In this work, we aim to obtain the optimal tradeoff between the average delay and the average power consumption in a communication system. In our system, the arrivals occur at each timeslot according to a Bernoulli arrival process and are buffered at the transmitter. The transmitter determines the scheduling policy of how many packets to transmit under an average power constraint. The power is assumed to be an increasing and convex function of the number of packets transmitted in each timeslot to capture the realism in communication systems. We also consider a finite buffer and allow the scheduling decision to depend on the buffer occupancy. This problem is modelled as a Constrained Markov Decision Process (CMDP). We first prove that the optimal policy of the (Lagrangian) relaxation of the CMDP is deterministic and threshold-based. We then show that the optimal delay-power tradeoff curve is convex and piecewise linear, where each of the vertices are obtained by the optimal solution to the relaxed problem. This allows us to show the optimal policies of the CMDP are threshold-based, and hence can be implemented by a proposed efficient algorithm. The theoretical results and the algorithm are validated by Linear Programming and simulations.
Cross-layer scheduling is a promising way to improve Quality of Service (QoS) given a power constraint. In this paper, we investigate the system with random data arrival and adaptive transmission. Probabilistic scheduling strategies aware of the buffer state are applied to generalize conventional deterministic scheduling. Based on this, the average delay and power consumption are analysed by Markov reward process. The optimal delay-power tradeoff curve is the Pareto frontier of the feasible delay-power region. It is proved that the optimal delay-power tradeoff is piecewise-linear, whose vertic…
Multi-User scheduling is a challenging problem under the relaying scenarios. Traditional schemes, which are based on the instantaneous signal-to-interference-plus-noises ratios (SINRs), cannot solve the inherent disparities of the qualities between different links. Hence, the system performance is always limited by the weaker links. In this paper, from the whole system throughput view, we propose an optimal multi-user scheduling scheme for the multi-user full-duplex (FD) buffer aided relay systems. We first formulate the throughput maximization problem. Then, according to the characteristics o…
We present a closed-form expression for the minimal delay that is achievable in a setting that combines a buffer and an erasure code, used to mitigate the packet delay variance. The erasure code is modeled according to the recent information-theoretic results on finite block length codes. Evaluations reveal that accurate knowledge of the network parameters is essential for optimal operation. Moreover, it is shown that, when the network packet delay variance is large, the buffer delay becomes negligible. Therefore, in this case the delay budget should be spent mainly on the erasure code.
In this paper, the downlink packet scheduling problem for cellular networks is modeled, which jointly optimizes throughput, fairness and packet drop rate. Two genie-aided heuristic search methods are employed to explore the solution space. A deep reinforcement learning (DRL) framework with A2C algorithm is proposed for the optimization problem. Several methods have been utilized in the framework to improve the sampling and training efficiency and to adapt the algorithm to a specific scheduling problem. Numerical results show that DRL outperforms the baseline algorithm and achieves similar perf…
This paper analyzes the impact of statistical delay constraints on the achievable rate of a two-hop wireless communication link, in which the communication between a source and a destination is accomplished via a buffer-aided relay node. It is assumed that there is no direct link between the source and the destination, and the buffer-aided relay forwards the information to the destination by employing the decode-and-forward scheme. Given statistical delay constraints specified via maximum delay and delay violation probability, the tradeoff between the statistical delay constraints imposed on a…
In this paper, we study the end-to-end distortion/delay tradeoff for a analogue source transmitted over a fading channel. The analogue source is quantized and stored in a buffer until it is transmitted. There are two extreme cases as far as buffer delay is concerned: no delay and infinite delay. We observe that there is a significant power gain by introducing a buffer delay. Our goal is to investigate the situation between these two extremes. Using recently proposed \emph{effective capacity} concept, we derive a closed-form formula for this tradeoff. For SISO case, an asymptotically tight uppe…
In this work, we study the effects of finite buffers on the throughput and delay of line networks with erasure links. We identify the calculation of performance parameters such as throughput and delay to be equivalent to determining the stationary distribution of an irreducible Markov chain. We note that the number of states in the Markov chain grows exponentially in the size of the buffers with the exponent scaling linearly with the number of hops in a line network. We then propose a simplified iterative scheme to approximately identify the steady-state distribution of the chain by decoupling…
