Battery lifetime is a key impediment to long-lasting low power sensor nodes and networks thereof. Energy harvesting -conversion of ambient energy into electrical energy -has emerged as a viable alternative to battery power. Indeed, the harvested energy mitigates the dependency on battery power and can be used to transmit data. However, unfair data delivery delay and energy expenditure among sensors remain important issues for such networks. We study performance of sensor networks with mobile sinks: a mobile sink moves towards the transmission range of the different static sensor nodes to collect their data. We propose and analyse a Markovian queueing system to study the impact of uncertainty in energy harvesting, energy expenditure, data acquisition and data transmission. In particular, the energy harvesting sensor node is described by a system with two queues, one queue corresponding to the battery and the other to the data buffer. We illustrate our approach by numerical examples which show that energy harvesting correlation considerably affects performance measures like the mean data delay and the effective data collection rate.