“ Strategic Customers in Systems with Batch Arrivals: How Much You Can Protect Your Party ”
by Dr. Olga Bountali
Southern Methodist University – Department of Engineering Management, Information, and Systems
Customers who arrive in groups at a service or production system but are served individually are faced with a convoluted manifestation of the \ join-balk” dilemma when they try to balance the payoff obtained from service with the costs caused by waiting in the queue: if they are bound to join or balk as a group, then some of them may be forced to join so that the net benefit of the entire group is maximized. On the other hand, if separate customer entrances are allowed, then their individual interest plays the major role in their decision. In this sense, when all arriving groups act strategically, it is of interest to predict the resulting join-balk strategies under equilibrium in both cases, as well as their differences in system performance, customer throughput, total customer welfare, etc. We consider these questions in the framework of a single server Markovian queue with batch arrivals and random batch sizes. We explicitly consider two cases with respect to the entrance decision rules: the 0-1 case, in which the entire batch (i.e., all its customers) decides to either join or balk, and the partial case, where the batch is allowed to join partially (i.e., only a fraction of the customers decides to join). We analyze and compare how the customers behave in equilibrium under both rules and the corresponding implications on the social welfare.