N-player Bertrand-Cournot games in queues: Existence of equilibrium

We develop a framework to study implications of Quality of service (QoS)-sensitive users on market equilibrium. We consider multiple competing providers each offering a queued service. Each provider posts a price and expected delay. Arriving users then pick the queue with the smallest price plus expected delay cost. We first consider the case where the providers are strategic and compete on price, when their capacity is fixed. We obtain conditions for existence of Nash equilibrium in such a game. We then consider the case where the providers invest in capacity and set price simultaneously. We intend to extend this to queues with multiple classes of service as a framework to study differentiated services in networks.