Approximated Calculations of Connection Level Access Waiting Time Distribution in OFDMA-Based Wireless Cellular Systems with AMC

In this paper, two analytical approaches to approximately calculate the access (at connection level) waiting time distribution for an OFDMA-based wireless cellular system with finite buffering under First-Come, First-Served (FCFS) discipline and Adaptive Modulation and Coding (AMC) are proposed. It has been demonstrated in previous published works that access waiting time is a random sum of random variables with the same distribution but random mean. Therefore, the computational complexity for the numerical evaluation of the access waiting time probability distribution increases exponentially with the size of the buffer and the number of coverage regions. In order to reduce the computational complexity, the use of negative exponential distribution is proposed to approximate the whole access waiting time distribution for certain conditions of traffic load. Moreover, an efficient way to calculate its parameter through the Little's theorem is proposed. A more general approach is based on the central limit theorem (CLT). In particular, it considers that the conditional access waiting time of a service request queued in the a given position can be adequately approximated by a Gaussian distribution. The proposed approximation approaches are numerically evaluated and compared against the exact mathematical analysis in terms of the cumulative distribution function. Numerical results show that the maximum percentage error between the both approximated CDFs is smaller than 10% relative to the exact analysis under certain conditions.