Siva Theja Maguluri

Stochastic models of load balancing and scheduling in cloud computing clusters

Cloud computing services are becoming ubiquitous, and are starting to serve as the primary source of computing power for both enterprises and personal computing applications. We consider a stochastic model of a cloud computing cluster, where jobs arrive according to a stochastic process and request virtual machines (VMs), which are specified in terms of resources such as CPU, memory and storage space. While there are many design issues associated with such systems, here we focus only on resource allocation problems, such as the design of algorithms for load balancing among servers, and algorithms for scheduling VM configurations. Given our model of a cloud, we first define its capacity, i.e., the maximum rates at which jobs can be processed in such a system. Then, we show that the widely-used Best-Fit scheduling algorithm is not throughput-optimal, and present alternatives which achieve any arbitrary fraction of the capacity region of the cloud. We then study the delay performance of these alternative algorithms through simulations.

Scheduling jobs with unknown duration in clouds

We consider a stochastic model of jobs arriving at a cloud data center. Each job requests a certain amount of CPU, memory, disk space, etc. Job sizes (durations) are also modeled as random variables, with possibly unbounded support. These jobs need to be scheduled nonpreemptively on servers. The jobs are first routed to one of the servers when they arrive and are queued at the servers. Each server then chooses a set of jobs from its queues so that it has enough resources to serve all of them simultaneously. This problem has been studied previously under the assumption that job sizes are known and upper-bounded, and an algorithm was proposed that stabilizes traffic load in a diminished capacity region. Here, we present a load balancing and scheduling algorithm that is throughput-optimal, without assuming that job sizes are known or are upper-bounded.We consider a stochastic model of jobs arriving at a cloud data center. Each job requests a certain amount of CPU, memory, disk space, etc. Job sizes (durations) are also modeled as random variables, with possibly unbounded support. These jobs need to be scheduled nonpreemptively on servers. The jobs are first routed to one of the servers when they arrive and are queued at the servers. Each server then chooses a set of jobs from its queues so that it has enough resources to serve all of them simultaneously. This problem has been studied previously under the assumption that job sizes are known and upper-bounded, and an algorithm was proposed that stabilizes traffic load in a diminished capacity region. Here, we present a load balancing and scheduling algorithm that is throughput-optimal, without assuming that job sizes are known or are upper-bounded.

Optimal Heavy-Traffic Queue Length Scaling in an Incompletely Saturated Switch

We consider an input queued switch operating under the MaxWeight scheduling algorithm. This system is interesting to study because it is a model for Internet routers and data center networks. Recently, it was shown that the MaxWeight algorithm has optimal heavy-traffic queue length scaling when all ports are uniformly saturated. Here we consider the case where a fraction of the ports are saturated and others are not (which we call the incompletely saturated case), and also the case where the rates at which the ports are saturated can be different. We use a recently developed drift technique to show that the heavy-traffic queue length under the MaxWeight scheduling algorithm has optimal scaling with respect to the switch size even in these cases.

The stability of longest-queue-first scheduling with variable packet sizes

It is well known that the MaxWeight scheduling algorithm is throughput-optimal in wireless networks. However, its complexity is exponential in the number of links in an ad hoc network. In this work, we consider a greedy variant of the MaxWeight algorithm, called Longest Queue First (LQF). A synchronous version of LQF is known to be throughput-optimal under a topological condition called local pooling. Here we study an asynchronous version of LQF which is suitable for implementation in networks with variable packet sizes. We show that asynchronous LQF is also throughput-optimal under the local pooling condition.

