This paper investigates the energy consumption minimization for resource scheduling in a wireless communication. We propose to take into account a strict delay constraint for each queued packet rather than an average delay constraint, in addition to a buffer overflow constraint. The associated optimization problem can be modeled as Constraint Markov Decision Problem where the actions are the number of packets sent on the known channel at each slot. The optimal random policy is exhibited through the resolution of standard linear programming. We show the gain in energy is substantial compared to naive policy.