Many-Sources Large Deviations for Max-Weight Scheduling

In this paper, a many-sources large deviations principle (LDP) for the transient workload of a multi-queue single-server system is established where the service rates are chosen from a compact, convex and coordinate-convex rate region and where the service discipline is the max-weight policy. Under the assumption that the arrival processes satisfy a many-sources LDP, this is accomplished by employing Garcia's extended contraction principle that is applicable to quasi-continuous mappings. For the simplex rate-region, an LDP for the stationary workload is also established under the additional requirements that the scheduling policy be work-conserving and that the arrival processes satisfy certain mixing conditions. The LDP results can be used to calculate asymptotic buffer overflow probabilities accounting for the multiplexing gain, when the arrival process is an average of \emph{i.i.d.} processes. The rate function for the stationary workload is expressed in term of the rate functions of the finite-horizon workloads when the arrival processes have \emph{i.i.d.} increments.Comment: 44 page

Achieving Optimal Throughput and Near-Optimal Asymptotic Delay Performance in Multi-Channel Wireless Networks with Low Complexity: A Practical Greedy Scheduling Policy

In this paper, we focus on the scheduling problem in multi-channel wireless networks, e.g., the downlink of a single cell in fourth generation (4G) OFDM-based cellular networks. Our goal is to design practical scheduling policies that can achieve provably good performance in terms of both throughput and delay, at a low complexity. While a class of $O(n^{2.5} \log n)$-complexity hybrid scheduling policies are recently developed to guarantee both rate-function delay optimality (in the many-channel many-user asymptotic regime) and throughput optimality (in the general non-asymptotic setting), their practical complexity is typically high. To address this issue, we develop a simple greedy policy called Delay-based Server-Side-Greedy (D-SSG) with a \lower complexity $2n^2+2n$, and rigorously prove that D-SSG not only achieves throughput optimality, but also guarantees near-optimal asymptotic delay performance. Specifically, we show that the rate-function attained by D-SSG for any delay-violation threshold $b$, is no smaller than the maximum achievable rate-function by any scheduling policy for threshold $b-1$. Thus, we are able to achieve a reduction in complexity (from $O(n^{2.5} \log n)$ of the hybrid policies to $2n^2 + 2n$) with a minimal drop in the delay performance. More importantly, in practice, D-SSG generally has a substantially lower complexity than the hybrid policies that typically have a large constant factor hidden in the $O(\cdot)$ notation. Finally, we conduct numerical simulations to validate our theoretical results in various scenarios. The simulation results show that D-SSG not only guarantees a near-optimal rate-function, but also empirically is virtually indistinguishable from delay-optimal policies.Comment: Accepted for publication by the IEEE/ACM Transactions on Networking, February 2014. A preliminary version of this work was presented at IEEE INFOCOM 2013, Turin, Italy, April 201

Scheduling analysis with martingales

This paper proposes a new characterization of queueing systems by bounding a suitable exponential transform with a martingale. The constructed martingale is quite versatile in the sense that it captures queueing systems with Markovian and autoregressive arrivals in a unified manner; the second class is particularly relevant due to Wold’s decomposition of stationary processes. Moreover, using the framework of stochastic network calculus, the martingales allow for a simple handling of typical queueing operations: (1) flows’ multiplexing translates into multiplying the corresponding martingales, and (2) scheduling translates into time-shifting the martingales. The emerging calculus is applied to estimate the per-flow delay for FIFO, SP, and EDF scheduling. Unlike state-of-the-art results, our bounds capture a fundamental exponential leading constant in the number of multiplexed flows, and additionally are numerically tight

Cooperative Access in Cognitive Radio Networks: Stable Throughput and Delay Tradeoffs

In this paper, we study and analyze fundamental throughput-delay tradeoffs in cooperative multiple access for cognitive radio systems. We focus on the class of randomized cooperative policies, whereby the secondary user (SU) serves either the queue of its own data or the queue of the primary user (PU) relayed data with certain service probabilities. The proposed policy opens room for trading the PU delay for enhanced SU delay. Towards this objective, stability conditions for the queues involved in the system are derived. Furthermore, a moment generating function approach is employed to derive closed-form expressions for the average delay encountered by the packets of both users. Results reveal that cooperation expands the stable throughput region of the system and significantly reduces the delay at both users. Moreover, we quantify the gain obtained in terms of the SU delay under the proposed policy, over conventional relaying that gives strict priority to the relay queue.Comment: accepted for publication in IEEE 12th Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), 201

Schedulers for next generation wireless networks : realizing QoE trade-offs for heterogeneous traffic mixes

In this thesis we will focus on the design of schedulers for next generation wireless networks which support application mixes, characterized by different, possibly complex, application/user Quality of Experience (QoE) metrics. The central problem underlying resource allocation for such systems is realizing QoE trade-offs among various applications/users given the dynamic loads and capacity variability they would typically see. In the first part of the thesis our focus is on applications where QoE depends on flow-level delay-based metrics. We consider system-wide metrics which directly capture both users' QoE metrics and appropriate QoE trade-offs among various applications for a wide range of system loads. This approach is different from the traditional wireless scheduler designs which have been driven by rate-based criteria, e.g., utility maximizing/proportionally fair, and/or queue-based packet schedulers which do not directly reflect the link between flow-level delays and users' QoE. In the second part of this thesis we address the key design challenges in networks supporting Ultra Reliable Low Latency Communications (URLLC) traffic which requires extremely high reliability (99.999%) and very low delays (1 msec). We will explore three different types flow delay-based metrics in this proposal, based on 1) overall mean delay; 2) functions of mean delays; and, 3) mean of functions of delays. We begin by considering minimization of mean flow delay for an M/GI/1 queuing model for a wireless Base Station (BS) where the flow size distributions are of the New Better than Used in Expectation + Decreasing Hazard Rate (NBUE +DHZ) type. Such a flow size distribution have been observed in real systems and we too validate this model based on collected data. Using a combination of analysis and simulation we show that our scheduler achieves good performance for users that might correspond to interactive applications like web browsing and/or stored video streaming and is robust to variations in system loads. Next we consider a generalization of this approach where we minimize a metric based on cost functions of the mean flow delays in a multi-class system where users/flows are classified based on their respective QoE requirements and each class's QoE requirement is modeled by its respective cost function. This approach helps us model QoE more accurately and gives us more flexibility in considering QoE trade-offs among heterogeneous user classes. We optimize two different metrics based on how we average the cost functions of delays, namely, functions of mean delays; and mean of functions of delays. The former can be used when users' experiences are sensitive to mean delays and while the latter can be used when user's experience is also sensitive to higher moments of delays, e.g., variance or soft thresholds on delay. Extensive simulations confirm the effectiveness of our proposed approaches at realizing various QoE trade-offs and performance. In 5G wireless networks URLLC traffic is expected to support many applications like industrial automation, mission critical traffic, virtual traffic etc, where the wireless network has to reliability transport small packets with very high reliability and low delays. We address the following aspects related to the system design for URLLC traffic, 1) quantifying the impact of various system parameters like system bandwidth, link SINR, delay and latency constraints on URLLC 'capacity'; 2) provisioning wireless system appropriately to meet URLLC Quality of Service (QoS) requirements; and, 3) designing efficient Hybrid Automatic Repeat Request (HARQ) schemes for transmitting small packets. Further, due the heterogeneity in delay requirements between URLLC and other types of traffic, sharing radio resources between them creates its own unique challenges. We develop efficient multiplexing schemes between URLLC traffic and other mobile broadband traffic based on preemptive puncturing/superposition of the mobile broadband transmissions by URLLC transmissions.Electrical and Computer Engineerin