On the Dynamic Control of Matching Queues

Abstract

We consider the optimal control of matching queues with random arrivals. In this model, items arrive to dedicated queues, and wait to be matched with items from other (possibly multiple) queues. A match type corresponds to the set of item classes required for a match. Once a decision has been made to perform a match, the matching itself is instantaneous and the matched items depart from the system. We consider the problem of minimizing finite-horizon cumulative holding costs. The controller must decide which matchings to execute given multiple options. In principle, the controller may choose to wait until some "inventory" of items builds up to facilitate more profitable matches in the future.We introduce a multi-dimensional imbalance process, that at each time t, is given by a linear function of the cumulative arrivals to each of the item classes. A non-zero value of the imbalance at time t means that no control could have matched all the items that arrived by time t. A lower bound based on the imbalance process can be specified, at each time point, by a solution to an optimization problem with linear constraints. While not achievable in general, this lower bound can be asymptotically approached under a dedicated item condition (an analogue of the local traffic condition in bandwidth sharing networks). We devise a myopic discrete-review matching control that asymptotically-as the arrival rates become large-achieves the imbalance-based lower bound.

Gaussian Limits for a Fork-Join Network with Nonexchangeable Synchronization in Heavy Traffic

“…Both dissertations of Zviran [72] and Zaied [71] are motivated from applications in patient flow analysis. Gurvich and Ward [25] study optimal matching policies for a pure join model (Markovian) with multiple classes of jobs under certain matching constraints.…”

Optimal Dynamic Matching

“…Some recent models in inventory control have a similar flavor to the compatibility-based matching process considered byÜnver (2010); see, e.g.,Gurvich and Ward (2014) andHu and Zhou (2018).…”

Dynamic Matching for Real-Time Ride Sharing

“…Dynamic matching control has been studied in the literature in the context of kidney exchanges (Ünver 2010), housing markets (Leshno 2016), online matching platforms such as Upwork or Airbnb (Arnosti, Johari and Kanoria 2016), assemble-to-order manufacturing systems (Plambeck andWard 2006, Reiman andWang 2015), and more abstract queueing models (Gurvich and Ward 2014). However, the ride-sharing model is different enough that it is not clear whether any of the results of these studies carry over.…”

“…We consider a large market asymptotic regime in which number of drivers and customers grow without a bound. A similar large market regime is considered by Plambeck and Ward (2006), Gurvich and Ward (2014), Arnosti, Johari and Kanoria (2016), and Leshno (2016).…”