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 @math . We then deduce the Whittle's indices for the original problem (i.e. with total average queue length minimization) by taking the limit @math . 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.
There are lot of works which study the problem of resource allocation in wireless networks. For instance, in @cite_12 @cite_4 @cite_10 @cite_6 , the authors give a throughput optimal policy for single channel, multi-channel and multi-user MIMO contexts using max weight rule, which is known to not be delay optimal. To overcome this matter, many works have been developed in the past to minimize the average delay of the traffic of the users (e.g. see @cite_1 and the references therein). Most of them describe the minimization problem as Markov Decision Process (MDP) and develop resource allocation policies using Bellman equation such as Value iteration algorithm. However, as we have already mentioned in abstract, MDP frameworks and Bellman equation are hard to solve them. @cite_15 @cite_9 try to minimize the average delay of the users' queues using stochastic learning algorithm. Indeed, the stochastic learning algorithm consumes lot of time and users memories. Besides, it requires high computational complexity.
@cite_4 @cite_9 @cite_1 @cite_6 @cite_15 @cite_10 @cite_12
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In this paper, the problem of feedback and active user selection in multiple-input single-output (MISO) wireless systems such that the system’s stability region is as big as possible is examined. The focus is on a system in a Rayleigh fading environment where zero forcing precoding is used to serve all active users in every slot. Acquisition of the channel states is done via uplink training in time division duplexing mode by the active users. Clearly, only a subset of users can perform uplink training and the selection of this subset is a challenging and interesting problem especially in MISO systems. The stability regions of a baseline centralized scheme and two novel decentralized policies are examined analytically. In the decentralized schemes, the transmitter broadcasts periodically the queue state information and the users contend for the channel in a carrier sense multiple access-based manner with parameters based on the outdated queue state information and real-time channel state information. We show that, using infrequent signaling between the base station and the users, the decentralized policies outperform the centralized policy. In addition, a threshold-based user selection and training scheme for discrete-time contention is proposed. The results of this paper imply that, as far as stability is concerned, the users must be involved in the active user selection and feedback training decision. This should be leveraged in future communication systems. In this paper, a comprehensive survey is given on several major systematic approaches in dealing with delay-aware control problems, namely the equivalentrate constraint approach, the Lyapunov stability drift approach, and the approximate Markov decision process approach using stochastic learning. These approaches essentially embrace most of the existing literature regarding delay-aware resource control in wireless systems. They have their relative pros and cons in terms of performance, complexity, and implementation issues. For each of the approaches, the problem setup, the general solution, and the design methodology are discussed. Applications of these approaches to delay-aware resource allocation are illustrated with examples in single-hop wireless networks. Furthermore, recent results regarding delay-aware multihop routing designs in general multihop networks are elaborated. Finally, the delay performances of various approaches are compared through simulations using an example of the uplink OFDMA systems. Information flow in a telecommunication network is accomplished through the interaction of mechanisms at various design layers with the end goal of supporting the information exchange needs of the applications. In wireless networks in particular, the different layers interact in a nontrivial manner in order to support information transfer. In this text we will present abstract models that capture the cross-layer interaction from the physical to transport layer in wireless network architectures including cellular, ad-hoc and sensor networks as well as hybrid wireless-wireline. The model allows for arbitrary network topologies as well as traffic forwarding modes, including datagrams and virtual circuits. Furthermore the time varying nature of a wireless network, due either to fading channels or to changing connectivity due to mobility, is adequately captured in our model to allow for state dependent network control policies. Quantitative performance measures that capture the quality of service requirements in these systems depending on the supported applications are discussed, including throughput maximization, energy consumption minimization, rate utility function maximization as well as general performance functionals. Cross-layer control algorithms with optimal or suboptimal performance with respect to the above measures are presented and analyzed. A detailed exposition of the related analysis and design techniques is provided. In this paper, a low-complexity delay-aware cross-layer scheduling algorithm for two-hop relay communication systems is proposed. The complex interactions of the queues at the source node and the M relay nodes (RSs) are modeled as an infinite horizon average reward Markov decision process (MDP), whose state space involves the joint queue state information (QSI) of the queues at the source node and the M RSs as well as the joint channel state information (CSI) of all S-R and R-D links. To address the curse of dimensionality, an equivalent MDP formulation is first proposed, where the system state depends only on global QSI. Furthermore, using approximate MDP and stochastic learning, an auction-based distributed online learning algorithm is derived, where each node iteratively estimates a per-node value function based on real-time observations of the local CSI and local QSI as well as signaling between relays. The combined distributed learning converges almost surely to a global optimal solution for large arrivals. Finally, it is showed by simulations that the proposed scheme achieves significant gain compared with various baselines such as the conventional CSIT-only control and the throughput optimal control (in stability sense). The stability of a queueing network with interdependent servers is considered. The dependency among the servers is described by the definition of their subsets that can be activated simultaneously. Multihop radio networks provide a motivation for the consideration of this system. The problem of scheduling the server activation under the constraints imposed by the dependency among servers is studied. The performance criterion of a scheduling policy is its throughput that is characterized by its stability region, that is, the set of vectors of arrival and service rates for which the system is stable. A policy is obtained which is optimal in the sense that its stability region is a superset of the stability region of every other scheduling policy, and this stability region is characterized. The behavior of the network is studied for arrival rates that lie outside the stability region. Implications of the results in certain types of concurrent database and parallel processing systems are discussed. > This paper characterizes the performance in terms of queueing stability of a network composed of multiple MIMO transmitter-receiver pairs taking into account the dynamic traffic pattern and the probing feedback cost. We adopt a centralized scheduling scheme that selects a number of active pairs in each time-slot. We consider that the transmitters apply interference alignment (IA) technique if two or more pairs are active, whereas in the special case where one pair is active point-to-point MIMO singular value decomposition (SVD) is used. We consider a time-division duplex (TDD) system where transmitters acquire their channel state information (CSI) by decoding the pilot sequences sent by the receivers. Since global CSI knowledge is required for IA, the transmitters have also to exchange their estimated CSIs over a backhaul of limited capacity (i.e. imperfect case). Under this setting, we characterize in this paper the stability region of the system under both the imperfect and perfect (i.e. unlimited backhaul) cases, then we examine the gap between these two resulting regions. Further, under each case we provide a centralized probing policy that achieves the max stability region. These stability regions and scheduling policies are given for the symmetric system, where all the path loss coefficients are equal to each other, as well as for the general system. For the symmetric system, we provide the conditions under which IA yields a queueing stability gain compared to SVD. Under the general system, the adopted scheduling policy is of a high computational complexity for moderate numbers of pairs, consequently we propose an approximate policy that has a reduced complexity but that achieves only a fraction of the system stability region. A characterization of this fraction is provided.