With the introduction of IEEE 802.11 power save mode (PSM), a lot of work has been done to enhance the energy saving ability of the wireless nodes. The ultimate goal of the research is to make the networking equipment carbon neutral and prolong the lifetime of the energy limited device for various applications; in some cases it is a trade-off between energy efficiency and delay. However, few studies have been made until now in the area of IEEE 802.11s based link specific power mode. The essence of this method is the ability of a node to maintain different power modes with its different peer nodes at the same time. A new peer service period (PSP) mechanism is also proposed in IEEE 802.11s amendment for transmitting to a receiver operating in PSM. In this paper the performance of the link specific power mode is studied for a single- and a multilink network in terms of energy, delay throughput, and sleep duration. It is found that at small load the energy saving could be as high as eighty percent when compared with the active mode operation. A stochastic model, based on discrete time discrete state Markov chain, is developed for one peer link operation to study the system behavior closely during PSM operation.