Dynamic Routing of Customers With General Delay Costs in a Multiserver Queuing System

Abstract

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We consider a network of parallel service stations each modeled as a single-server queue. Each station serves its own dedicated customers as well as generic customers who are routed from a central controller. We suppose that the cost incurred by a customer is an increasing function of her time spent in the system. In a significant advance on most previous work, we do not require waiting costs to be convex, still less linear. With the objective of minimizing the long-run average waiting cost, we develop two heuristic routing policies, one of which is based on dynamic programming policy improvement and the other on Lagrangian relaxation. In developing the latter policy, we show that each station is "indexable" under mild conditions for customers' waiting costs and also prove some structural results on the admission control problem that naturally arises as a result of the Lagrangian relaxation. We then test the performance of our heuristics in an extensive numerical study and show that the Lagrangian heuristic demonstrates a strong level of performance in a range of traffic conditions. In particular, it clearly outperforms both a greedy heuristic, which is a standard proposal in complex routing problems, and a recent proposal from the heavy traffic literature.

Dynamic Scheduling of Home Health Care Patients to Medical Providers

“…Zenios et al (2000) use it to derive fair allocation polices to maximize quality-adjusted lifeyears for patients on the kidney transplant list. Opp et al (2005) and Argon et al (2009) apply the technique to route customers in a queueing network. Liu et al (2010) use the approach to compare scheduling polices in a primary care practice.…”

Beyond Shortest Queue Routing with Heterogeneous Servers and General Cost Functions

“…This approach, referred to as first policy iteration (FPI), tends to yield an efficient, though generally not optimal, policy. The FPI approach has been utilized in numerous papers [2,8,10].…”

Containment of socially optimal policies in multiple-facility Markovian queueing systems

“…Stidham and Weber (1993) provide an overview of MDP models for the control of queueing networks. It is well-known that optimal policies for the allocation of customers to parallel heterogeneous queues are not easy to characterize; for this reason, heuristic approaches have been developed which have achieved promising results in applications (see Argon et al, 2009;Glazebrook et al, 2009). In attempting to identify or approximate an optimal policy, one aims to find a dynamic decision-making scheme which optimizes the overall performance of the system with respect to a given criterion; we refer to such a scheme as a socially optimal solution to the optimization problem associated with the MDP.…”