Koyel Mukherjee

Saving on cooling: the thermal scheduling problem

In this abstract we define some very basic scheduling problems motivated by increasing power density and consequent cooling considerations in data centers and multi-core chips. Modern data centers consist of thousands of computers closely packed in a dense space, typically arranged as hundreds of racks of processors. The energy costs of a data center have been compared to that of a small town, with a significant portion contributed by the cost incurred in cooling the machines [1]. The energy cost of cooling is directly driven by the supply temperature (denoted Tsup) of the cold air being blown in to cool the data center – the incoming air is often kept at a lower than necessary temperature to prevent hotspots from forming since those can damage the hardware. For instance, it has been observed that servers near the top of a rack often run hotter and are subject to higher failure rates [3]. Thermal balancing through judicious task scheduling can lead to fewer hotspots and thus lower overall cooling costs and lower failure rates. Similarly in multi-core chip architectures, the increasing density of cores and a movement toward 3D architectures [7] has made dynamic thermal management a key challenge. Increasing temperatures affect circuit reliability and longevity over the long term, and result in increased power consumption (because of increased leakage power) and overall high cooling costs. In this framework we study a basic scheduling problem, called the thermal scheduling problem. We would like to minimize the maximum temperature of the machines in a data center while executing a set of jobs, or maximize assigned jobs while keeping the maximum temperature below a pre-specified red-line temperature (Tred). The key differentiating factor here from much of the prior work in scheduling is the notion of spatial cross-interference: the heat generated by jobs running on a machine raises its own temperature as well as the temperatures of nearby machines due to recirculation effects. Such effects are well-documented both for data centers [6, 5] and for multi-core chips [7]. In addition, the

To send or not to send: Reducing the cost of data transmission

Frequently, ISPs charge for Internet use not based on peak bandwidth usage, but according to a percentile (often the 95th percentile) cost model. In other words, the time slots with the top 5 percent (in the case of 95th percentile) of data transmission volume do not affect the cost of transmission. Instead, we are charged based on the volume of traffic sent in the 95th percentile slot. In such an environment, by allowing a short delay in transmission of some data, we may be able to reduce our cost considerably. We provide an optimal solution to the offline version of this problem (in which the job arrivals are known), for any delay D > 0. The algorithm works for any choice of percentile. We also show that there is no efficient deterministic online algorithm for this problem. However, for a slightly different problem, where the maximum amount of data transmitted is used for cost accounting, we provide an online algorithm with a competitive ratio of 2D+1/D+1. Furthermore, we prove that no online algorithm can achieve a competitive ratio better than 2D+1/D+F(D) where F(D) = Σi=1D+1 i/D+i for any D > 0 in an adversarial setting. We also provide a heuristic that can be used in an online setting where the network traffic has a strong correlation over consecutive accounting cycles, based on the solution to the offline percentile problem. Experimental results are used to illustrate the performance of the algorithms proposed in this work.

Algorithms for the Thermal Scheduling Problem

The energy costs for cooling a data center constitute a significant portion of the overall running costs. Thermal imbalance and hot spots that arise due to imbalanced workloads lead to significant wasted cooling effort - in order to ensure that no equipment is operating above a certain temperature, the data center may be cooled more than necessary. Therefore it is desirable to schedule the workload in a data center in a thermally aware manner, assigning jobs to machines not just based on local load of the machines, but based on the overall thermal profile of the data center. This is challenging because of the spatial cross-interference between machines, where a job assigned to a machine may impact not only that machines temperature, but also nearby machines. Here, we continue formal analysis of the thermal scheduling problem that we initiated recently [25]. In that work, the notion of effective load of a machine which is a function of the local load on the machine as well as the load on nearby machines, was introduced, and optimal scheduling policies for a simple model (where cross-effects are restricted within a rack) were presented, under the assumption that jobs can be split among different machines. Here we consider the more realistic problem of integral assignment of jobs, and allow for cross-interference among different machines in adjacent racks in the data center. The integral assignment problem with cross-interference is NP-hard, even for a simple two machine model. We consider three different heat flow models, and give constant factor approximation algorithms for maximizing the number (or total profit) of jobs assigned in each model, without violating thermal constraints. We also consider the problem of minimizing the maximum temperature on any machine when all jobs need to be assigned, and give constant factor algorithms for this problem.

