# A new cross-layer scheme that combines grey relational analysis with multiple attributes and knapsack algorithms for WiMAX uplink bandwidth allocation

- Ruey-Rong Su
^{1, 2}Email author, - I-Shyan Hwang
^{1}and - Bor-Jiunn Hwang
^{3}

**2016**:170

https://doi.org/10.1186/s13638-016-0665-6

© Su et al. 2016

**Received: **21 June 2014

**Accepted: **27 June 2016

**Published: **15 July 2016

## Abstract

To compensate for the adverse effects caused by radio link in worldwide interoperability for Microwave Access (WiMAX) networks, many radio resource management approaches have been present to assign orthogonal frequency division multiplexing access slots for seeking better performance. However, no WiMAX standards for optimal slot allocation have been defined. In this study, a new uplink bandwidth allocation scheme, GRAMA, which combines grey relational analysis with multiple attributes and the knapsack algorithms, is proposed to improve resource utilization while satisfying the user’s requirements of throughput and fairness. Channel aware technology and service flow priority are used in the proposed scheme to achieve the highest performance index. A series of simulation is conducted under the scenarios of constant-bit-rate (CBR) voice traffic, variable-bit-rate (VBR) video traffic, and VBR data traffic. The performance is evaluated in terms of bandwidth utilization, transmission throughput, and fairness and simulation result which indicate that the proposed GRAMKA outperforms the conventional fuzzy and knapsack algorithms.

## Keywords

## 1 Introduction

The mobile worldwide interoperability for Microwave Access (WiMAX) system is defined as a broadband wireless metropolitan area network (WMAN) in the IEEE 802.16e standard [1]. It aims to provide broadband wireless services anytime and anywhere by connecting mobile devices to base stations (BSs). In 2009, the WiMAX system was launched in Taiwan. WiMAX users in Taiwan numbered approximately 135,500 at the end of March 2013. Both orthogonal frequency division multiplexing (OFDM) and orthogonal frequency division multiplexing access (OFDMA) modulation technologies are used in the WiMAX system. In an OFDM system, a frame is composed of sub-channels with several sub-carriers. Each sub-channel consists of symbols in the time domain [2] and sub-carriers in the frequency domain. The two types of data channel are the uplink channel (UL) in which data are sent from mobile station (MS) to the BS and the downlink channel (DL) in which data are sent from the BS to MS. These channels operate in a bandwidth that is distributed over 1.25–20 MHz, based on the available frequency resources and service demands. The WiMAX physical layer selects appropriate frames that are adapted to the time division duplex (TDD) mode for uplink and downlink directions to meet the user’s demands. The OFDMA in mobile WiMAX systems is used to alleviate the adverse effect of multipath fading in non-line-of-sight (NLOS) environments. The OFDMA multiplexes multiple data streams onto DL and UL sub-channels [3]. In an OFDMA system, a data stream is divided into several parallel sub-streams with a reduced data rate (increasing the symbol duration), and each sub-stream is modulated and transmitted on a separate orthogonal sub-carrier. Five service types that are considered in mobile WiMAX systems are unsolicited grant service (UGS), real-time polling service (rtPS), extended rtPS (ertPS), non-real-time polling service (nrtPS), and best effort service (BES) [3]. In this work, to allocate the resources for data bursts [4], three services, voice service at a constant bit rate (CBR), video service at a variable bit rate (VBR), and the VBR data service, are considered. IEEE 802.16 defines burst profiles based on the combination of the modulation and coding schemes in each connection of physical configuration to adapt the data rate for the user. To compensate for the adverse effects of radio link fading, interference, and noise effects [4], many radio resource management (RRM) techniques have been developed, improving the efficiency and reliability of wireless transmission [5]. Channel aware technology enables a BS to choose the modulation and coding scheme based on the carrier-to-interference noise ratio (CINR) by link adaptation. In IEEE 802.16e, the CINR of every mobile station changes dynamically. Many RRM algorithms have been presented to assign OFDMA slots according to the channel conditions for meeting user’s demand [6]. However, no WiMAX standard for optimal slot allocation has been defined.

