Dynamic Service Rate Control for a Single Server Queue with Markov Modulated Arrivals

We consider the problem of service rate control of a single server queueing system with a finite-state Markov-modulated Poisson arrival process. We show that the optimal service rate is non-decreasing in the number of customers in the system; higher congestion rates warrant higher service rates. On the contrary, however, we show that the optimal service rate is not necessarily monotone in the current arrival rate. If the modulating process satisfies a stochastic monotonicity property the monotonicity is recovered. We examine several heuristics and show where heuristics are reasonable substitutes for the optimal control. None of the heuristics perform well in all the regimes. Secondly, we discuss when the Markov-modulated Poisson process with service rate control can act as a heuristic itself to approximate the control of a system with a periodic non-homogeneous Poisson arrival process. Not only is the current model of interest in the control of Internet or mobile networks with bursty traffic, but it is also useful in providing a tractable alternative for the control of service centers with non-stationary arrival rates.Comment: 32 Pages, 7 Figure

Towards Optimality in Parallel Scheduling

To keep pace with Moore's law, chip designers have focused on increasing the number of cores per chip rather than single core performance. In turn, modern jobs are often designed to run on any number of cores. However, to effectively leverage these multi-core chips, one must address the question of how many cores to assign to each job. Given that jobs receive sublinear speedups from additional cores, there is an obvious tradeoff: allocating more cores to an individual job reduces the job's runtime, but in turn decreases the efficiency of the overall system. We ask how the system should schedule jobs across cores so as to minimize the mean response time over a stream of incoming jobs. To answer this question, we develop an analytical model of jobs running on a multi-core machine. We prove that EQUI, a policy which continuously divides cores evenly across jobs, is optimal when all jobs follow a single speedup curve and have exponentially distributed sizes. EQUI requires jobs to change their level of parallelization while they run. Since this is not possible for all workloads, we consider a class of "fixed-width" policies, which choose a single level of parallelization, k, to use for all jobs. We prove that, surprisingly, it is possible to achieve EQUI's performance without requiring jobs to change their levels of parallelization by using the optimal fixed level of parallelization, k*. We also show how to analytically derive the optimal k* as a function of the system load, the speedup curve, and the job size distribution. In the case where jobs may follow different speedup curves, finding a good scheduling policy is even more challenging. We find that policies like EQUI which performed well in the case of a single speedup function now perform poorly. We propose a very simple policy, GREEDY*, which performs near-optimally when compared to the numerically-derived optimal policy

A Hierarchical Framework of Cloud Resource Allocation and Power Management Using Deep Reinforcement Learning

Automatic decision-making approaches, such as reinforcement learning (RL), have been applied to (partially) solve the resource allocation problem adaptively in the cloud computing system. However, a complete cloud resource allocation framework exhibits high dimensions in state and action spaces, which prohibit the usefulness of traditional RL techniques. In addition, high power consumption has become one of the critical concerns in design and control of cloud computing systems, which degrades system reliability and increases cooling cost. An effective dynamic power management (DPM) policy should minimize power consumption while maintaining performance degradation within an acceptable level. Thus, a joint virtual machine (VM) resource allocation and power management framework is critical to the overall cloud computing system. Moreover, novel solution framework is necessary to address the even higher dimensions in state and action spaces. In this paper, we propose a novel hierarchical framework for solving the overall resource allocation and power management problem in cloud computing systems. The proposed hierarchical framework comprises a global tier for VM resource allocation to the servers and a local tier for distributed power management of local servers. The emerging deep reinforcement learning (DRL) technique, which can deal with complicated control problems with large state space, is adopted to solve the global tier problem. Furthermore, an autoencoder and a novel weight sharing structure are adopted to handle the high-dimensional state space and accelerate the convergence speed. On the other hand, the local tier of distributed server power managements comprises an LSTM based workload predictor and a model-free RL based power manager, operating in a distributed manner.Comment: accepted by 37th IEEE International Conference on Distributed Computing (ICDCS 2017