A System with a Choice of Highest-Bidder-First and FIFO Services

Service systems using a highest-bidder-first (HBF) policy have been studied in queueing literature for various applications and in economics literature to model corruption. Such systems have applications in modern problems like scheduling jobs in cloud computing scenarios or placement of ads on web pages. However, using a HBF service is like using a spot market and may not be preferred by many users. For such users, it may be good to provide a simple scheduler, e.g., a FIFO service. Further, in some situations it may even be necessary that a free service queue operates alongside a HBF queue. Motivated by such a scenario, we propose and analyze a service system with a FIFO server and a HBF server in parallel. Arriving customers are from a heterogeneous population with different valuations of their delay costs. They strategically choose between FIFO and HBF service; if HBF is chosen, they also choose the bid value to optimize an individual cost. We characterize the Wardrop equilibrium in such a system and analyze the revenue to the server. We see that when the total capacity is fixed and is shared between the FIFO and HBF servers, revenue is maximised when the FIFO capacity is non zero. However, if the FIFO server is added to an HBF server, then the revenue decreases with increasing FIFO capacity. We also discuss the case when customers are allowed to balk.