Weighted k-Server Bounds via Combinatorial Dichotomies

The weighted $k$-server problem is a natural generalization of the $k$-server problem where each server has a different weight. We consider the problem on uniform metrics, which corresponds to a natural generalization of paging. Our main result is a doubly exponential lower bound on the competitive ratio of any deterministic online algorithm, that essentially matches the known upper bounds for the problem and closes a large and long-standing gap. The lower bound is based on relating the weighted $k$-server problem to a certain combinatorial problem and proving a Ramsey-theoretic lower bound for it. This combinatorial connection also reveals several structural properties of low cost feasible solutions to serve a sequence of requests. We use this to show that the generalized Work Function Algorithm achieves an almost optimum competitive ratio, and to obtain new refined upper bounds on the competitive ratio for the case of $d$ different weight classes.Comment: accepted to FOCS'1

A Bicriteria Approximation for the Reordering Buffer Problem

In the reordering buffer problem (RBP), a server is asked to process a sequence of requests lying in a metric space. To process a request the server must move to the corresponding point in the metric. The requests can be processed slightly out of order; in particular, the server has a buffer of capacity k which can store up to k requests as it reads in the sequence. The goal is to reorder the requests in such a manner that the buffer constraint is satisfied and the total travel cost of the server is minimized. The RBP arises in many applications that require scheduling with a limited buffer capacity, such as scheduling a disk arm in storage systems, switching colors in paint shops of a car manufacturing plant, and rendering 3D images in computer graphics. We study the offline version of RBP and develop bicriteria approximations. When the underlying metric is a tree, we obtain a solution of cost no more than 9OPT using a buffer of capacity 4k + 1 where OPT is the cost of an optimal solution with buffer capacity k. Constant factor approximations were known previously only for the uniform metric (Avigdor-Elgrabli et al., 2012). Via randomized tree embeddings, this implies an O(log n) approximation to cost and O(1) approximation to buffer size for general metrics. Previously the best known algorithm for arbitrary metrics by Englert et al. (2007) provided an O(log^2 k log n) approximation without violating the buffer constraint.Comment: 13 page

Online VNF Scaling in Datacenters

Network Function Virtualization (NFV) is a promising technology that promises to significantly reduce the operational costs of network services by deploying virtualized network functions (VNFs) to commodity servers in place of dedicated hardware middleboxes. The VNFs are typically running on virtual machine instances in a cloud infrastructure, where the virtualization technology enables dynamic provisioning of VNF instances, to process the fluctuating traffic that needs to go through the network functions in a network service. In this paper, we target dynamic provisioning of enterprise network services - expressed as one or multiple service chains - in cloud datacenters, and design efficient online algorithms without requiring any information on future traffic rates. The key is to decide the number of instances of each VNF type to provision at each time, taking into consideration the server resource capacities and traffic rates between adjacent VNFs in a service chain. In the case of a single service chain, we discover an elegant structure of the problem and design an efficient randomized algorithm achieving a e/(e-1) competitive ratio. For multiple concurrent service chains, an online heuristic algorithm is proposed, which is O(1)-competitive. We demonstrate the effectiveness of our algorithms using solid theoretical analysis and trace-driven simulations.Comment: 9 pages, 4 figure

Datacenter Traffic Control: Understanding Techniques and Trade-offs

Datacenters provide cost-effective and flexible access to scalable compute and storage resources necessary for today's cloud computing needs. A typical datacenter is made up of thousands of servers connected with a large network and usually managed by one operator. To provide quality access to the variety of applications and services hosted on datacenters and maximize performance, it deems necessary to use datacenter networks effectively and efficiently. Datacenter traffic is often a mix of several classes with different priorities and requirements. This includes user-generated interactive traffic, traffic with deadlines, and long-running traffic. To this end, custom transport protocols and traffic management techniques have been developed to improve datacenter network performance. In this tutorial paper, we review the general architecture of datacenter networks, various topologies proposed for them, their traffic properties, general traffic control challenges in datacenters and general traffic control objectives. The purpose of this paper is to bring out the important characteristics of traffic control in datacenters and not to survey all existing solutions (as it is virtually impossible due to massive body of existing research). We hope to provide readers with a wide range of options and factors while considering a variety of traffic control mechanisms. We discuss various characteristics of datacenter traffic control including management schemes, transmission control, traffic shaping, prioritization, load balancing, multipathing, and traffic scheduling. Next, we point to several open challenges as well as new and interesting networking paradigms. At the end of this paper, we briefly review inter-datacenter networks that connect geographically dispersed datacenters which have been receiving increasing attention recently and pose interesting and novel research problems.Comment: Accepted for Publication in IEEE Communications Surveys and Tutorial

A gentle transition from Java programming to Web Services using XML-RPC

Exposing students to leading edge vocational areas of relevance such as Web Services can be difficult. We show a lightweight approach by embedding a key component of Web Services within a Level 3 BSc module in Distributed Computing. We present a ready to use collection of lecture slides and student activities based on XML-RPC. In addition we show that this material addresses the central topics in the context of web services as identified by Draganova (2003)