Our aim is to create an automatic third umpire for giving lbw decisions in cricket matches. Recon... more Our aim is to create an automatic third umpire for giving lbw decisions in cricket matches. Reconstruction of any 3-D object requires atleast 2 nondegenerate views. However if we place more than one cameras to find the location of the ball at any instant during delivery, we need to ensure that the pictures of the ball taken are taken at exactly the same instant. This can be done by synchronising the cameras in hardware. However we wish to develop a purely software based system.
Abstract: Motivated by the problem of packing Virtual Machines on physical servers in the cloud, ... more Abstract: Motivated by the problem of packing Virtual Machines on physical servers in the cloud, we study the problem of one-dimensional online stochastic bin packing. Items with sizes iid from an unknown distribution with integral support arrive as a stream and must be packed on arrival in bins of size B, also an integer. The size of an item is known when it arrives and the goal is to minimize the waste, defined to be the total unused space in non-empty bins.
Abstract We propose a new research direction to reinvigorate research into better understanding o... more Abstract We propose a new research direction to reinvigorate research into better understanding of the M/G/K and other queueing systems—via obtaining tight bounds on the mean waiting time as functions of the moments of the service distribution. Analogous to the classical Markov–Krein theorem, we conjecture that the bounds on the mean waiting time are achieved by service distributions corresponding to the upper/lower principal representations of the moment sequence.
Join the Shortest Queue (JSQ) is a popular routing policy for server farms. However, until now al... more Join the Shortest Queue (JSQ) is a popular routing policy for server farms. However, until now all analysis of JSQ has been limited to First-Come-First-Serve (FCFS) server farms, whereas it is known that web server farms are better modeled as Processor Sharing (PS) server farms. We provide the first approximate analysis of JSQ in the PS server farm model for general job-size distributions, obtaining the distribution of queue length at each queue. To do this, we approximate the queue length of each queue in the server farm by a one-dimensional Markov chain, in a novel fashion. We also discover some interesting insensitivity properties of PS server farms with JSQ routing, and discuss the near-optimality of JSQ.
Notice: This is the technical report version of a paper to be presented at the conference IEEE In... more Notice: This is the technical report version of a paper to be presented at the conference IEEE Infocom 2008, in Phoenix, AZ, on April 15-17, 2008. The paper has attracted some discussion in media following an article published by NewScientist (http://technology. newscientist.com/channel/tech/electronic-threats/dn13318-friendly-worms-could-spread-software-fixes.html), hence this note. Please note that we are part of the Systems and Networking group at Microsoft Research in Cambridge conducting basic computer science research which covers topics from improving the performance of individual computers to designing novel distributed systems that can scale to hundreds of thousands of hosts. Our focus is fundamental research on improving the efficiency of data distribution of all types across networks, and is not limited to certain scenarios or types of data, but investigating underlying networking techniques.Using understanding from the field of epidemiology is one of the methods that we are investigating in this area, and we hope that our research will help inform future computer science research and networking technology. This project is a basic computer science research, and there are no current plans to incorporate this into Microsoft products.
Power-proportional cluster-based storage is an important component of an overall cloud computing ... more Power-proportional cluster-based storage is an important component of an overall cloud computing infrastructure. With it, substantial subsets of nodes in the storage cluster can be turned off to save power during periods of low utilization. Rabbit is a distributed file system that arranges its data-layout to provide ideal power-proportionality down to very low minimum number of powered-up nodes (enough to store a primary replica of available datasets). Rabbit addresses the node failure rates of large-scale clusters with data layouts that minimize the number of nodes that must be powered-up if a primary fails. Rabbit also allows different datasets to use different subsets of nodes as a building block for interference avoidance when the infrastructure is shared by multiple tenants. Experiments with a Rabbit prototype demonstrate its power-proportionality, and simulation experiments demonstrate its properties at scale.
