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

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