  Rapid progress made in the field of sensor technology, wireless
communication, and computer networks in recent past, led to the development of
wireless Ad-hoc sensor networks, consisting of small, low-cost sensors, which
can monitor wide and remote areas with precision and liveliness unseen to the
date without the intervention of a human operator. This work comes up with a
stochastic model for periodic sensor-deployment (in face of their limited
amount of battery-life) to maintain a minimal node-connectivity in wireless
sensor networks. The node deployment cannot be modeled by using results from
conventional continuous birth-death process, since new nodes are added to the
network in bursts, i.e. the birth process is not continuous in practical
situations. We analyze the periodic node deployment process using discrete
birth-continuous death process and obtain two important statistical measures of
the existing number of nodes in the network, namely the mean and variance. We
show that the above mentioned sequences of mean and variances always converge
to finite steady state values, thus ensuring the stability of the system. We
also develop a cost function for the process of periodic deployment of sensor
nodes and minimize it to find the optimal time ({\tau}) and optimum number of
re-deployment (q) for maintaining minimum connectivity in the network.
