We consider the problem of load balancing in parallel queues by transferring customers between them at discrete points in time. Holding costs accrue as customers wait in the queue, while transfer decisions incur both fixed (setup) costs and variable costs that increase with the number of transfers and travel distance, and vary by transfer direction. Our work is primarily motivated by inter-facility patient transfers to address imbalanced congestion and inequity in access to care during surges in hospital demand. Analyzing an associated fluid control problem, we show that under general assumptions, including time-varying arrivals and convex holding costs, the optimal policy partitions the state-space into a well-defined $\textit{no-transfer region}$ and its complement, implying that transferring is optimal if and only if the system is sufficiently imbalanced. In the absence of fixed transfer costs, an optimal policy moves the state to the no-transfer region's boundary; in contrast, with fixed costs, the state is moved to its relative interior. Leveraging our structural results, we propose a simulation-based approximate dynamic programming (ADP) algorithm to find effective transfer policies for the stochastic system. We investigate the performance and robustness of the fluid and ADP policies in a case study calibrated using data during the COVID-19 pandemic in the Greater Toronto Area, which demonstrates that transferring patients between hospitals could result in up to 27.7% reduction in total cost with relatively few transfers.
This paper considers a Markovian model for the optimal dynamic routing of homogeneous traffic to parallel heterogeneous queues, each having its own finite input buffer and server pool, where buffer and server-pool sizes, as well as service rates, may differ across queues. The main goal is to identify a heuristic index-based routing policy with low complexity that consistently attains a nearly minimum average loss rate (or, equivalently, maximum throughput rate). A second goal is to compare alternative policies, with respect to computational demands and empirical performance. A novel routing po…
We study the design of dynamic scheduling controls in closed queueing networks with a fixed number of jobs. Each time a server becomes available, the controller has (limited) flexibility in choosing the buffer from which to serve a job. If no jobs are available at any compatible buffer, the server idles. If the job is served, it relocates to a ``destination'' buffer. We study how to maximize throughput in steady state via a large deviations analysis. We propose a family of simple state-dependent policies called Scaled MaxWeight (SMW) policies that dynamically manage the distribution of jobs in…
The paper deals with Age of Information (AoI) in a network of multiple sources and parallel queues with buffering capabilities, preemption in service and losses in served packets. The queues do not communicate between each other and the packets are dispatched through the queues according to a predefined probabilistic routing. By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average AoI of a system of two parallel queues (with and without buffer capabilities) and compare the results with those of a single queue. We show that known results of packets del…
A New Condition for the Existence of Optimal Stationary Policies in Denumerable State Average Cost Continuous Time Markov Decision Processes with Unbounded Cost and Transition Rates
We consider a single server queueing system with two classes of jobs: eager jobs with small sizes that require service to begin almost immediately upon arrival, and tolerant jobs with larger sizes that can wait for service. While blocking probability is the relevant performance metric for the eager class, the tolerant class seeks to minimize its mean sojourn time. In this paper, we discuss the performance of each class under dynamic scheduling policies, where the scheduling of both classes depends on the instantaneous state of the system. This analysis is carried out under a certain fluid limi…
University of California, Berkeley（加州大学伯克利分校）；UCLA Anderson School of Management（加州大学洛杉矶分校安德森管理学院）；Cornell University（康奈尔大学）；Columbia Business School（哥伦比亚商学院）；Uber Technologies, Inc.（优步科技有限公司）
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 full refund if deadlines are missed. The service provider leases computing resources from an infrastructure provider in a two-tier scheme: long-term leasing of basic infrastructure, consisting of heterogeneous parallel service nodes, each modeled as a multi-server queue, and short-term leasing of external servers. Given the intractability of computing an optima…
We consider an auto-scaling technique in a cloud system where virtual machines hosted on a physical node are turned on and off depending on the queue's occupation (or thresholds), in order to minimise a global cost integrating both energy consumption and performance. We propose several efficient optimisation methods to find threshold values minimising this global cost: local search heuristics coupled with aggregation of Markov chain and with queues approximation techniques to reduce the execution time and improve the accuracy. The second approach tackles the problem with a Markov Decision Proc…
