arXiv subjects

Maialen Larranaga

Publications and source records attributed to Maialen Larranaga.

4 recordsLinked to original sources

arXiv2020

Asymptotically Optimal Delay-aware Scheduling in Queueing Systems

In this paper, we investigate a general delay-aware channel allocation problem where the number of channels is less than that of users. Due to the proliferation of delay sensitive applications, the objective of our problem is chosen to be the minimization of the total average backlog queues of the network in question. First, we show that our problem falls in the framework of Restless Bandit Problems (RBP), for which obtaining the optimal solution is known to be out of reach. To circumvent this difficulty, we tackle the problem by adopting a Whittle index approach. To that extent, we employ a Lagrangian relaxation of the original problem and prove it to be decomposable into multiple one-dimensional independent subproblems. Afterwards, we provide structural results on the optimal policy of each of the subproblems. More specifically, we prove that a threshold policy is able to achieve the optimal operating point of the considered subproblem. Armed with that, we show the indexability of the subproblems and characterize the Whittle's indices which are the basis of our proposed heuristic. We then provide a rigorous mathematical proof that our policy is optimal in the infinitely many users regime. Finally, we provide numerical results that showcase the remarkable good performance of our proposed policy and that corroborate the theoretical findings.

cs.IT↗

arXiv2019

Whittle Index Policy for Multichannel Scheduling in Queueing Systems

In this paper, we consider a queueing system with multiple channels (or servers) and multiple classes of users. We aim at allocating the available channels among the users in such a way to minimize the expected total average queue length of the system. This known scheduling problem falls in the framework of Restless Bandit Problems (RBP) for which an optimal solution is known to be out of reach for the general case. The contributions of this paper are as follows. We rely on the Lagrangian relaxation method to characterize the Whittle index values and to develop an index-based heuristic for the original scheduling problem. The main difficulty lies in the fact that, for some queue states, deriving the Whittle's index requires introducing a new approach which consists in introducing a new expected discounted cost function and deriving the Whittle's index values with respect to the discount parameter $β$. We then deduce the Whittle's indices for the original problem (i.e. with total average queue length minimization) by taking the limit $β\rightarrow 1$. The numerical results provided in this paper show that this policy performs very well and is very close to the optimal solution for high number of users.

cs.NI↗

arXiv2018

Queue-aware Energy Efficient Control for Dense Wireless Networks

We consider the problem of long term power allocation in dense wireless networks. The framework considered in this paper is of interest for machine-type communications (MTC). In order to guarantee an optimal operation of the system while being as power efficient as possible, the allocation policy must take into account both the channel and queue states of the devices. This is a complex stochastic optimization problem, that can be cast as a Markov Decision Process (MDP) over a huge state space. In order to tackle this state space explosion, we perform a mean-field approximation on the MDP. Letting the number of devices grow to infinity the MDP converges to a deterministic control problem. By solving the Hamilton-Jacobi-Bellman Equation, we obtain a well-performing power allocation policy for the original stochastic problem, which turns out to be a threshold-based policy and can then be easily implemented in practice.

cs.IT↗

arXiv2016

Asymptotically optimal pilot allocation over Markovian fading channels

We investigate a pilot allocation problem in wireless networks over Markovian fading channels. In wireless systems, the Channel State Information (CSI) is collected at the Base Station (BS), in particular, this paper considers a pilot-aided channel estimation method (TDD mode). Typically, there are less available pilots than users, hence at each slot the scheduler needs to decide an allocation of pilots to users with the goal of maximizing the long-term average throughput. There is an inherent tradeoff in how the limited pilots are used: assign a pilot to a user with up-to-date CSI and good channel condition for exploitation, or assign a pilot to a user with outdated CSI for exploration. As we show, the arising pilot allocation problem is a restless bandit problem and thus its optimal solution is out of reach. In this paper, we propose an approximation that, through the Lagrangian relaxation approach, provides a low-complexity heuristic, the Whittle index policy. We prove this policy to be asymptotically optimal in the many users regime (when the number of users in the system and the available pilots for channel sensing grow large). We evaluate the performance of Whittle's index policy in various scenarios and illustrate its remarkably good performance.

math.OC↗