We consider the sleep mode with multimedia application in WiMAX 2 networks, where the real-time traffic includes the real-time and the best-effort traffic mixed. We present a queueing model with multiple heterogeneous vacations to characterize the system probability behavior in the networks with multimedia application. Taking into account the correlation of the real-time traffic, we assume the arrival process as a discrete-time Markovian arrival process (D-MAP) and analyze this queueing model by using the method of an embedded Markov chain. Then, we present the probability distribution for the number of data packets. Accordingly, we give the formulas for the performance measures in terms of the average response time of data packets, the energy saving ratio, and the standard deviation of the number of data packets. We also develop a cost function to determine the optimal length of the sleep cycle in order to maximize the energy saving ratio while satisfying the Quality of Service (QoS) constraint on the average response time of data packets. Finally, we provide numerical results to investigate the influence of the system parameters on the system performance. 1. Introduction Wireless mesh networks are undergoing rapid development. They are intended to deliver wireless services for a large variety of applications in personal, local, campus, and metropolitan areas. Some protocol designs for wireless mesh networks have focused on power efficiency mechanisms. IEEE 802.16 standard has been designed for fixed subscriber stations. As an enhancement of the IEEE 802.16 standard, IEEE 802.16e, called WiMAX [1], has improved the original standard supporting mobility so that the Mobile Station (MS) can move during services. Aiming at the next generation mobile WiMAX, called WiMAX 2, IEEE 802.16m [2] is currently being processed for standardization. There have been many studies analyzing the performance of the sleep mode operations for Types I–III in WiMAX [3–7]. In [3], the authors evaluated and compared the sleep mode operations for Type I and Type II power saving classes using the method of an embedded Markov chain. In order to avoid too frequent switching between the sleep state and the awake state, an enhanced power saving class Type III was provided in [4] and the system performances were analyzed for user initiated data packet arrivals. In [5], by increasing the unavailability interval, the authors proposed an enhanced power saving mechanism (ePSM), where both activated Type I and Type II power saving classes exist in an MS. The performance evaluation confirms
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