In this paper, we consider energy efficient multiuser scheduling. Packet loss tolerance of the applications is exploited to minimize average system energy. There is a constraint on average packet drop rate and maximum number of packets dropped successively (bursty loss). A finite buffer size is assumed. We propose a scheme which schedules the users opportunistically according to the channel conditions, packet loss constraints and buffer size parameters. We assume imperfect channel state information at the transmitter side and analyze the scheme in large user limit using stochastic optimization…
Buffer aided relaying has recently attracted a lot of attention due to the improvement in the system throughput. However, a side effect usually deemed is that buffering at relay nodes results in the increase in packet delays. In this paper, we study the effect of buffering relays on the end-to-end delay of users' data, from the time they arrive at source until delivery to the destination. We use simple discussions to provide an insight on the overall waiting time of the packets in the system. By studying the Bernoulli distributed channel conditions, and using intuitive generalizations, we conc…
Age of information is a new network performance metric that captures the freshness of information at end-users. This paper studies the age of information from a scheduling perspective. To that end, we consider a wireless broadcast network where a base-station (BS) is updating many users on random information arrivals under a transmission capacity constraint. For the offline case when the arrival statistics are known to the BS, we develop a structural MDP scheduling algorithm and an index scheduling algorithm, leveraging Markov decision process (MDP) techniques and the Whittle's methodology for…
In this paper, link selection for half-duplex buffer-aided relay systems is revisited. A new fixed scheduling policy referred as alternate distributed beamforming (ADB) is proposed, in which the relays are divided into two groups, with one group receiving the same information broadcast from the source and the other group transmitting the common messages to the destination via distributed beamforming in each time slot. It is worth noting that the relays used for reception and transmission are determined without the need of instantaneous channel state information (CSI). Theoretical analysis of t…
In this paper, we study the throughput utility functions in buffer-equipped monostatic backscatter communication networks with multi-antenna Readers. In the considered model, the backscatter nodes (BNs) store the data in their buffers before transmission to the Reader. We investigate three utility functions, namely, the sum, the proportional and the common throughput. We design online admission policies, corresponding to each utility function, to determine how much data can be admitted in the buffers. Moreover, we propose an online data link control policy for jointly controlling the transmit …
In this paper, we consider a simple network consisting of a source, a half-duplex decode-and-forward relay, and a destination. We propose a new relaying protocol employing adaptive link selection, i.e., in any given time slot, based on the channel state information of the source-relay and the relay-destination link a decision is made whether the source or the relay transmits. In order to avoid data loss at the relay, adaptive link selection requires the relay to be equipped with a buffer such that data can be queued until the relay-destination link is selected for transmission. We study both d…
We consider a simple network consisting of a source, a half-duplex DF relay with a buffer, and a destination. We assume that the direct source-destination link is not available and all links undergo fading. We propose two new buffer-aided relaying schemes. In the first scheme, neither the source nor the relay have CSIT, and consequently, both nodes are forced to transmit with fixed rates. In contrast, in the second scheme, the source does not have CSIT and transmits with fixed rate but the relay has CSIT and adapts its transmission rate accordingly. In the absence of delay constraints, for bot…
In this paper, we investigate the performance of a three-node dual-hop cognitive radio network (CRN) with a half-duplex (HD) decode-and-forward (DF) buffer-aided relay. We derive expressions for the average rate and symbol error rate (SER) performance of an adaptive link selection based channel-aware buffer-aided relay (CABR) scheme that imposes peak-power and peak-interference constraints on the secondary nodes, and compare them with those of conventional non-buffer-aided relay (CNBR) and conventional buffer-aided relay (CBR) schemes for a delay-tolerant system. For finite-delay systems, we a…
Source-channel coding for an energy limited wireless sensor node is investigated. The sensor node observes independent Gaussian source samples with variances changing over time slots and transmits to a destination over a flat fading channel. The fading is constant during each time slot. The compressed samples are stored in a finite size data buffer and need to be delivered in at most $d$ time slots. The objective is to design optimal transmission policies, namely, optimal power and distortion allocation, over the time slots such that the average distortion at destination is minimized. In parti…
In this paper a scheduling policy is presented which minimizes the average delay of the users. The scheduling scheme is investigated both by analysis and simulations carried out in the context of Orthogonal Frequency Division Multiplexing (OFDM) broadcast channels (BC). First the delay optimality is obtained for a static scenario providing solutions for specific subproblems, then the analysis is carried over to the dynamic scheme. Furthermore auxiliary tools are given for proving throughput optimality. Finally simulations show the superior performance of the presented scheme.
