Decentralized rate-based flow control with bidding for priorities: equilibrium conditions and stability

We study rate-based flow control in a communication network, in which each link is modeled as an M/M/1 queue. The performance criterion is steady-state expected net benefit (reward minus cost) per unit time. Assuming that entering customers make payments that determine their priority in the queue, Hassin (1995) has shown that the equilibrium and optimal arrival rates coincide, so that flow control can be decentralized. We derive an explicit expression for the equilibrium distribution of priority payments and study the stability of the equilibrium under an iterative algorithm corresponding to periodic adaptive customer response to congestion.