arXiv subjects

Sigrún Andradóttir

Publications and source records attributed to Sigrún Andradóttir.

3 recordsLinked to original sources

arXiv2026

Indifference-Zone Relaxation Procedures for Finding Feasible Systems

We consider the problem of finding feasible systems with respect to stochastic constraints when system performance is evaluated through simulation. Our objective is to solve this problem with high computational efficiency and statistical validity. Existing indifference-zone (IZ) procedures introduce a fixed tolerance level, which denotes how much deviation the decision-maker is willing to accept from the threshold in the constraint. These procedures are developed under the assumption that all systems' performance measures are exactly the tolerance level away from the threshold, leading to unnecessary simulations. In contrast, IZ-free procedures, which eliminate the tolerance level, perform well when systems' performance measures are far from the threshold. However, they may significantly underperform compared to IZ procedures when systems' performance measures are close to the threshold. To address these challenges, we propose the Indifference-Zone Relaxation (IZR) procedure, IZR introduces a set of relaxed tolerance levels and utilizes two subroutines for each level: one to identify systems that are clearly feasible and the other to exclude those that are clearly infeasible. We also develop the IZR procedure with estimation (IZE), which introduces two relaxed tolerance levels for each system and constraint: one matching the original tolerance level and the other based on an estimate of the system's performance measure. By employing different tolerance levels, these procedures facilitate early feasibility determination with statistical validity. We prove that IZR and IZE determine system feasibility with the desired probability and show through experiments that they significantly reduce the number of observations required compared to an existing procedure.

eess.SY↗

arXiv2026

Pricing in Queues with Abandonments: Optimal Policies and Practical Heuristics

We investigate the optimal pricing strategy in a service-providing framework, where customers can leave the system prior to service completion. In this setting, a price is quoted to an incoming customer based on the current number of customers in the system. When the quoted price is lower than the price the incoming customer is willing to pay (which follows a fixed probability distribution), then the customer joins the system and a reward equal to the quoted price is earned. A cost is incurred upon abandonment and a holding cost is incurred for customers waiting to be served. Our goal is to determine the pricing policy that maximizes the long-run average profit. Unlike traditional queueing systems without abandonments, we show that the optimal quoted prices do not always increase with the queue length in this setting. We fully characterize the possible structure of the optimal dynamic pricing policy and provide conditions guaranteeing that the optimal policy is increasing in the number of customers in the system. Moreover, we introduce two heuristics that simplify the optimal dynamic pricing policy. Both heuristics admit customers until the number of customers in the system reaches a certain threshold. The cutoff-static policy charges all admitted customers a fixed price while the two-price policy charges one price when the arriving customer can enter service immediately and another price if the customer needs to wait. By selecting the price(s) and threshold that maximize the long-run average profit, both heuristics achieve near optimality in general and the two-price policy provides more robustness compared to the cutoff-static policy.

math.OC↗

arXiv2026

Collaboration versus Specialization in Service Systems with Impatient Customers

We study tandem queueing systems in which servers work more efficiently in teams than on their own and customers are impatient in that they may leave the system while waiting for service. Our goal is to determine the server assignment policy that maximizes the long-run average throughput. We show that when each server is equally skilled at all tasks, the optimal policy has all the servers working together at all times. We also provide a complete characterization of the optimal policy for Markovian systems with two stations and two servers when each server's efficiency may be task dependent. We show that the throughput is maximized under the policy which assigns one server to each station (based on their relative skill at that station) unless station 2 has no work (in which case both servers work at station 1) or the number of customers in the buffer reaches a threshold whose value we characterize (in which case both servers work at station 2). We study how the optimal policy varies with the level of server synergy (including no synergy) and also compare the optimal policy for systems with different customer abandonment rates (including no abandonments). Finally, we investigate the case where the synergy among collaborating servers can be task-dependent and provide numerical results.

math.PR↗