Energy-Efficient Transmission Scheduling with Strict Underflow Constraints

We consider a single source transmitting data to one or more receivers/users over a shared wireless channel. Due to random fading, the wireless channel conditions vary with time and from user to user. Each user has a buffer to store received packets before they are drained. At each time step, the source determines how much power to use for transmission to each user. The source’s objective is to allocate power in a manner that minimizes an expected cost measure, while satisfying strict buffer underflow constraints and a total power constraint in each slot. The expected cost measure is composed of costs associated with power consumption from transmission and packet holding costs. The primary application motivating this problem is wireless media streaming. For this application, the buffer underflow constraints prevent the user buffers from emptying, so as to maintain playout quality. In the case of a single user with linear power-rate curves, we show that a modified base-stock policy is optimal under the finite horizon, infinite horizon discounted, and infinite horizon average expected cost criteria. For a single user with piecewise-linear convex power-rate curves, we show that a finite generalized base-stock policy is optimal under all three expected cost criteria. We also present the sequences of critical numbers that complete the characterization of the optimal control laws in each of these cases when some additional technical conditions are satisfied. We then analyze the structure of the optimal policy for the case of two users. We conclude with a discussion of methods to identify implementable near-optimal policies for the most general case of M users.

💡 Research Summary

The paper addresses the problem of allocating transmission power from a single source to one or more receivers over a shared wireless channel that experiences random fading. Each receiver maintains a buffer that stores incoming packets before they are consumed for playback. The source must decide, at every discrete time slot, how much power to allocate to each user while respecting two hard constraints: (1) a total power budget per slot, and (2) strict underflow constraints that prevent any user’s buffer from emptying, which is essential for uninterrupted media streaming. The objective is to minimize the expected long‑run cost, which is the sum of a power‑consumption cost and a holding (buffer) cost.

System model. Time is slotted, and in each slot the channel state for user i is a random variable (h_t^i) drawn independently from a known distribution. The buffer level for user i at the beginning of slot t is (x_t^i). The source can transmit (f_i(p_t^i, h_t^i)) packets to user i by spending power (p_t^i); the function (f_i) captures the physical layer relationship between power, channel quality, and achievable rate. The total power used in a slot must satisfy (\sum_i p_t^i \le P_{\max}). After transmission, each user consumes a deterministic amount (d_i) of packets for playback, leading to the buffer dynamics
(x_{t+1}^i = \bigl