Adaptive Matching for Expert Systems with Uncertain Task Types

A matching in a two-sided market often incurs an externality: a matched resource may become unavailable to the other side of the market, at least for a while. This is especially an issue in online platforms involving human experts as the expert resources are often scarce. The efficient utilization of experts in these platforms is made challenging by the fact that the information available about the parties involved is usually limited. To address this challenge, we develop a model of a task-expert matching system where a task is matched to an expert using not only the prior information about the task but also the feedback obtained from the past matches. In our model the tasks arrive online while the experts are fixed and constrained by a finite service capacity. For this model, we characterize the maximum task resolution throughput a platform can achieve. We show that the natural greedy approaches where each expert is assigned a task most suitable to her skill is suboptimal, as it does not internalize the above externality. We develop a throughput optimal backpressure algorithm which does so by accounting for the `congestion' among different task types. Finally, we validate our model and confirm our theoretical findings with data-driven simulations via logs of Math.StackExchange, a StackOverflow forum dedicated to mathematics.Comment: A part of it presented at Allerton Conference 2017, 18 page

Spare parts provisioning for multiple k-out-of-n:G systems

In this paper, we consider a repair shop that fixes failed components from different k-out-of-n:G systems. We assume that each system consists of the same type of component; to increase availability, a certain number of components are stocked as spare parts. We permit a shared inventory serving all systems and/or reserved inventories for each system; we call this a hybrid model. Additionally, we consider two alternative dispatching rules for the repaired component. The destination for a repaired component can be chosen either on a first-come-first-served basis or by following a static priority rule. Our analysis gives the steady-state system size distribution of the two alternative models at the repair shop. We conduct numerical examples minimizing the spare parts held while subjecting the availability of each system to exceed a targeted value. Our findings show that unless the availabilities of systems are close, the HP policy is better than the HF policy

Analysis of Scheduling Policies for a M/G/I Queue with Rework

This thesis analyzes a multi-class M/G/1 priority queueing system in which distinct job types require one service cycle and, with non-zero probability, require a second service cycle. The main objective is to find a new heuristic scheduling policy that minimizes the long-run expected holding and preemption costs. Arrival rates, service rates, and the probability of undertaking second service are all class specific. A mean value analysis (MVA) approach was employed to derive the long- run mean time in queue for each job type under each policy, thereby providing the appropriate cost equations. Numerical experiments suggest that the preemptive resume scheduling policy yields the lowest cost most frequently

Recent Advances in Accumulating Priority Queues

This thesis extends the theory underlying the Accumulating Priority Queue (APQ) in three directions. In the first, we present a multi-class multi-server accumulating priority queue with Poisson arrivals and heterogeneous services. The waiting time distributions for different classes have been derived. A conservation law for systems with heterogeneous servers has been studied. We also investigate an optimization problem to find the optimal level of heterogeneity in the multi-server system. Numerical investigations through simulation are carried out to validate the model. We next focus on a queueing system with Poisson arrivals, generally distributed service times and nonlinear priority accumulation functions. We start with an extension of the power-law APQ in Kleinrock and Finkelstein (1967), and use a general argument to show that there is a linear system of the form discussed in Stanford, Taylor, and Ziedins (2014) which has the same priority ordering of all customers present at any given instant in time, for any sample path. Beyond the power-law case, we subsequently characterize the class of nonlinear accumulating priority queues for which an equivalent linear APQ can be found, in the sense that the waiting time distributions for each of the classes are identical in both the linear and nonlinear systems. Many operational queuing systems must adhere to waiting time targets known as Key Performance Indicators (KPIs), particularly in health care applications. In the last aspect, we address an optimization problem to minimize the weighted average of the expected excess waiting time (WAE), so as to achieve the optimal performance of a system operating under KPIs. We then find that the Accumulating Priority queuing discipline is well suited to systems with KPIs, in that each class of customers progresses fairly towards timely access by its own waiting time limit. Due to the difficulties in minimizing the WAE, we introduce a surrogate objective function, the integrated weighted average excess (IWAE), which provides a useful proxy for WAE. Finally, we propose a rule of thumb in which patients in the various classes accumulate priority credit at a rate that is inversely proportional to their time limits