Optimal and equilibrium solutions to the backup server selection problem

Backup servers are commonly employed in service systems when primary servers become overloaded. These backup servers typically operate at a reduced service rate or offer lower service quality. This paper derives socially and individually optimal server-selection strategies in a system with one primary server and one backup server. These strategies are compared with two simple alternatives: (i) always using the primary server; and (ii) never waiting for the primary server when the backup is available. The better of these two simpler strategies closely approximates the socially optimal strategy in terms of social welfare. We also investigate the decentralised equilibrium behaviour and its deviation from the social optimum, showing that system efficiency under selfish agent behaviour can deteriorate arbitrarily. An admission fee together with a high-quality server usage fee can align individual incentives with socially optimal results.