Gupta and Chandavarkar [7] proposed a bandwidth management algorithm for WiMAX networks that provided reasonable performance, but it did not take the advantage of channel aware features [6]. A bandwidth request analysis mechanism [8] that focuses on rtPS and nrtPS traffic has been presented, but voice traffic (unsolicited granted service) was not considered. A radio resource allocation algorithm for uplink bandwidth allocation and recovery has been developed [9] to provide proportional and fair bandwidth utilization. The problems of the aforementioned methods are that the bandwidth is not allocated efficiently and the user’s requirements are not well considered. A grant allocation algorithm, called half-duplex allocation (HDA), which was developed by Bacioccola et al. [10] aims to ensure a consistent and feasible grant allocation. However, the HDA algorithm does not efficiently allocate bandwidth because it exhibits poor throughput. An adaptive bandwidth allocation scheme (ABAS) is proposed by Chiang et al. [11] to vary the allocated bandwidth ratio according to the current traffic profiles. However, it does not consider service flow priority, resulting in poor throughput performance.

Grey relational analysis (GRA) [12] is an accurate predictor which needs smaller samples than required by conventional schemes, such as fuzzy and knapsack. The computational burden is thus significantly lower. Unlike the fuzzy [13] and knapsack algorithms [14], the GRA yields consistent results in both quantitative and qualitative analysis. In this paper, a new uplink bandwidth allocation scheme, grey relational analysis with multiple attributes and knapsack algorithms (GRAMAKA), which combines GRA with multiple attributes [13] and the knapsack algorithm [14], is proposed to improve resource utilization while satisfying the user’s requirements of throughput and fairness. The performance is evaluated in terms of bandwidth utilization, transmission throughput, and fairness. Channel aware technology [6] and service flow priority are applied in the proposed scheme to achieve the highest performance index. The rest of this paper is organized as follows. Section 2 elucidates the proposed GRAMAKA scheme. Section 3 presents the simulation results, and finally, Section 4 draws conclusions.

## 2 Proposed GRAMAKA scheme

Firstly, this section elucidates the structure of the system for simulation. Then, the fuzzy theory, the knapsack algorithm (KA), GRA, and the proposed GRAMAKA are described.

### 2.1 System structure

System parameters

Parameter | Value |
---|---|

Channel bandwidth | 10 MHz |

Peak uplink data rate | 28 Mbps per sector in a 10 MHz channel |

Frame duration | 5 ms |

Maximum number of users | 600 |

### 2.2 Fuzzy theory

Fuzzy logic [13] is a form of many-valued logic, which supports reasoning that is approximate rather than fixed or exact. Whereas traditional binary sets (in which variables may have true or false values), fuzzy logic variables may have a truth value that ranges in degree between 0 and 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value ranges between completely true and completely false. The values of these linguistic variables can be managed using specific functions, such as Trimf, Sigmf, and Gaussmf [16].

### 2.3 Knapsack algorithm

*w*

_{ i }and a value

*v*

_{ i }determines the number of each item to be included in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. All values and weights are usually assumed to be non-negative. The most common formulation is the 0–1 knapsack problem, which restricts the number

*x*

_{ i }of each item to zero or one. Mathematically, the 0–1 knapsack problem [14] is formulated as,

### 2.4 GRA

GRA [12] can be applied to the WiMAX resource allocation with the following definitions.

###
**Definition 1:**

*P*{

*x*},

*Q*}, with combination of the influence factors. Weight

*P*{

*x*} represents the number of OFDMA symbol, and value

*Q*denotes the number of sub-channel. The slots of UL-MAP are denoted as the original sequence \( {\mathrm{x}}_{\mathrm{i}}^{(0)}\left(\mathrm{k}\right) \) for user

*i*, where

*i*= 1, 2,..,

*N*;

*N*is the maximum number of users.