Systems whose arrival or service rates fluctuate over time are very common, but are still not wel... more Systems whose arrival or service rates fluctuate over time are very common, but are still not well understood analytically. Stationary formulas are poor predictors of systems with fluctuating load. When the arrival and service processes fluctuate in a Markovian manner, computational methods, such as Matrix-analytic and spectral analysis, have been instrumental in the numerical evaluation of quantities like mean response time. However, such computational tools provide only limited insight into the functional behavior of the system with respect to its primitive input parameters: the arrival rates, service rates, and rate of fluctuation. For example, the shape of the function that maps rate of fluctuation to mean response time is not well understood, even for an M/M/1 system. Is this function increasing, decreasing, monotonic? How is its shape affected by the primitive input parameters? Is there a simple closed-form approximation for the shape of this curve? Turning to user experience: How is the performance experienced by a user arriving into a "high load" period different from that of a user arriving into a "low load" period, or simply a random user. Are there stochastic relations between these? In this work, we provide the first answers to these fundamental questions.
We consider the problem of admission control in resource sharing systems, such as web servers and... more We consider the problem of admission control in resource sharing systems, such as web servers and transaction processing systems, when the job size distribution has high variability, with the aim of minimizing the mean response time. It is well known that in such resource sharing systems, as the number of tasks concurrently sharing the resource is increased, the server throughput initially increases, due to more efficient utilization of resources, but starts falling beyond a certain point, due to resource contention and thrashing. Most admission control mechanisms solve this problem by imposing a fixed upper bound on the number of concurrent transactions allowed into the system, called the Multi-Programming-Limit (MPL), and making the arrivals which find the server full queue up. Almost always, the MPL is chosen to be the point that maximizes server efficiency. In this paper we abstract such resource sharing systems as a Processor Sharing (PS) server with state-dependent service rate and a First-Come-First-Served (FCFS) queue, and we analyze the performance of this model from a queueing theoretic perspective. We start by showing that, counter to the common wisdom, the peak efficiency point is not always optimal for minimizing the mean response time. Instead, significant performance gains can be obtained by running the system at less than the peak efficiency. We provide a simple expression for the static MPL that achieves near-optimal mean response time for general distributions. Next we present two traffic-oblivious dynamic admission control policies that adjust the MPL based on the instantaneous queue length while also taking into account the variability of the job size distribution. The structure of our admission control policies is a mixture of fluid control when the number of jobs in the system is high, with a stochastic component when the system is near-empty. We show via simulations that our dynamic policies are much more robust to unknown traffic intensities and burstiness in the arrival process than imposing a static MPL.
The M/G/K queueing system is the oldest model for multi-server systems, and has been the topic of... more The M/G/K queueing system is the oldest model for multi-server systems, and has been the topic of performance papers for almost half a century. However, even now, only coarse approximations exist for its mean waiting time. All the closed-form (non-numerical) approximations in the literature are based on the first two moments of the job size distribution. In this paper we prove that no approximation based on only the first two moments can be accurate for all job size distributions, and we provide a lower bound on the inapproximability ratio. This is the first such result in the literature. The proof technique behind this result is novel as well and combines mean value analysis, sample path techniques, scheduling, regenerative arguments, and asymptotic estimates. Finally, our work provides insight into the effect of higher moments of the job size distribution on the mean waiting time.
A central question in designing server farms today is how to efficiently provision the number of ... more A central question in designing server farms today is how to efficiently provision the number of servers to extract the best performance under unpredictable demand patterns while not wasting energy. While one would like to turn servers off when they become idle to save energy, the large setup cost (both, in terms of setup time and energy penalty) needed to switch the server back on can adversely affect performance. The problem is made more complex by the fact that today's servers provide multiple sleep or standby states which trade off the setup cost with the power consumed while the server is 'sleeping'. With so many controls, finding the optimal server farm management policy is an almost intractable problem -How many servers should be on at any given time, how many should be off, and how many should be in some sleep state? In this paper, we employ the popular metric of Energy-Response time Product (ERP) to capture the energy-performance tradeoff, and present the first theoretical results on the optimality of server farm management policies. For a stationary demand pattern, we prove that there exists a very small, natural class of policies that always contains the optimal policy for a single server, and conjecture it to contain a near-optimal policy for multi-server systems. For time-varying demand patterns, we propose a simple, traffic-oblivious policy and provide analytical and empirical evidence for its near-optimality.
