Pooling Queues with Strategic Servers: The Effects of Customer Ownership

Although pooling queues offers in principle many operational benefits, these may not always be achieved in practice. One reason, observed in the empirical study by Song et al. (2015), relates to customer ownership. In this paper, we formalize these empirical observations by developing a game-theoretic model to assess the performance of pooling when servers choose their capacities strategically and exhibit varying scopes of customer ownership, captured by two cost components, respectively associated with the processing time and the waiting time of a server's customers. We show that the core benefits of pooling are mostly annihilated in this setting. In fact, for any given scope of customer ownership, the queue configuration has almost no impact on the customers' average throughput time unless (i) servers' degree of customer ownership is so low that they choose to operate at high utilization and (ii) they care much more about their customers' processing times than about their waiting times. Under these conditions, adopting a dedicated queue configuration can yield significantly lower throughput times. This prescription becomes even more pertinent if the switch to a dedicated queue configuration is associated with an expansion in the scope of customer ownership, as may happen in practice.