Join, Balk, or Jettison? The Effect of Flexibility and Ranking Knowledge in Systems with Batch-Arrivals

Customers that arrive in groups but are served individually face a convoluted manifestation of the join-balk dilemma: shall they all join, all balk, or join partially and jettison some entities? The answer depends on the level of flexibility provided to the group, the knowledge (or absence) of the service discipline within the group, and the configuration of the pertinent environment. We consider two levels of flexibility: an inflexible level under which a batch makes a common decision and all its entities obey (that reflects the batch interests), and a flexible level, under which each individual customer makes her own decision (that reflects the individual interests). We pair each level with two sub-levels with respect to the discipline knowledge: the case where customers know their ranking within their batch, and the case where they do not and assume they will be served according to a random order. We provide a full characterization of the equilibrium and socially optimal strategies considering a single server Markovian queue with a generic batch size distribution. We provide insights as to why the individual and batch level interests are not aligned and explain under which circumstances entity jettison is preferable. More importantly, we investigate the interplay between the notions of flexibility and ranking knowledge, their interaction with the batch size variability, and the corresponding implications on system throughput and social welfare. Further, we highlight key quantitative and qualitative differences between the performance of single and batch-arrival models