Modeling and performance analysis of user equipment with sleep modes and activation overhead

Sleep modes are important for user equipment to reduce power consumption or to reduce battery reloading. To keep the user equipment connected, it has to be activated for uplink or downlink data transfer which causes overhead and additional delay. Wireless or mobile equipment has to be monitored repeatedly for location updates. These classes of problems can be modeled by queuing systems with modified busy and idle periods. In this paper, we consider a generalized infinite-buffer, single-server queuing systems with activation overhead and under various types of sleep modes during inactive periods. For the special assumption of Markovian arrival processes of data units and generally distributed activation times and vacation (sleep) periods, the models can be analyzed exactly by a mean value analysis method which is based on regenerative stochastic processes, renewal theory and classical queuing theorems. The method allows also for dynamic sleep periods which are dependent on each other as in the case of the standard IEEE 802.16m for wireless equipment. Explicit results are derived for average values of data unit delays, resource utilization and power- saving margins dependent on given parameters for activation times and wakeup signaling frequencies. The models include the special cases of M/G/1 queuing systems with a modified service time of the first arrival initiating a busy period and M/G/1 queuing systems with vacation periods, respectively, which are well known from literature providing general solutions for the state and delay distributions. Finally, all models are extended to the exact analysis of Batch Poisson arrival processes.