We analyze the delay performance of small cell networks operating under random scheduling (RS) and round robin (RR) protocols. Based on stochastic geometry and queuing theory, we derive accurate and tractable expressions for the distribution of mean delay, which accounts for the impact of random traffic arrivals, queuing interactions, and failed packet retransmissions. Our analysis asserts that RR outperforms RS in terms of mean delay, regardless of traffic statistic. Moreover, the gain from RR is more pronounced in the presence of heavy traffic, which confirms the importance of accounting fai…
Despite lots of literature has been dedicated to researching the delay performance in two-hop relay (2HR) mobile ad hoc networks (MANETs), however, they usually assume the buffer size of each node is infinite, so these studies are not applicable to and thus may not reflect the real delay performance of a practical MANET with limited buffer. To address this issue, in this paper we explore the packet end-to-end delay in a 2HR MANET, where each node is equipped with a bounded and shared relay-buffer for storing and forwarding packets of all other flows. The transmission range of each node can be …
In this paper, we propose a cross-layer scheduling algorithm that achieves a throughput "epsilon-close" to the optimal throughput in multi-hop wireless networks with a tradeoff of O(1/epsilon) in delay guarantees. The algorithm aims to solve a joint congestion control, routing, and scheduling problem in a multi-hop wireless network while satisfying per-flow average end-to-end delay guarantees and minimum data rate requirements. This problem has been solved for both backlogged as well as arbitrary arrival rate systems. Moreover, we discuss the design of a class of low-complexity suboptimal algo…
We study an uplink multi secondary user (SU) cognitive radio system suffering statistical heterogeneity among SUs' channels. This heterogeneity may result in differentiated delay performances to these SUs and result in harmful interference to the PU. We first derive an explicit closed-form expression for the average delay in terms of an arbitrary power-control policy. Then, we propose a delay-optimal closed-form scheduling and power-control policy that can provide the required average delay guarantees to all SUs besides protecting the PU from harmful interference. We support our findings by ex…
We study an uplink multi secondary user (SU) system having statistical delay constraints, and an average interference constraint to the primary user (PU). SUs with heterogeneous interference channel statistics, to the PU, experience heterogeneous delay performances since SUs causing low interference are scheduled more frequently than those causing high interference. We propose a scheduling algorithm that can provide arbitrary average delay guarantees to SUs irrespective of their statistical channel qualities. We derive the algorithm using the Lyapunov technique and show that it yields bounded …
In this work, the achievable rate of three-node relay systems with selection relaying under statistical delay constraints, imposed on the limitations of the maximum end-to-end delay violation probabilities, is investigated. It is assumed that there are queues of infinite size at both the source and relay node, and the source can select the relay or destination for data reception. Given selection relaying policy, the effective bandwidth of the arrival processes of the queue at the relay is derived. Then, the maximum constant arrival rate can be identified as the maximum effective capacity as a …
Optical switching has been considered as a natural choice to keep pace with growing fiber link capacity. One key research issue of all-optical switching is the design of optical queues by using optical crossbar switches and fiber delay lines (SDL). In this paper, we focus on the construction of an optical priority queue with a single $(M+2)\times (M+2)$ crossbar switch and $M$ fiber delay lines, and evaluate it in terms of the buffer size of the priority queue. Currently, the best known upper bound of the buffer size is $O(2^M)$, while existing methods can only construct a priority queue with …
Emergence of new types of services has led to various traffic and diverse delay requirements in fifth generation (5G) wireless networks. Meeting diverse delay requirements is one of the most critical goals for the design of 5G wireless networks. Though the delay of point-to-point communications has been well investigated, the delay of multi-point to multi-point communications has not been thoroughly studied since it is a complicated function of all links in the network. In this work, we propose a novel tractable approach to analyze the delay in the heterogenous cellular networks with spatio-te…
In this paper, throughput and energy efficiency of secure wireless transmission of delay sensitive data generated by random sources is studied. A fading broadcast model in which the transmitter sends confidential and common messages to two receivers is considered. It is assumed that the common and confidential data, generated from Markovian sources, is stored in buffers prior to transmission, and the transmitter operates under constraints on buffer/delay violation probability. Under such statistical quality of service (QoS) constraints, effective capacity of time-varying wireless transmissions…