*k*= 1, 2, …,

*K*. \( {\mathbf{x}}_{\mathbf{i}}^{\left(\mathbf{0}\right)}\left(\mathbf{k}\right) \) is used as a benchmark of sequence selection if the original sequence satisfies normalization, scaling, and polarization conditions.

###
**Definition 2:**

*k*= 1, 2,..

*K*, and \( {\mathbf{x}}_{\mathbf{i}}^{\mathbf{k}}\left(\mathbf{k}\right) \) is the normalized value of sequence of GRA, where 1 ≤

*i*≤

*N*, with index

*k*= 1, 2,..

*K*.

###
**Definition 3:**

*i*≤

*N*, with index

*k*= 1, 2,..,

*K*, and \( {\mathbf{x}}_{\mathbf{i}}^{*}\left(\mathbf{k}\right) \) is the normalized value sequence of GRA.

###
**Definition 4:**

*i*th combination of influence factors is denoted as

*i*≤

*N*,

*j*= 1, 2, …

*J*,

*k*= 1, 2, …

*K*, and ζ is a distinguishing coefficient.

*x*

_{ i }(

*k*) is another set to be compared, where

- Step 1:
GRA initializes the grey relational space {

*P*{*x*},*Q*} - Step 2:GRA modeling yields the local maximum and local minimum of the grey relational measure as,and$$ {\mathbf{x}}_{\mathbf{i}}^{*}\left(\mathbf{k}\right)=\left[\left({x}_i^{(0)}(k)- \min {x}_i^{(0)}(k)\right)/\left( \max {x}_i^{(0)}(k)- \min {x}_i^{(0)}(k)\right)\right] $$(8)$$ {\mathbf{x}}_{\mathbf{i}}^{*}\left(\mathbf{k}\right)=\left[ \max \left({x}_i^{(0)}(k)-{x}_i^{(0)}(k)\right)/\left( \max {x}_i^{(0)}(k)- \min {x}_i^{(0)}(k)\right)\right] $$(9)
- Step 3:GRA coefficients are generated to obtained the grey relational coefficients of the
*i*th combination of influence factors as$$ \gamma \left({x}_0(k),{x}_i(k)\right)=\left[\left({\varDelta}_{\min }+\varsigma \cdot {\varDelta}_{\max}\right)/\left({\varDelta}_{0j}(k)+\varsigma \cdot {\varDelta}_{\max}\right)\right] $$(10) - Step 4:
Grey decision-making yields the priority of the selected sequence: a sequence with larger grey relational coefficients (GRC) has higher priority.

### 2.5 Proposed GRAMAKA

*i*th combination of influence factors is determined using Eq. (10) in step 3 of Section 2.4, as follows:

*x*

_{0}(

*k*) is the reference sequence,

*x*

_{ i }(

*k*) is the sequence to be compared with,

*Δ*

_{0j }is the absolute value of the difference between

*x*

_{0}(

*k*) and

*x*

_{ i }(

*k*), and

*ς*∈ [0, 1] is the distinguishing coefficient. Finally, the grey decision-making process in step 4 in Section 2.4 yields the priority of the selected sequence. A sequence with a larger GRC has a higher priority being chosen as the best slots solution for allocating the resources of UL-MAP. Figure 2 presents the WiMAX OFDMA frame structure for UP-MAP.

### 2.6 GRAMAKA scheduling algorithm

- (1)
If a user call is made, then record the type of call.

- (2)
Increase the number of the user call type.

- (3)
Process and record the user calls using the channel aware technology.

- (4)
Execute the GRAMAKA, fuzzy, and knapsack algorithms, respectively, for all user calls.

- (5)
Allocate the slots with the largest weights.

- (6)
Count the total number of slots for the user calls.

