Related papers: An Infinite Dimensional Model for a Many Server Pr…
In this paper we look at content placement in the high-dimensional regime: there are n servers, and O(n) distinct types of content. Each server can store and serve O(1) types at any given time. Demands for these content types arrive, and…
In this paper, we analyze a retrial queueing system with Batch Markovian Arrival Processes and two types of customers. The rate of individual repeated attempts from the orbit is modulated according to a Markov Modulated Poisson Process.…
This paper considers a Markov decision model for profit maximization of a cloud computing service provider catering to customers submitting jobs with firm real-time random deadlines. Customers are charged on a per-job basis, receiving a…
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…
We consider a strategic M/M/1 queueing model under a first-come-first-served regime, where customers are split into two classes and class $A$ has priority over class $B$. Customers can decide whether to join the queue or balk, and, in case…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
We consider the following distributed service model: jobs with unit mean, general distribution, and independent processing times arrive as a renewal process of rate $\lambda n$, with $0<\lambda<1$, and are immediately dispatched to one of…
We study a fundamental model of resource allocation in which a finite number of resources must be assigned in an online manner to a heterogeneous stream of customers. The customers arrive randomly over time according to known stochastic…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
We study the problem of strategic choice of arrival time to a single-server queue with opening and closing times when there is uncertainty regarding service speed. A Poisson population of customers choose their arrival time with the goal of…
We present a simple dynamic equilibrium model for an online exchange where both buyers and sellers arrive according to a exogenously defined stochastic process. The structure of this exchange is motivated by the limit order book mechanism…
Motivated by the increasing importance of providing delay-guaranteed services in general computing and communication systems, and the recent wide adoption of learning and prediction in network control, in this work, we consider a general…
Modern Internet services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers. Because these services operate under strict performance requirements, a statistical…
We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal.…
In this paper we analyze a single server queue with batch arrivals and semi-Markovian service times. We also include the feature that the first service of each busy period might have a different distribution than subsequent service times.…
In this paper, we consider discrete-time D-BMAP/G/\inf queueing model. We construct effective discrete-time Markovian dynamics for this model and utilize it to derive exact time-dependent distribution of customer number and the…
This paper considers a BMAP/M/$\infty$ queue with a batch Markovian arrival process (BMAP) and an exponential service time distribution. We first prove that the BMAP/M/$\infty$ queue is stable if and only if the expectation of the logarithm…
Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…
We consider a multi-class queueing model of a telephone call center, in which a system manager dynamically allocates available servers to customer calls. Calls can terminate through either service completion or customer abandonment, and the…
In this study, we consider multi-class multi-server asymmetric queueing systems consisting of $N$ queues on one side and $K$ servers on the other side, where jobs randomly arrive in queues at each time. The service rate of each job-server…