Related papers: Scheduling in the high uncertainty heavy traffic r…
We consider a system of $N$ parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any,…
Modern computing workloads are often composed of parallelizable jobs. A parallelizable job can be completed more quickly when run on additional servers. However, each job can only use a limited number of servers, known as its…
We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates are i.i.d. random…
We consider optimal control of a stochastic network,where service is controlled to prevent buffer overflow. We use a risk-sensitive escape time criterion, which in comparison to the ordinary escape time criteria heavily penalizes exits…
In this paper, we study the stability of light traffic achieved by a scheduling algorithm which is suitable for heterogeneous traffic networks. Since analyzing a scheduling algorithm is intractable using the conventional mathematical tool,…
Proportional fairness is a popular service allocation mechanism to describe and analyze the performance of data networks at flow level. Recently, several authors have shown that the invariant distribution of such networks admits a product…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
We consider the steady-state distribution of the sojourn time of a job entering an M/GI/1 queue with the foreground-background scheduling policy in heavy traffic. The growth rate of its mean, as well as the limiting distribution, are…
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift…
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…
We study infinite-horizon asymptotic average optimality for parallel server network with multiple classes of jobs and multiple server pools in the Halfin-Whitt regime. Three control formulations are considered: 1) minimizing the queueing…
Healthcare systems are facing serious challenges in balancing their human resources to cope with volatile service demand, while at the same time providing necessary job satisfaction to the healthcare workers. We propose in this paper a…
We consider the traffic assignment problem in nonatomic routing games where the players' cost functions may be subject to random fluctuations (e.g., weather disturbances, perturbations in the underlying network, etc.). We tackle this…
We consider general large-scale service systems with multiple customer classes and multiple server (agent) pools, mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing…
In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of…
For a multiclass G/G/1 queue with finite buffers, admission and scheduling control, and holding and rejection costs, we construct a policy that is asymptotically optimal in the heavy traffic limit. The policy is specified in terms of a…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
In this paper, we study a distributed optimization problem for a class of high-order multi-agent systems with unknown dynamics. In comparison with existing results for integrators or linear agents, we need to overcome the difficulties…
In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…