Service capacity decision and incentive compatible cost allocation for reporting usage forecasts

We consider an M/G/1 queue with multiple users where service capacity can be improved at a cost by reducing the mean and variance of service time and each user has private information on his expected usage. The firm's headquarters requires information on expected usage to determine the optimum service capacity. We develop a simple cost allocation scheme where a charge is applied to realized usage. This charge is computed by dividing the service capacity costs by the total reported expected usage weighted by the cost per unit time delay. The difference between the service capacity cost and the total charge applied to realized usage is credited/charged to the users based on the proportion of reported expected usage weighted by the cost per unit time delay. This cost allocation scheme (a) induces truthful reports of expected usage, (b) maximizes the expected net benefit of each user with respect to the service capacity, (c) shares all the service capacity costs, (d) achieves the same service capacity that the firm's headquarters would choose in an unconstrained maximization problem with no private information, and (e) uses only the realized and reported expected usages. We also examine whether the cost allocation scheme provides incentives for each user to obtain good forecasts on expected usage.