Optimal control of service in branching exponential queueing networks

This paper studies the optimal control of the service rate of an arbitrarily located key node in a general acyclic queueing network in which an exogenous arrival can join any node and customers, upon service completion, are routed probablistically. The objective function for the model is the sum of the holding costs, service costs, and the service completion rewards from all the nodes in the network. The exponential service rate for the key node is controlled dynamically as the state of the network system evolves in time. It is shown, for usual cost models, that the optimal service rate for the key node is nonincreasing or nondecreasing, depending on where a service completion occurs in the network. The effect of adding a marginal customer somewhere in the network is also shown. The analysis can be approximate for extreme cost models.