Strategic Behavior and Optimization of an M/M/1 Queue with N-Policy and Hysteretic Control

Lingjiao Zhang, Jinting Wang () and Yilin Wang
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Lingjiao Zhang: Central University of Finance and Economics
Jinting Wang: Central University of Finance and Economics
Yilin Wang: Central University of Finance and Economics

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 4, 1-29

Abstract: Abstract This work aims to study customer strategic behavior and operational optimization of an M/M/1 queue with N-policy and dynamic service-rate control in general, and of a make-to-order production system with a strategic manufacturer as a practical example in particular. With the N-policy and hysteretic control, the service rate is dynamically adjusted according to the queue length. An empty system is required to initiate service only when the number of waiting customers reaches a given threshold N. If the queue length exceeds $$M(>N)$$ M ( > N ) , the server serves customers with a higher service rate until the number of customers is lower than another threshold m. Based on a linear reward-cost structure, arriving customers are allowed to decide whether to join the system or not. The focus is on comparing the self equilibrium performance and socially-optimal arrival under the interaction between the server’s states and customers’ joining decisions. The influence of N-policy and hysteretic control on customer’s equilibrium joining probability under unobservable scenario is analysed. The optimal value of threshold N and m are discussed by taking server’s operational cost into consideration. These findings have important managerial implications on the overall social welfare with dynamic service rate.

Keywords: Queueing; Equilibrium strategies; Hysteretic control; N-policy; Strategic customers; 60K25; 90B22; 91A80 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10054-x

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