Online Packet Scheduling with Bounded Delay and Lookahead

We study the online bounded-delay packet scheduling problem (PacketScheduling), where packets of unit size arrive at a router over time and need to be transmitted over a network link. Each packet has two attributes: a non-negative weight and a deadline for its transmission. The objective is to maximize the total weight of the transmitted packets. This problem has been well studied in the literature, yet its optimal competitive ratio remains unknown: the best upper bound is 1.828 [Englert and Westermann, SODA 2007], still quite far from the best lower bound of phi approx 1.618 [Hajek, CISS 2001; Andelman et al, SODA 2003; Chin and Fung, Algorithmica, 2003]. In the variant of PacketScheduling with s-bounded instances, each packet can be scheduled in at most s consecutive slots, starting at its release time. The lower bound of phi applies even to the special case of 2-bounded instances, and a phi-competitive algorithm for 3-bounded instances was given in [Chin et al, JDA, 2006]. Improving that result, and addressing a question posed by Goldwasser [SIGACT News, 2010], we present a phi-competitive algorithm for 4-bounded instances. We also study a variant of PacketScheduling where an online algorithm has the additional power of 1-lookahead, knowing at time t which packets will arrive at time t+1. For PacketScheduling with 1-lookahead restricted to 2-bounded instances, we present an online algorithm with competitive ratio frac{1}{2}(sqrt{13} - 1) approx 1.303 and we prove a nearly tight lower bound of frac{1}{4}(1 + sqrt{17}) approx 1.281

Online packet scheduling with bounded delay and lookahead

We study the online bounded-delay packet scheduling problem (Packet Scheduling), where packets of unit size arrive at a router over time and need to be transmitted over a network link. Each packet has two attributes: a non-negative weight and a deadline for its transmission. The objective is to maximize the total weight of the transmitted packets. This problem has been well studied in the literature; yet currently the best published upper bound is 1.828 [8],still quite far from the best lower bound ofφ≈1.618 [11, 2, 6].In the variant of Packet Scheduling with s-bounded instances, each packet can be scheduled in at most s consecutive slots, starting at its release time. The lower bound of φ applies even to the special case of 2-bounded instances, and a φ-competitive algorithm for 3-boundedinstances was given in [5]. Improving that result, and addressing a question posed by Goldwasser [9], we present a φ-competitive algorithm for 4-boundedinstances. We also study a variant of Packet Scheduling where an online algorithm has the additional power of1-lookahead, knowing at time t which packets will arrive at time t+ 1. For Packet Scheduling with 1-lookahead restricted to 2-bounded instances, we present an online algorithm with competitive ratio12(√13−1)≈1.303 and we prove a nearly tight lower boundof14(1 +√17)≈1.281. In fact, our lower bound result is more general: using only 2-boundedinstances, for any integer`≥0 we prove a lower bound of12(`+1)(1 +√5 + 8`+ 4`2) for online algorithms with`-look ahead, i.e., algorithms that at time t can see all packets arriving by time t+`. Finally, for non-restricted instances we show a lower bound of 1.25 for randomized algorithms with`-lookahead, for any`≥0

When Backpressure Meets Predictive Scheduling

Motivated by the increasing popularity of learning and predicting human user behavior in communication and computing systems, in this paper, we investigate the fundamental benefit of predictive scheduling, i.e., predicting and pre-serving arrivals, in controlled queueing systems. Based on a lookahead window prediction model, we first establish a novel equivalence between the predictive queueing system with a \emph{fully-efficient} scheduling scheme and an equivalent queueing system without prediction. This connection allows us to analytically demonstrate that predictive scheduling necessarily improves system delay performance and can drive it to zero with increasing prediction power. We then propose the \textsf{Predictive Backpressure (PBP)} algorithm for achieving optimal utility performance in such predictive systems. \textsf{PBP} efficiently incorporates prediction into stochastic system control and avoids the great complication due to the exponential state space growth in the prediction window size. We show that \textsf{PBP} can achieve a utility performance that is within $O(\epsilon)$ of the optimal, for any $\epsilon>0$, while guaranteeing that the system delay distribution is a \emph{shifted-to-the-left} version of that under the original Backpressure algorithm. Hence, the average packet delay under \textsf{PBP} is strictly better than that under Backpressure, and vanishes with increasing prediction window size. This implies that the resulting utility-delay tradeoff with predictive scheduling beats the known optimal $[O(\epsilon), O(\log(1/\epsilon))]$ tradeoff for systems without prediction

