Service pooling strategy in service systems with impatient customers

We consider a group of homogeneous and independent single server service providers with impatient customers, who quit the system without receiving service whenever theirs waiting times in the queue are longer than the patience times. The collaboration strategies for the capacity pooling situation are studied between the service providers. The undisputed advantage of the collaboration is the sharing of the instant idle resources, that improves resource utilisation in overall system. In order to analyze the profitable collaborative organization and the cost-sharing method, the cooperative game theory is considered. The total operation cost of the system is defined as the sum of a holding cost, a waiting cost and an abandonment cost. Under Markovian assumptions for inter-arrival, service and patience times, corresponding cost game with transferable utility is constructed with a fixed service capacity for each coalition. We prove that the grand coalition is the most profitable regime and that the game has a nonempty core. Moreover, we illustrate the coalition and individual profits of the pooling system.