Monotonicity properties of user equilibrium policies for parallel batch systems

Chen, Yizheng; Holmes, Mark H.; Ziedins, Ilze

doi:10.1007/s11134-011-9264-8

Cited by 10 publications

(3 citation statements)

References 31 publications

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“…Wang et al [22] studied the strategic behavior of passengers in the queueing system with batch transfer under threshold policy and obtained the threshold joining strategies of passengers. Afimeimounga et al [23], Chen et al [24], and the references therein are recommended for the interested readers who want to know more about the customer behavior analysis in batch queueing systems.…”

Section: Literature Reviewmentioning

confidence: 99%

Customer Behavior Analysis in Ticket Windows at Scenic Spots from Game-Theoretic Perspective

Jiang

Liu

Ammar

2021

Discrete Dynamics in Nature and Society

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In service industries, especially in some ticket windows at scenic spots, affected by congestion, some customers often find excuses or ask the acquaintances in the queue so as to jump the queue and complete their corresponding service as early as possible. In this paper, we model the queueing phenomenon in the ticket windows at scenic spots as a special queue, namely, the so-called “team queue.” Although this phenomenon often happens in daily life, it is less well known to people. In a team queue, an arriving customer first searches the queue from the top to bottom to see if some of his teammates are already in the queue. If yes, he would join the queue and be served with his teammates; otherwise, he would join the queue at the tail. To this end, arising from the customers’ perspective, the strategic behavior of queueing customers in the ticket windows at scenic spots is analyzed. On the basis of considering the waiting cost and reward, the individual strategies and social optimal strategies of queueing customers are derived, regarding the joining or balking dilemma and for the observable and unobservable cases. Finally, to demonstrate how various parameters affect the joining strategies, some numerical examples are provided.

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Section: Literature Reviewmentioning

confidence: 99%

Customer Behavior Analysis in Ticket Windows at Scenic Spots from Game-Theoretic Perspective

Jiang

Liu

Ammar

2021

Discrete Dynamics in Nature and Society

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“…Most papers in this area are motivated by transportation systems (see, for example, the introductory example in Section 1.5 of Hassin and Haviv [32]). More concretely, a first thread of research deals with strategic customer routing behavior in networks with infinite server systems with batches and single-server systems with single services (see, for example, Calvert [14], Afimeimounga et al [3,4], Afimeimounga [2], Chen et al [16], and Wang and Ziedins [44]). These works have shown the occurrence of Downs-Thompson and Braess-type paradoxes in the context of simple queueing networks (for a thorough overview, see Hassin [30], Chapters 8.6 and 8.7).…”

Section: Literature Reviewmentioning

confidence: 99%

Strategic customer behavior in a two-stage batch processing system

Bountali

Economou

2019

Queueing Syst

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We consider a two-stage service system with batch processing. More specifically, customers arrive according to a Poisson process at the first stage of the system, where they do not receive any service, but wait until a number K of them are accumulated. Then, these K customers form a batch which is instantaneously transferred to the second stage where the batches are served sequentially, as single units, by a single server. We derive customer equilibrium strategies, regarding the joining/balking dilemma, for the (partially) observable case where the customers are informed upon arrival about the number of present customers at the first stage. We prove the existence and study the uniqueness of equilibrium strategies and give a simple procedure for their computation. Moreover, we juxtapose the customer strategic behavior in this system with the corresponding behavior in the unobservable system and study the effect of information on the resulting social welfare per time unit under equilibrium.

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“…• Choice among multiple capacity services. Several studies have been conducted on the strategic choice among infinite server systems with regular batches and single-server systems of single service [37][38][39][40][41]. These studies showed interesting Downs-Thompson and Braess-type paradoxes through the equilibrium analyses of this type of model.…”

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confidence: 99%

Equilibrium Analysis for Batch Service Queueing Systems with Strategic Choice of Batch Size

Nakamura,

Phung-Duc

2023

Mathematics

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Various transportation services exist, such as ride-sharing or shared taxis, in which customers receive services in a batch of flexible sizes and share fees. In this study, we conducted an equilibrium analysis of a variable batch service model in which customers who observe no waiting customers in an incomplete batch can strategically select a batch size to maximize the individual utilities. We formulated this model as a three-dimensional Markov chain and created a book-type transition diagram. To consider the joining/balking dilemma of customers for this model, we proposed an effective algorithm to construct a necessary and sufficient size of state space for the Markov chain provided that all customers adopt the threshold-type equilibrium strategy. Moreover, we proved that the best batch size is a non-decreasing function for i if the reward for the completion of batch service with size l is an increasing function of l assuming that a tagged customer observes i complete batches in the system upon arrival; in other words, the fee decreases as the batch becomes larger. We then derive several performance measures, such as throughput, social welfare, and monopolist’s revenue. Throughout the numerical experiment, a comparison between the present variable batch service model and regular batch service model in which customers were served in a constant batch, was discussed. It was demonstrated that the three performance measures can be optimized simultaneously in the variable batch service model, as long as the fee was set relatively high.

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Monotonicity properties of user equilibrium policies for parallel batch systems

Cited by 10 publications

References 31 publications

Customer Behavior Analysis in Ticket Windows at Scenic Spots from Game-Theoretic Perspective

Customer Behavior Analysis in Ticket Windows at Scenic Spots from Game-Theoretic Perspective

Strategic customer behavior in a two-stage batch processing system

Equilibrium Analysis for Batch Service Queueing Systems with Strategic Choice of Batch Size

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