contention window_Min | 15 |

Contention window_Max | 1023 |

Time Slot | 9 $\mathsf{\mu}$s |

Short Interframe Space | 16 $\mathsf{\mu}$s |

DCF Interframe Space | 34 $\mathsf{\mu}$s |

Preamble Length | 16 $\mathsf{\mu}$s |

Physical Layer Convergence Protocol Header | 48 bits |

Physical Layer Convergence Protocol Rate | 6 Mbps |

Basic Data Rate | 54 Mbps |

Data Rate | 300 Mbps |

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**MDPI and ACS Style**

Hassan, W.; Farag, T.
Adaptive Allocation Algorithm for Multi-Radio Multi-Channel Wireless Mesh Networks. *Future Internet* **2020**, *12*, 127.
https://doi.org/10.3390/fi12080127

**AMA Style**

Hassan W, Farag T.
Adaptive Allocation Algorithm for Multi-Radio Multi-Channel Wireless Mesh Networks. *Future Internet*. 2020; 12(8):127.
https://doi.org/10.3390/fi12080127

**Chicago/Turabian Style**

Hassan, Walaa, and Tamer Farag.
2020. "Adaptive Allocation Algorithm for Multi-Radio Multi-Channel Wireless Mesh Networks" *Future Internet* 12, no. 8: 127.
https://doi.org/10.3390/fi12080127