Analysis of mean packet delay for upstream transmissions in passive optical networks with sleep mode

The sleep mode has been introduced to improve the energy efficiency of passive optical networks (PONs) with interleaved polling with adaptive cycle time (IPACT) as a medium access control (MAC) scheme. For energy saving, the sleep mode of each optical network unit (ONU) is activated based on the packet queue length for upstream traffic. We model such a PON as an N-user M/G/1 queue with reservations and vacations. Based on the framework of M/G/1 queueing analysis with some modification made to incorporate the nature of IPACT as well as the sleep mode, we derive a closed form expression of the mean packet delay. A unique challenge in our analysis is that certain quantities such as the residual time of an on-going sleep period for the upstream channel must be considered from the network's viewpoint while the delay due to the sleep mode experienced by a packet must be considered from the ONU's viewpoint. Simulation experiments are conducted to validate the analytical results and to show that the results are relatively insensitive to packet arrival statistics for large sleep periods. Finally, we demonstrate how a sleep period can be chosen given the quality-of-service (QoS) requirement on the mean packet delay.