## DELAY MINIMIZATION IN ENERGY CONSTRAINED WIRELESS COMMUNICATIONS

##### Abstract

In wireless communications and networks, especially for many
real-time applications, the average delay packets experience is an
important quality of service criterion. Therefore, it is imperative
to design advanced transmission schemes to jointly address the goals of reliability, high rates and low delay. Achieving these objectives often requires careful allocation of given resources, such as energy, power, rate, among users. It also requires a close collaboration between physical layer, medium access control layer, and upper layers, and yields cross-layer solutions.
We first investigate the problem of minimizing the overall transmission
delay of packets in a multiple access wireless communication system,
where the transmitters have average power constraints. We formulate the problem as a constrained optimization problem, and then transform it into a linear programming problem. We show that the optimal policy has a threshold structure: when the sum of the queue lengths is larger than a threshold, both users should transmit a packet during the current slot; when the sum of the queue lengths is smaller than a threshold, only one of the users, the one with the longer queue, should transmit a packet during the current slot.
Then, we study the delay-optimal rate allocation in a multiple access
wireless communication system. Our goal is to allocate rates to users, from the multiple access capacity region, based on their current queue
lengths, in order to minimize the average delay of the system. We formulate the problem as a Markov decision problem (MDP) with an average cost criterion. We first show that the value function is increasing, symmetric and convex in the queue length vector. Taking advantage of these properties, we show that the optimal rate allocation policy is one which tries to equalize the queue lengths as much as possible in each slot, while working on the dominant face of the capacity region.
Next, we extend the delay-optimal rate allocation problem to a communication channel with two transmitters and one receiver, where the underlying rate region is approximated as a general pentagon. We show that the delay-optimal policy has a switch curve structure. For the discounted-cost problem, we prove that the switch curve has a limit along one of the dimensions. The existence of a limit in the switch curve along one of the dimensions implies that, once the queue state is beyond the limit, the system always operates at one of the corner points, implying that the queues can be operated partially distributedly.
Next, we shift our focus from the average delay minimization problem to transmission completion time minimization problem in energy harvesting communication systems. We first consider the optimal packet scheduling problem in a single-user energy harvesting wireless communication system. In this system, both the data packets and the harvested energy are modeled to arrive at the source node randomly. Our goal is to adaptively change the transmission rate according to the traffic load and available energy, such that the time by which all packets are delivered is minimized. Under a deterministic system setting, we develop an optimal off-line scheduling policy which minimizes the transmission completion time, under causality constraints on both data and energy arrivals.
Then, we investigate the transmission completion time minimization problem in a two-user additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature. We first analyze the structural properties of the optimal transmission policy. We prove that the optimal total transmit power has the same structure as the optimal single-user transmit power. We also prove that there exists a cut-off power level for the stronger user. If the optimal total transmit power is lower than this level, all transmit power is allocated to the stronger user, and when the optimal total transmit power is larger than this level, all transmit power above this level is allocated to the weaker user. Based on these structural properties of the optimal policy, we propose an algorithm that yields the globally optimal off-line scheduling policy.
Next, we investigate the transmission completion time minimization problem in a two-user AWGN multiple access channel. We first develop a generalized iterative backward waterfilling algorithm to characterize the maximum departure region of the transmitters for any given deadline. Then, based on the sequence of maximum departure regions at energy arrival epochs, we decompose the transmission completion time minimization problem into a convex optimization problem and solve it efficiently.
Finally, we investigate the average delay minimization problem in a single-user communication channel with an energy harvesting transmitter. We consider three different cases. In the first case, both the data packets and the energy to be used to transmit them are assumed to be available at the transmitter at the beginning. In the second case, while the energy is available at the transmitter at the beginning, packets arrive during the transmissions. In the third case, the packets are available at the transmitter at the beginning and the energy arrives during the transmissions, as a result of energy harvesting. In each scenario, we find the structural properties of the optimal solution, and develop iterative algorithms to obtain the solution.

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