Partial Server Pooling in Delay Systems

We consider a strategic resource pooling interaction between two service providers, each of which is modelled as a multi-server queue. The traditional full resource pooling mechanism, while improving the overall system performance measure, may not always benefit the providers individually. For rational service providers, there will therefore be no incentive to form a stable coalition. We address this issue by proposing three partial sharing mechanisms: two of these, Partial Pooling with Dedicated Servers and Partial Pooling with Repacking, allow each provider to designate a certain number of servers to potentially serve jobs of the other provider, while the third mechanism, Differential Queue Length, maintains an upper bound on the difference between occupancies of the two queues. We determine the probability of waiting for each of the three mechanisms and show through several numerical examples that their Pareto frontiers are non-empty. In particular, this shows that the proposed partial pooling mechanisms are individually beneficial to both providers and incentivize coalition formation in all situations. Finally, we apply bargaining theory to determine the operating point on the Pareto frontier.