相关论文: The Gittins Policy in the M/G/1 Queue
In this paper we describe a perfect simulation algorithm for the stable $M/G/c$ queue. Sigman (2011: Exact Simulation of the Stationary Distribution of the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209--213) showed how to build…
In the budgeted learning problem, we are allowed to experiment on a set of alternatives (given a fixed experimentation budget) with the goal of picking a single alternative with the largest possible expected payoff. Approximation algorithms…
This paper considers the efficient exact computation of the counterpart of the Gittins index for a finite-horizon discrete-state bandit, which measures for each initial state the average productivity, given by the maximum ratio of expected…
We study a multiclass M/M/1 queueing control problem with finite buffers under heavy-traffic where the decision maker is uncertain about the rates of arrivals and service of the system and by scheduling and admission/rejection decisions…
Scheduling a stream of jobs whose holding cost changes over time is a classic and practical problem. Specifically, each job is associated with a holding cost (penalty), where a job's instantaneous holding cost is some increasing function of…
Gittins indices provide an optimal solution to the classical multi-armed bandit problem. An obstacle to their use has been the common perception that their computation is very difficult. This paper demonstrates an accessible general…
The trade-off between the cost of acquiring and processing data, and uncertainty due to a lack of data is fundamental in machine learning. A basic instance of this trade-off is the problem of deciding when to make noisy and costly…
In this paper, we analyze how well a machine can solve a general problem in queueing theory. To answer this question, we use a deep learning model to predict the stationary queue-length distribution of an $M/G/1$ queue (Poisson arrivals,…
In this paper,we consider the restless bandit problem, which is one of the most well-studied generalizations of the celebrated stochastic multi-armed bandit problem in decision theory. However, it is known be PSPACE-Hard to approximate to…
We consider the problem of scheduling to minimize mean response time in M/G/1 queues where only estimated job sizes (processing times) are known to the scheduler, where a job of true size $s$ has estimated size in the interval $[\beta s,…
We consider a multi-class G/G/1 queue with a finite shared buffer. There is task admission and server scheduling control which aims to minimize the cost which consists of holding and rejection components. We construct a policy that is…
This note gives a short, self-contained, proof of a sharp connection between Gittins indices and Bayesian upper confidence bound algorithms. I consider a Gaussian multi-armed bandit problem with discount factor $\gamma$. The Gittins index…
The Knowledge Gradient (KG) policy was originally proposed for online ranking and selection problems but has recently been adapted for use in online decision making in general and multi-armed bandit problems (MABs) in particular. We study…
We consider the minimax setup for Gaussian one-armed bandit problem, i.e. the two-armed bandit problem with Gaussian distributions of incomes and known distribution corresponding to the first arm. This setup naturally arises when the…
The subject of this paper is the problem of estimating service time distribution of the $M/G/\infty$ queue from incomplete data on the queue. The goal is to estimate $G$ from observations of the queue--length process at the points of the…
Whittle index is a generalization of Gittins index that provides very efficient allocation rules for restless multi-armed bandits. In this work, we develop an algorithm to test the indexability and compute the Whittle indices of any…
We study the asymptotic response time tail in the M/G/n multi-server queue with heavy-tailed (regularly varying) job sizes, a setting representative of modern computing workloads. For single-server systems, tail optimization is well…
This paper presents a new \emph{fast-pivoting} algorithm that computes the $n$ Gittins index values of an $n$-state bandit -- in the discounted and undiscounted cases -- by performing $(2/3) n^3 + O(n^2)$ arithmetic operations, thus…
In this paper, we study the $G/\mathit{GI}/N$ queue in the Halfin--Whitt regime. Our first result is to obtain a deterministic fluid limit for the properly centered and scaled number of customers in the system which may be used to provide a…
This paper examines multi-armed bandits in which actions are taken at random discrete times. The model consists of $J$ independent arms. When an arm is operated, it must remain active for a random duration, modeled by the inter-arrival time…