In this paper, we study joint queue-aware and channel-aware scheduling of arbitrarily bursty traffic over multi-state time-varying channels, where the bursty packet arrival in the network layer, the backlogged queue in the data link layer, and the power adaptive transmission with fixed modulation in the physical layer are jointly considered from a cross-layer perspective. To achieve minimum queueing delay given a power constraint, a probabilistic cross-layer scheduling policy is proposed, and characterized by a Markov chain model. To describe the delay-power tradeoff, we formulate a non-linear…
In this paper, we consider an unmanned aerial vehicle (UAV) aided mobile relaying system under a buffer constraint. We propose a new relaying protocol employing mixed free-space optical/radio frequency (FSO/RF) communication, i.e., the source-relay and relay-destination links utilize FSO and RF links, respectively, under the buffer constraint at the UAV relay node. Taking the conditions of an imbalance in transmission rate between RF and FSO links into consideration, we study the trajectory optimization problem of buffer-constrained UAV relay node in order to maximize the end-to-end data throu…
This paper investigates delay-distortion-power trade offs in transmission of quasi-stationary sources over block fading channels by studying encoder and decoder buffering techniques to smooth out the source and channel variations. Four source and channel coding schemes that consider buffer and power constraints are presented to minimize the reconstructed source distortion. The first one is a high performance scheme, which benefits from optimized source and channel rate adaptation. In the second scheme, the channel coding rate is fixed and optimized along with transmission power with respect to…
Age of Information (AoI), which measures the time elapsed since the generation of the last received packet at the destination, is a new metric for real-time status update tracking applications. In this paper, we consider a status-update system in which a source node samples updates and sends them to an edge server over a delay channel. The received updates are processed by the server with an infinite buffer and then delivered to a destination. The channel can send only one update at a time, and the server can process one at a time as well. The source node applies generate-at-will model accordi…
This paper is motivated by the observation that the average queueing delay can be decreased by sacrificing power efficiency in wireless communications. In this sense, we naturally wonder what is the minimum queueing delay when the available power is limited and how to achieve the minimum queueing delay. To answer these two questions in the scenario where randomly arriving packets are transmitted over multi-state wireless fading channel, a probabilistic cross-layer scheduling policy is proposed in this paper, and characterized by a constrained Markov Decision Process (MDP). Using the steady-sta…
We study an uplink multi secondary user (SU) cognitive radio system having average delay constraints as well as an instantaneous interference constraint to the primary user (PU). If the interference channels from the SUs to the PU have independent but not identically distributed fading coefficients, then the SUs will experience heterogeneous delay performances. This is because SUs causing low interference to the PU will be scheduled more frequently, and/or allocated more transmission power than those causing high interference. We propose a dynamic scheduling-and-power-control algorithm that ca…
A point-to-point discrete-time scheduling problem of transmitting $B$ information bits within $T$ hard delay deadline slots is considered assuming that the underlying energy-bit cost function is a convex monomial. The scheduling objective is to minimize the expected energy expenditure while satisfying the deadline constraint based on information about the unserved bits, channel state/statistics, and the remaining time slots to the deadline. At each time slot, the scheduling decision is made without knowledge of future channel state, and thus there is a tension between serving many bits when th…
This work investigates the effect of finite buffer sizes on the throughput capacity and packet delay of line networks with packet erasure links that have perfect feedback. These performance measures are shown to be linked to the stationary distribution of an underlying irreducible Markov chain that models the system exactly. Using simple strategies, bounds on the throughput capacity are derived. The work then presents two iterative schemes to approximate the steady-state distribution of node occupancies by decoupling the chain to smaller queueing blocks. These approximate solutions are used to…
In this paper, transmission over buffer-aided diamond relay systems under statistical quality of service (QoS) constraints is studied. The statistical QoS constraints are imposed as limitations on delay violation probabilities. In the absence of channel state information (CSI) at the transmitter, truncated hybrid automatic repeat request-incremental redundancy (HARQ-IR) is incorporated to make better use of the wireless channel and the resources for each communication link. The packets that cannot be successfully received upon the maximum number of transmissions will be removed from buffer, i.…