A central question in designing server farms today is how to efficiently provision the number of ... more A central question in designing server farms today is how to efficiently provision the number of servers to handle unpredictable demand patterns, so as to extract the best performance while not wasting energy. While one would like to turn servers off when they become idle to save energy, the large setup cost (both, in terms of setup time and energy penalty) needed to switch the server back on can adversely affect performance. The problem is made more complex by the fact that today's servers provide multiple sleep or standby states which trade off the setup cost with the power consumed while the server is 'sleeping'. With so many controls, finding the optimal server pool management policy is an almost intractable problem -How many servers should be on at any given time, how many should be off, and how many should be in some sleep state?
ACM SIGMETRICS Performance Evaluation Review, Jan 1, 2008
We consider the round robin (RR) scheduling policy where the server processes each job in its buf... more We consider the round robin (RR) scheduling policy where the server processes each job in its buffer for at most a fixed quantum, q, in a round-robin fashion. The processor sharing (PS) policy is an idealization of the quantum-based round-robin scheduling in the limit where the quantum size becomes infinitesimal, and has been the subject of many papers. It is well known that the mean response time in an M/G/1/P S queue depends on the job size distribution via only its mean. However, almost no explicit results are available for the round-robin policy. For example, how does the variability of job sizes affect the mean response time in an M/G/1/RR queue? How does one choose the optimal quantum size in the presence of switching overheads? In this paper we present some preliminary answers to these fundamental questions.
The M/G/K queueing system is the oldest model for multi-server systems, and has been the topic of... more The M/G/K queueing system is the oldest model for multi-server systems, and has been the topic of performance papers for almost half a century. However, even now, only coarse approximations exist for its mean waiting time. All the closed-form (non-numerical) approximations in the literature are based on the first two moments of the job size distribution. In this paper we prove that no approximation based on only the first two moments can be accurate for all job size distributions, and we provide a lower bound on the inapproximability ratio. This is the first such result in the literature. The proof technique behind this result is novel as well and combines mean value analysis, sample path techniques, scheduling, regenerative arguments, and asymptotic estimates. Finally, our work provides insight into the effect of higher moments of the job size distribution on the mean waiting time.
ACM SIGMETRICS Performance Evaluation …, Jan 1, 2008
We obtain the Laplace transform of the fluid level probability density function, in terms of the ... more We obtain the Laplace transform of the fluid level probability density function, in terms of the on-period density function, for a fluid queue (or reservoir) with on-off input at equilibrium. We further obtain explicit expressions for the moments of fluid level in terms of the moments of the on-period and hence derive an algorithm for the moments of fluid level at every queue in a tandem network. It turns out that to calculate the kth moment at the ith queue, only the first k + 1 moments of the on-period of the input process to the first queue are required.
We consider the bipartite matching model of customers and servers introduced by Caldentey, Kaplan... more We consider the bipartite matching model of customers and servers introduced by Caldentey, Kaplan, and Weiss (Adv. Appl. Probab., 2009). Customers and servers play symmetrical roles. There is a finite set C, resp. S, of customer, resp. server, classes. Time is discrete and at each time step, one customer and one server arrive in the system according to a joint probability measure µ on C × S, independently of the past. Also, at each time step, pairs of matched customer and server, if they exist, depart from the system. Authorized matchings are given by a fixed bipartite graph (C, S, E ⊂ C × S). A matching policy is chosen, which decides how to match when there are several possibilities. Customers/servers that cannot be matched are stored in a buffer. The evolution of the model can be described by a discrete time Markov chain. We study its stability under various admissible matching policies including: ML (Match the Longest), MS (Match the Shortest), FIFO (match the oldest), priorities. There exist natural necessary conditions for stability (independent of the matching policy) defining the maximal possible stability region. For some bipartite graphs, we prove that the stability region is indeed maximal for any admissible matching policy. For the ML policy, we prove that the stability region is maximal for any bipartite graph. For the MS and priority policies, we exhibit a bipartite graph with a non-maximal stability region.
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Papers by Varun Gupta