Heavy traffic queue length behavior in switches with reconfiguration delay

Optical switches have been drawing attention due to their large data bandwidth and low power consumption. However, scheduling policies need to account for the schedule reconfiguration delay of optical switches to achieve good performance. The Adaptive MaxWeight policy achieves optimal throughput for switches with nonzero reconfiguration delay, and has been shown in simulation to have good delay performance. In this paper, we analyze the queue length behavior of a switch with nonzero reconfiguration delay operating under the Adaptive MaxWeight. We first show that the Adaptive MaxWeight policy exhibits a weak state space collapse behavior in steady-state, which could be viewed as an inheritance of the MaxWeight policy in a switch with zero reconfiguration delay. We then use the weak state space collapse result to obtain a steady state delay bound under the Adaptive MaxWeight algorithm in heavy traffic by applying a recently developed drift technique. The resulting delay bound is dependent on the expected schedule duration. We then derive the relation between the expected schedule duration and the steady state queue length through drift analysis, and obtain asymptotically tight queue length bounds in the heavy traffic regime.

Heavy-Traffic Behavior of the MaxWeight Algorithm in a Switch with Uniform Traffic

We consider a switch with uniform traffic operating under the MaxWeight scheduling algorithm. This traffic pattern is interesting to study in the heavy-traffic regime since the queue lengths exhibit a multi-dimensional state-space collapse. We use a Lyapunov-type drift technique to characterize the heavy-traffic behavior of the expectation of the sum queue lengths in steady-state. Specifically, in the case of Bernoulli arrivals, we show that the heavy-traffic scaled queue length is (n -- 3/2 + 1/2n). Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern. This settles the heavy-traffic version of an open conjecture.

Heavy-traffic delay insensitivity in connection-level models of data transfer with proportionally fair bandwidth sharing

Motivated by the stringent requirements on delay performance in data center networks, we study a connection-level model for bandwidth sharing among data transfer flows, where file sizes have phase-type distributions and proportionally fair bandwidth allocation is used. We analyze the expected number of files in steady-state by setting the steady-state drift of an appropriately chosen Lyapunov function equal to zero. We consider the heavy-traffic regime and obtain asymptotically tight bounds on the expected number of files in the system. Our results show that the expected number of files under proportionally fair bandwidth allocation is insensitive in heavy traffic to file size distributions, thus complementing the diffusion approximation result of Vlasiou et al. [20].

An Optimal Scheduling Policy for the 2 X 2 Input-Queued Switch with Symmetric Arrival Rates

We investigate a cannonical input-queued switch scheduling problem in which the objective is to minimize the infinite horizon discounted queue length under symmetric arrivals, for which we derive an optimal scheduling policy and establish its theoretical properties with respect to delay. We then compare via simulation these theoretical properties of our optimal policy with those of the well-known MaxWeight scheduling algorithm in order to gain insights on the delay optimality of the MaxWeight scheduling policy.We investigate a cannonical input-queued switch scheduling problem in which the objective is to minimize the infinite horizon discounted queue length under symmetric arrivals, for which we derive an optimal scheduling policy and establish its theoretical properties with respect to delay. We then compare via simulation these theoretical properties of our optimal policy with those of the well-known MaxWeight scheduling algorithm in order to gain insights on the delay optimality of the MaxWeight scheduling policy.

Optimal heavy-traffic queue length scaling in an incompletely saturated switch

We consider an input-queued switch operating under the MaxWeight scheduling algorithm. This system is interesting to study because it is a model for Internet routers and data center networks. Recently, it was shown that the MaxWeight algorithm has optimal heavy-traffic queue length scaling when all ports are uniformly saturated. Here we consider the case when an arbitrary number of ports are saturated (which we call the incompletely saturated case), and each port is allowed to saturate at a different rate. We use a recently developed drift technique to show that the heavy-traffic queue length under the MaxWeight scheduling algorithm has optimal scaling with respect to the switch size even in these cases.

On optimal portfolios of dynamic resource allocations

We consider the optimal allocation of generic resources among multiple generic entities of interest over a finite planning horizon, where each entity generates stochastic returns as a function of its resource allocation during each period. The main objective is to maximize the expected return while at the same time managing risk to an acceptable level for each period. We devise a general solution framework and establish how to obtain the optimal dynamic resource allocation.