Mean and Variance of a Multi-Rate M/G/1 Queuing Model Over Time Correlated Nakagami-m Fading Channel

The advent of multimedia applications over wireless networks has necessitated the need for high data rates and a reliable communication over dynamic wireless links. Adaptive Modulation and coding (AMC), Automatic Repeat re-Quest (ARQ) and Forward Error Correction (FEC) have been widely used to overcome the time varying nature of these links and consequently enhancing their performance. When AMC is used, variable number of packets can be transmitted per Coherence Time Interval (CTI) depending on the Transmission Mode (TM). The number of packets transmitted per CTI is a function of the received Signal-to-Noise Ratio (SNR). For time correlated fading, this entails that the service process is non-Markovian. In this paper we derive the first and Second Moments of the service time distribution for an M/G/1 queuing model that employs AMC for TDMA systems over time correlated Nakagamim Fading channel. We consider service times for geometrically distributed message lengths with fixed packet lengths whose arrivals are Markovian. However, individual packet service times are correlated, due to the correlated fading process and affects overall message service time which subsequently determines the delay experienced by a message in a queue awaiting transmission/service.