Hindawi Publishing Corporation Modelling and Simulation in Engineering Volume 2010, Article ID 804939, 7 pages doi:10.1155/2010/804939 Research Article On the Modelling of the Mobile WiMAX (IEEE 802.16e) Uplink Scheduler Darmawaty Mohd Ali 1, 2 and Kaharudin Dimyati 3 1 Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia 2 Faculty of Electrical Engineering, Mara University of Technology (UiTM) Shah Alam, 40450 Selangor, Malaysia 3 Electrical and Electronic Engineering Department, Faculty of Engineering, National Defense University of Malaysia, Kem Sungai Besi, 57000 Kuala Lumpur, Malaysia Correspondence should be addressed to Darmawaty Mohd Ali, darma504@yahoo.com.my Received 18 May 2010; Revised 9 November 2010; Accepted 22 December 2010 Academic Editor: Farouk Yalaoui Copyright © 2010 D. Mohd Ali and K. Dimyati. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Packet scheduling has drawn a great deal of attention in the field of wireless networks as it plays an important role in distributing shared resources in a network. The process involves allocating the bandwidth among users and determining their transmission order. In this paper an uplink (UL) scheduling algorithm for the Mobile Worldwide Interoperability for Microwave Access (WiMAX) network based on the cyclic polling model is proposed. The model in this study consists of five queues (UGS, ertPS, rtPS, nrtPS, and BE) visited by a single server. A threshold policy is imposed to the nrtPS queue to ensure that the delay constraint of real time traffic (UGS, ertPS, and rtPS) is not violated making this approach original in comparison to the existing contributions. A mathematical model is formulated for the weighted sum of the mean waiting time of each individual queues based on the pseudo-conservation law. The results of the analysis are useful in obtaining or testing approximation for individual mean waiting time especially when queues are asymmetric (where each queue may have different stochastic characteristic such as arrival rate and service time distribution) and when their number is large (more than 2 queues). 1. Introduction Mobile WiMAX is a promising Broadband Wireless Access (BWA) that has received great interest due to the need for data access at all time. The salient features of the Mobile WiMAX that are attractive are the capability of handling the quality of service (QoS) and the physical layer (PHY), scalability, and the medium access control (MAC) layer, which are exclusively designed to meet different kinds of traffic. IEEE 802.16e does define the means and method in supporting the different classes of traffic. However, it does not specify how to effectively schedule and guarantee the QoS according to the different types of applications. An extensive numbers of scheduling schemes have been proposed by researchers, and the most common approach has been by means of simulation. Simulation is a widely used technique for computing the performance measures of all kinds of models. With such manner, the performance of the Mobile WiMAX system in terms of delay, throughput, jitter, and packet loss is evaluated. However, despite of the flexibility, simulation may be rather inefficient in many cases and results based on simulation are relatively inaccurate as compared to the mathematical analysis [1]. A number of works have been focusing on evaluating the analytical model of the scheduling scheme in the context of Mobile WiMAX system. The authors in [2] put forward the idea of scheduling algorithm for the voice over IP (VoIP) services. The algorithm is claimed to solve the problem of the waste of the uplink resources algorithm caused by Unsolicited Grant Service (UGS) and MAC overhead and access delay due to the Real-Time Polling Service (rtPS) algorithm. The system model is represented as a one- dimensional Markov chain with an on-off model for the voice traffic. From here the average number of voice users in on-state, the maximum number of users that can be serviced in one MAC frame, the system throughput, and the access delay were established. In [3] a novel scheduling scheme was presented to provide QoS satisfaction and service differentiation in terms of delay. The time window, T i , of the Proportional Fairness