- (7)
If the total number of slots reaches the full size of the UL-MAP, then go to step (8); otherwise, go to step (1).

- (8)
Evaluate the simulation results and terminate the scheduling process.

## 3 Simulation results

Parameters of traffic types

Traffic type | Data rate (kbps) | Mean duration (sec) | Arrival rate (call/s) | Traffic rate |
---|---|---|---|---|

Voice services | 64 | 210 | 0.1–10 | CBR |

Video services | 550–15550 | 360 | 0.1–10 | VBR |

Data services | 280–7670 | 180 | 0.1–10 | VBR |

Jane’s equation rates the fairness of a set of values where the number of users is *N* and *x*
_{
i
} is the throughput of the *i*th connection.

Throughput improvements obtained using fuzzy and GRAMAKA schemes over throughput obtained using knapsack algorithm, which serves as base line for voice traffic (CBR)

Users number | Fuzzy (%) | GRAMAKA (%) |
---|---|---|

100 | 1.1 | 2.9 |

200 | 1.4 | 3.9 |

300 | 4.8 | 13 |

400 | 6.6 | 17.9 |

500 | 6.6 | 23.9 |

600 | 11.2 | 29.9 |

Throughput improvements obtained using fuzzy and GRAMAKA schemes over throughput obtained using knapsack algorithm which provides base line for video traffic (VBR)

Users number | Fuzzy (%) | GRAMAKA (%) |
---|---|---|

100 | 15.1 | 50.1 |

200 | 15.6 | 56.9 |

300 | 18.9 | 70.6 |

400 | 18.9 | 72.9 |

500 | 19.6 | 76.1 |

600 | 29.1 | 79.2 |

Throughput improvements obtained using fuzzy approach and GRAMAKA over throughput obtained using knapsack algorithm which provides base line for data traffic (VBR)

Users number | Fuzzy (%) | GRAMAKA (%) |
---|---|---|

100 | 0.61 | 1.63 |

200 | 0.61 | 1.63 |

300 | 1.31 | 3.75 |

400 | 1.59 | 5.04 |

500 | 1.66 | 5.16 |

600 | 1.89 | 6.04 |

## 4 Conclusions

A new scheme, GRAMAKA, which combines GRA with multiple attributes and the knapsack algorithms, has been proposed to improve resource utilization of the WiMAX networks. A series of simulations has been conducted using knapsack, fuzzy, and the proposed GRAMAKA algorithms under scenarios of constant-bit-rate (CBR) voice traffic, variable-bit-rate (VBR) video traffic, and variable-bit-rate (VBR) data traffic, where the throughputs obtained using knapsack algorithm serve as benchmark for performance comparison. Simulation results demonstrate that the proposed GRAMAKA performed best under all scenarios. GRAMAKA provides improvements of 2.9–29.9, 50.1–79.2, and 1.63–6.04 %, respectively, which are better than that, 1.1–11.2, 15.1–29.1, and 0.61–1.89 %, achieved using the fuzzy algorithm, in the cases of voice traffic (CBR), video traffic (VBR), and data traffic (VBR), respectively. Furthermore, simulation results indicate that the proposed GRAMAKA performs best in terms of performance index which consists of throughput and fairness index. The reason why GRAMAKA outperforms other two algorithms is because it offers greater flexibility in the insertion of the slots into the UL-MAP than do the other two approaches.

In the near future, the performance of heterogeneous network which consists of both WiMAX and Long-Term Evolution (LTE) will be investigated by using modified GRAMAKA and other optimization algorithms, where packet delay will be analyzed.

## Declarations

### Acknowledgements

The authors would like to thank the anonymous reviewers and the editor for their valuable comments. Also, the authors are sincerely grateful to Prof. Tan-Hsu Tan, in the Department of Electrical Engineering, National Taipei University of Technology, Taipei, Taiwan, for his valuable suggestions in refining this article.

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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