Xhare-a-Ride: A Search Optimized Dynamic Ride Sharing System with Approximation Guarantee

Ride sharing is a sustainable, environmentallyfriendly mode of commute that is gaining in popularity. Though there are well-established commercial service providers, there are not many platforms for facilitating peer-to-peer ride sharing, especially in a dynamic scenario, integrated with multi-modal trip planners. Such systems would need to be highly searchoptimized for retrieval of multiple potential ride matches in real time, especially because multi-modal trip planners have a high look-to-book ratio. At the same time, validity of the matches need to be ensured, even in a dynamic setting, while addressing quality considerations and constraints such as maximum detour incurred by rides, walking distance for commuters, and time windows of requests. We describe Xhare-a-Ride (XAR) system, a platform for dynamic peer-to-peer ride sharing, that is scalable, efficient, and highly search-optimized for retrieving multiple potential matches for every ride request, while handling quality considerations. We propose a hierarchical discretization of the geographical region using grids, landmarks and clusters with theoretical guarantees, along with an efficient in-memory indexing of rides for maintaining spatio-temporal validity within a specified error tolerance. This helps eliminate shortest path computation in realtime during search, thus making XAR search-optimized, hence, suitable for integration with a multi-modal trip planner. We discuss modes of integrating XAR with such a trip planner for building an integrated system. Finally, we evaluate XAR thoroughly on ride share request data generated from the NY taxi trip data set on three fronts: (i) empirical performance against the theoretical guarantees as well as trade-off of performance with system parameters, (ii) benchmark XAR against a state-of the-art ride share system, showing a significant improvement in the search efficiency, and finally, (iii) the efficacy of combining ride sharing with public transportation.

Fair Resource Allocation for Heterogeneous Tasks

We consider the problem of fair resource allocation for tasks where a resource can be assigned to at most one task, without any fractional allocation. The system is heterogeneous: capacity and cost may vary across resources, and different tasks may have different resource demand. Due to heterogeneity of resources, the cost of allocating a task in isolation, without any other competing task, may differ significantly from its allocation cost when the task is allocated along with other tasks. In this context, we consider the problem of allocating resource to tasks, while ensuring that the cost is distributed fairly across the tasks, namely, the ratio of allocation cost of a task to its isolation cost is minimized over all tasks. We show that this fair resource allocation problem is strongly NP-Hard even when the resources are of unit size by a reduction from 3-partition. Our central results are an LP rounding based algorithm with an approximation ratio of 2+ O(ϵ) for the problem when resources are of unit size, and a near-optimal greedy algorithm for a more restricted version. The above fair allocation problem arises for resource allocation in various context, such as, allocating computing resources for reservations requests from tenants in a data centre, allocating resources to computing tasks in grid computing, or allocating personnel for tasks in service delivery organizations.

TRaining AssigNment Service (TRANS) to Meet Organization Level Skill Need

The need for training employees in new skills in an organization generally arises due to the changing skill requirements coming from the introduction of new products, technology and customers. Efficient assignment of employees to trainings so that the overall training cost is minimized while considering the career goals of employees is a challenging problem and to the best of our knowledge there is no existing work in literature that solves this problem. This paper presents TRaining AssigNment Service (TRANS) that minimizes an organization’s overall training costs while assigning employees to trainings that match their learning ability and career goals. TRANS uses an ORGanization and Skills ontology (ORGS) to calculate the cost for training each available employee for a potential role taking into account constructivist learning theory. TRANS uses TRaining assIgnMent algorithm (TRIM), based on Hungarian method for bipartite matching, for assigning employees to trainings. In our experiments with real-world data, proposed allocation algorithm performs better than the existing strategy of the organization.

Brief announcement: a game-theoretic model motivated by the darpa network challenge

In this paper we propose a game-theoretic model to analyze events similar to the 2009 DARPA Network Challenge, which was organized by the Defense Advanced Research Projects Agency (DARPA) for exploring the roles that the Internet and social networks play in incentivizing wide-area collaborations. The challenge was to form a group that would be the first to find the locations of ten moored weather balloons across the United States. We consider a model in which N people (who can form groups) are located in some topology with a fixed coverage volume around each persons geographical location. We consider various topologies where the players can be located such as the Euclidean d-dimension space and the vertices of a graph. A balloon is placed in the space and a group wins if it is the first one to report the location of the balloon. A larger team has a higher probability of finding the balloon, but we assume that the prize money is divided equally among the team members. Hence there is a competing tension to keep teams as small as possible. Risk aversion is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff. In our model we consider the isoelastic utility function derived from the Arrow-Pratt measure of relative risk aversion. The main aim is to analyze the structures of the groups in Nash equilibria for our model. For the d-dimensional Euclidean space (d ≥ 1) and the class of bounded degree regular graphs we show that in any Nash Equilibrium the richestgroup (having maximum expected utility per person) covers a constant fraction of the total volume. The objective of events like the DARPA Network Challenge is to mobilize a large number of people quickly so that they can cover a big fraction of the total area. Our results suggest that this objective can be met under certain conditions.