We consider downlink max-based scheduling in which the base station and each user are equipped with a single antenna. In each time slot, the base station obtains channel gains of all users and selects the user with the largest squared channel gain. Assuming that channel state information at the transmitter (CSIT), i.e., squared channel gain, can be inaccurate, we derive lower bounds for probability of outage, which occurs when a required data rate is not satisfied under a delay constraint. The bounds are tight for Rayleigh fading and show how required rate and CSIT error affect outage performa…
All-optical switching has been considered as a natural choice to keep pace with growing fiber link capacity. One key research issue of all-optical switching is the design of optical buffers for packet contention resolution. One of the most general buffering schemes is optical priority queue, where every packet is associated with a unique priority upon its arrival and departs the queue in order of priority, and the packet with the lowest priority is always dropped when a new packet arrives but the buffer is full. In this paper, we focus on the feedback construction of an optical priority queue …
In this paper, we aim to minimize the average file transmission delay via bandwidth allocation and cache placement in two-tier heterogeneous networks with limited storage capacity, which consists of cache capacity and buffer capacity. For average delay minimization problem with fixed bandwidth allocation, although this problem is nonconvex, the optimal solution is obtained in closed form by comparing all locally optimal solutions calculated from solving the Karush-Kuhn-Tucker conditions. To jointly optimize bandwidth allocation and cache placement, the optimal bandwidth allocation is first der…
This paper focuses on a class of important two-hop relay mobile ad hoc networks (MANETs) with limited-buffer constraint and any mobility model that leads to the uniform distribution of the locations of nodes in steady state, and develops a general theoretical framework for the end-to-end (E2E) delay modeling there. We first combine the theories of Fixed-Point, Quasi-Birth-and-Death process and embedded Markov chain to model the limiting distribution of the occupancy states of a relay buffer, and then apply the absorbing Markov chain theory to characterize the packet delivery process, such that…
Cloud radio access network (C-RAN) architecture is a new mobile network architecture that enables cooperative baseband processing and information sharing among multiple cells and achieves high adaptability to nonuniform traffic by centralizing the baseband processing resources in a virtualized baseband unit (BBU) pool. In this work, we formulate the utility of each user using a convex delay cost function, and design a two-step scheduling algorithm with good delay performance for the C-RAN architecture. In the first step, all users in multiple cells are grouped into small user groups, according…
Real-time video demands quality-of-service (QoS) guarantees such as delay bounds for end-user satisfaction. Furthermore, the tolerable delay varies depending on the use case such as live streaming or two-way video conferencing. Due to the inherently stochastic nature of wireless fading channels, deterministic delay bounds are difficult to guarantee. Instead, we propose providing statistical delay guarantees using the concept of effective capacity. We consider a multiuser setup whereby different users have (possibly different) delay QoS constraints. We derive the resource allocation policy that…
In this paper, we adopt a cross layer design approach for analyzing the throughput-delay tradeoff of the multicast channel in a single cell system. To illustrate the main ideas, we start with the single group case, i.e., pure multicast, where a common information stream is requested by all the users. We consider three classes of scheduling algorithms with progressively increasing complexity. The first class strives for minimum complexity by resorting to a static scheduling strategy along with memoryless decoding. Our analysis for this class of scheduling algorithms reveals the existence of a s…
An uplink cognitive radio system with a single primary user (PU) and multiple secondary users (SUs) is considered. The SUs have an individual average delay constraint and an aggregate average interference constraint to the PU. If the interference channels between the SUs and the PU are statistically different due to the different physical locations of the SUs, the SUs will experience different delay performances. This is because SUs located closer to the PU transmit with lower power levels. A dynamic scheduling-and-power-allocation policy that uses the dynamic programming, is proposed. The pro…
In the half-duplex single relay selection network, comprised of a source, $M$ half-duplex relays, and a destination, only one relay is active at any given time, i.e., only one relay receives or transmits, and the other relays are inactive, i.e., they do not receive nor transmit. The capacity of this network, when all links are affected by independent slow time-continuous fading and additive white Gaussian noise (AWGN), is still unknown, and only achievable average rates have been reported in the literature so far. In this paper, we present new achievable average rates for this network which ar…
