To extend the life time of a wireless sensor network, sensor nodes usually switch between dormant and active states according to a duty cycling scheme. In randomized schemes, sensors use only partial or no information about their neighbors, and rely on randomness to generate working schedules. Duty cycling schemes are often evaluated in terms of the connection delay, i.e., the time until two neighboring nodes are simultaneously active, and the connection duration, i.e., the time until at least one of them switches to the dormant state. In this paper, we argue that duty cycling time (energy) efficiency, i.e., the ratio of time (energy) employed in ancillary operations when switching from and into deep sleep mode, is an important performance metric too. We present experimental results using Sun SPOT sensors that support our claim and highlight the performance trade-off between connection delay and time (energy) efficiency for a traditional scheme based on independent and identically distributed (i.i.d.) random variables. We propose a novel randomized duty cycling scheme based on Markov chains with the goal of (i) reducing the connection delay, while maintaining a given time (energy) efficiency, or (ii) keeping a constant connection delay, while increasing the time (energy) efficiency. The proposed scheme is analyzed mathematically by deriving the time efficiency, connection delay and duration in terms of the time slot length, duty cycle, and cost of set up and tear down operations. Analytical results demonstrate that the Markov chain-based scheme can improve the performance in terms of connection delay without affecting the time efficiency, or vice versa, as opposed to the trade-off observed in traditional schemes. Experimental results using Sun SPOT sensor nodes with the minimum number of operations during transitions from and into deep sleep mode confirm the mathematical analysis of the proposed Markov chain-based randomized scheme.