Customer Equilibrium and Optimal Strategies in a Batch-Service Queueing System with a Proportional Pricing Coefficient

This work analyzes an observable batch service queuing system with a proportional pricing coefficient and multiple access points. Based on whether the system is idle upon arrival, we derive the equilibrium threshold strategy for customers to either wait for batch formation or take service alone. When the server is idle, we derive the optimal waiting rate for customers in the queue. When it is occupied, we analyze the equilibrium threshold strategy and find the threshold value via a binary search algorithm. Furthermore, we quantify the system’s key performance measures for subsequent numerical experiments, establish a bi-level optimization model to maximize social welfare, and determine the optimal proportional pricing coefficient via a grid search. Finally, through numerical experiments, we conduct sensitivity analyses of the optimal proportional pricing coefficient, examine the impact of parameters such as the arrival rate and the number of access points on performance measures, and demonstrate the advantages of the strategic batch mechanism over the fixed batch mode.