Dynamic Server Allocation over Time Varying Channels with Switchover Delay

We consider a dynamic server allocation problem over parallel queues with randomly varying connectivity and server switchover delay between the queues. At each time slot the server decides either to stay with the current queue or switch to another queue based on the current connectivity and the queue length information. Switchover delay occurs in many telecommunications applications and is a new modeling component of this problem that has not been previously addressed. We show that the simultaneous presence of randomly varying connectivity and switchover delay changes the system stability region and the structure of optimal policies. In the first part of the paper, we consider a system of two parallel queues, and develop a novel approach to explicitly characterize the stability region of the system using state-action frequencies which are stationary solutions to a Markov Decision Process (MDP) formulation. We then develop a frame-based dynamic control (FBDC) policy, based on the state-action frequencies, and show that it is throughput-optimal asymptotically in the frame length. The FBDC policy is applicable to a broad class of network control systems and provides a new framework for developing throughput-optimal network control policies using state-action frequencies. Furthermore, we develop simple Myopic policies that provably achieve more than 90% of the stability region. In the second part of the paper, we extend our results to systems with an arbitrary but finite number of queues.Comment: 38 Pages, 18 figures. arXiv admin note: substantial text overlap with arXiv:1008.234

Approximating fluid schedules in packet-switched networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 145-151).We consider a problem motivated by the desire to provide exible, rate-based, quality of service guarantees for packets sent over switches and switch networks. Our focus is solving a type of on-line, traffic scheduling problem, whose input at each time step is a set of desired traffic rates through the switch network. These traffic rates in general cannot be exactly achieved since they treat the incoming data as fluid, that is, they assume arbitrarily small fractions of packets can be transmitted at each time step. The goal of the traffic scheduling problem is to closely approximate the given sequence of traffic rates by a sequence of switch uses throughout the network in which only whole packets are sent. We prove worst-case bounds on the additional delay and buffer use that result from using such an approximation. These bounds depend on the network topology, the resources available to the scheduler, and the types of fluid policy allowed.by Michael Aaron Rosenblum.Ph.D

Semi-online Scheduling with Lookahead

The knowledge of future partial information in the form of a lookahead to design efficient online algorithms is a theoretically-efficient and realistic approach to solving computational problems. Design and analysis of semi-online algorithms with extra-piece-of-information (EPI) as a new input parameter has gained the attention of the theoretical computer science community in the last couple of decades. Though competitive analysis is a pessimistic worst-case performance measure to analyze online algorithms, it has immense theoretical value in developing the foundation and advancing the state-of-the-art contributions in online and semi-online scheduling. In this paper, we study and explore the impact of lookahead as an EPI in the context of online scheduling in identical machine frameworks. We introduce a $k$-lookahead model and design improved competitive semi-online algorithms. For a $2$-identical machine setting, we prove a lower bound of $\frac{4}{3}$ and design an optimal algorithm with a matching upper bound of $\frac{4}{3}$ on the competitive ratio. For a $3$-identical machine setting, we show a lower bound of $\frac{15}{11}$ and design a $\frac{16}{11}$-competitive improved semi-online algorithm.Comment: 14 pages, 1 figur

Dynamic Scaling of VoD Services into Hybrid Clouds with Cost Minimization and QoS Guarantee

A large-scale video-on-demand (VoD) service demands huge server costs, to provision thousands of videos to millions of users with high streaming quality. As compared to the traditional practice of relying on large on-premise server clusters, the emerging platforms of geo-distributed public clouds promise a more economic solution: their on-demand resource provisioning can constitute ideal supplements of resources from on-premise servers, and effectively support dynamic scaling of the VoD service at different times. Promising though it is, significant technical challenges persist before it turns into reality: how shall the service provider dynamically replicate videos and dispatch user requests over the hybrid platform, such that the service quality and the minimization of overall cost can be guaranteed over the long run of the system? In this paper, we present a dynamic algorithm that optimally makes decisions on video replication and user request dispatching in a hybrid cloud of on-premise servers and geo-distributed cloud data centers, based on the Lyapunov optimization framework. We rigorously prove that this algorithm can nicely bound the streaming delays within the preset QoS target in cases of arbitrary request arrival patterns, and guarantee that the overall cost is within a small constant gap from the optimum achieved by a T-slot lookahead mechanism with known information into the future. We evaluate our algorithm with extensive simulations under realistic settings, and demonstrate that cost minimization and smooth playback can be achieved in cases of volatile user demands.published_or_final_versio