We consider a scenario where a power constrained transmitter delivers randomly arriving packets to the destination over Markov time-varying channel and adapts different transmission power to each channel state in order to guarantee successful transmission. To minimize the expected average transmission delay of each packet, we formulate the problem into a constrained Markov decision process (CMDP). We reveal the queue-length threshold structure of the optimal policy, i.e., the transmitter sends packets if and only if the queue length surpasses a threshold and obtain the optimal cross-layer sche…
Millimeter wave (mmWave) technologies have the potential to achieve very high data rates, but suffer from intermittent connectivity. In this paper, we provision an architecture to integrate sub-6 GHz and mmWave technologies, where we incorporate the sub-6 GHz interface as a fallback data transfer mechanism to combat blockage and intermittent connectivity of the mmWave communications. To this end, we investigate the problem of scheduling data packets across the mmWave and sub-6 GHz interfaces such that the average delay of system is minimized. This problem can be formulated as Markov Decision P…
Uplink scheduling/resource allocation under the single-carrier FDMA constraint is investigated, taking into account the queuing dynamics at the transmitters. Under the single-carrier constraint, the problem of MaxWeight scheduling, as well as that of determining if a given number of packets can be served from all the users, are shown to be NP-complete. Finally, a matching-based scheduling algorithm is presented that requires only a polynomial number of computations per timeslot, and in the case of a system with large bandwidth and user population, provably provides a good delay (small-queue) p…
Throughput optimal scheduling policies in general require the solution of a complex and often NP-hard optimization problem. Related literature has shown that in the context of time-varying channels, randomized scheduling policies can be employed to reduce the complexity of the optimization problem but at the expense of a memory requirement that is exponential in the number of data flows. In this paper, we consider a Linear-Memory Randomized Scheduling Policy (LM-RSP) that is based on a pick-and-compare principle in a time-varying network with $N$ one-hop data flows. For general ergodic channel…
In this paper, we study the scheduling problem for downlink transmission in a multi-channel (e.g., OFDM-based) wireless network. We focus on a single cell, with the aim of developing a unifying framework for designing low-complexity scheduling policies that can provide optimal performance in terms of both throughput and delay. We develop new easy-to-verify sufficient conditions for rate-function delay optimality (in the many-channel many-user asymptotic regime) and throughput optimality (in general non-asymptotic setting), respectively. The sufficient conditions allow us to prove rate-function…
Mobile-edge computing (MEC) emerges as a promising paradigm to improve the quality of computation experience for mobile devices. Nevertheless, the design of computation task scheduling policies for MEC systems inevitably encounters a challenging two-timescale stochastic optimization problem. Specifically, in the larger timescale, whether to execute a task locally at the mobile device or to offload a task to the MEC server for cloud computing should be decided, while in the smaller timescale, the transmission policy for the task input data should adapt to the channel side information. In this p…
Green communication attracts increasing research interest recently. Equipped with a rechargeable battery, a source node can harvest energy from ambient environments and rely on this free and regenerative energy supply to transmit packets. Due to the uncertainty of available energy from harvesting, however, intolerably large latency and packet loss could be induced, if the source always waits for harvested energy. To overcome this problem, one Reliable Energy Source (RES) can be resorted to for a prompt delivery of backlogged packets. Naturally, there exists a tradeoff between the packet delive…
In this work, we address the delay optimal scheduling problem for wireless transmission with fixed modulation over multi-state fading channels. We propose a stochastic scheduling policy which schedules the source to transmit with probability jointly based on the buffer and channel states, with an average power constraint at the transmitter. Our objective is to minimize the average queueing delay by choosing the optimal transmission probabilities. Using Markov chain modeling, we formulate a power-constrained delay minimization problem, and then transform it into a Linear Programming (LP) one. B…
This paper considers optimization of power and delay in a time-varying wireless link using rateless codes. The link serves a sequence of variable-length packets. Each packet is coded and transmitted over multiple slots. Channel conditions can change from slot to slot and are unknown to the transmitter. The amount of mutual information accumulated on each slot depends on the random channel realization and the power used. The goal is to minimize average service delay subject to an average power constraint. We formulate this problem as a frame-based stochastic optimization problem and solve it vi…
