Matched Queues with Flexible Customers and Impatient Customers

This paper studies a double-ended queue with four Poisson inputs and flexible customers, and its stability is guaranteed by customers’ impatient behavior. We show that such a queue can be expressed as a quasi birth-and-death (QBD) process with infinitely many phases. For this purpose, we provide a detailed analysis for the QBD process, including the system stability, the stationary probability vector, the sojourn time, and so forth. Finally, numerical examples are employed to verify the correctness of our theoretical results, and demonstrate how the performance measures of this queue are influenced by key system parameters. We believe that the methodology and results described in this paper can be applied to analyze many practical issues, such as those encountered in sharing economy, organ transplantation, employee recruitment, onlinedating, and so on.

SRPT Scheduling Discipline in Many-Server Queues with Impatient Customers

The shortest-remaining-processing-time (SRPT) scheduling policy has been extensively studied, for more than 50 years, in single-server queues with infinitely patient jobs. Yet, much less is known about its performance in multiserver queues. In this paper, we present the first theoretical analysis of SRPT in multiserver queues with abandonment. In particular, we consider the [Formula: see text] queue and demonstrate that, in the many-sever overloaded regime, performance in the SRPT queue is equivalent, asymptotically in steady state, to a preemptive two-class priority queue where customers with short service times (below a threshold) are served without wait, and customers with long service times (above a threshold) eventually abandon without service. We prove that the SRPT discipline maximizes, asymptotically, the system throughput, among all scheduling disciplines. We also compare the performance of the SRPT policy to blind policies and study the effects of the patience-time and service-time distributions. This paper was accepted by Baris Ata, stochastic models & simulation.

Assortment Optimization and Pricing Under the Multinomial Logit Model with Impatient Customers: Sequential Recommendation and Selection

Sequential Recommendation Under the Multinomial Logit Model with Impatient Customers In many applications, customers incrementally view a subset of offered products and make purchasing decisions before observing all the offered products. In this case, the decision faced by a firm is not only what assortment of products to offer, but also in what sequence to offer the products. In “Assortment Optimization and Pricing Under the Multinomial Logit Model with Impatient Customers: Sequential Recommendation and Selection”, Gao, Ma, Chen, Gallego, Li, Rusmevichientong, and Topaloglu propose a choice model where each customer incrementally view the assortment of products in multiple stages, and their patience level determines the maximum number of stages. Under this choice model, the authors develop a polynomial-time algorithm that finds a revenue-maximizing sequence of assortments. If the sequence of assortments is fixed, the problem of finding revenue-maximizing prices can be transformed to a convex program. They combine these results to develop an effective approximation algorithm when both the sequence of assortments and prices are decision variables.

Perishable Inventory System with N-Policy, MAP Arrivals, and Impatient Customers

In this study, we consider a perishable inventory system that has an (s, Q) ordering policy, along with a finite waiting hall. The single server, which provides an item to the customer after completing the required service performance for that item, only begins serving after N customers have arrived. Impatient demand is assumed in that the customers waiting to be served lose patience and leave the system if the server’s idle time overextends or if the arriving customers find the system to be full and will not enter the system. This article analyzes the impatient demands caused by the N-policy server to an inventory system. In the steadystate, we obtain the joint probability distribution of the level of inventory and the number of customers in the system. We analyze some measures of system performance and get the total expected cost rate in the steadystate. We present a beneficial cost function and confer the numerical illustration that describes the impact of impatient customers caused by N-policy on the inventory system’s total expected cost rate.