Queueing models that are used to capture various service settings typically assume that customers require a single unit of resource (server) to be processed. However, there are many service settings where such an assumption may fail to capture the heterogeneity in resource requirements of different customers. We propose a multiserver queueing model with multiple customer classes in which customers from different classes may require different amounts of resources to be served. We study the optimal scheduling policy for such systems. To balance holding costs, service rates, resource requirement, and priority-induced idleness, we develop an index-based policy that we refer to as the idle-avoid [Formula: see text] rule. For a two-class two-server model, where policy-induced idleness can have a big impact on system performance, we characterize cases where the idle-avoid [Formula: see text] rule is optimal. In other cases, we establish a uniform performance bound on the amount of suboptimality incurred by the idle-avoid [Formula: see text] rule. For general multiclass multiserver queues, we establish the asymptotic optimality of the idle-avoid [Formula: see text] rule in the many-server regime. For long-time horizons, we show that the idle-avoid [Formula: see text] is throughput optimal. Our theoretical results, along with numerical experiments, provide support for the good and robust performance of the proposed policy.
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Dynamic Pricing and Matching for Two-Sided Queues
Motivated by applications from gig economy and online marketplaces, we study a two-sided queueing system under joint pricing and matching controls. The queueing system is modeled by a bipartite graph, where the vertices represent customer or server types and the edges represent compatible customer-server pairs. We propose a threshold-based two-price policy and queue length-based maximum-weight matching policy and show that it achieves a near-optimal profit. We study the system under the large-scale regime, wherein the arrival rates are scaled up, and under the large-market regime, wherein both the arrival rates and numbers of customer and server types increase. We show that two-price policy is a primary driver for optimality in the large-scale regime. We demonstrate the advantage of maximum-weight matching with respect to the number of customer and server types. Concurrently, we show that the interplay of pricing and matching is crucial for optimality in the large-market regime.
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- Award ID(s):
- 2145661
- PAR ID:
- 10482722
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- Operations Research
- Volume:
- 71
- Issue:
- 1
- ISSN:
- 0030-364X
- Page Range / eLocation ID:
- 83 to 100
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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