Equilibrium Allocation of Variable Resources for Elastic Traffics

Consider a set of connections sharing a network node under an allocation scheme that provides each connection with a fixed minimum and a random extra amount of bandwidth and buffer. Allocations and prices are adjusted to adapt to resource availability y and user demands. We consider two scenarios of user behavior. In the first scenario a connection purchases an allocation to maximize its expected utility in such a way that the resource cost of the new allocation, and hence its connection charge, remains the same as that for the old allocation. In the second scenario this budget constraint is relaxed and a connection tries to maximize its benefit, expected utility minus the resource cost. Equilibrium is achieved when all connections ach]eve their optimality and demand equals supply for non-free resources. We show that at equilibrium expected return on purchasing variable resources can be higher than that on fixed resources. Thus connections must balance the marginal increase in utility due to higher return on variable resources and the marginal decrease in utility due to their variability. We further show that in equilibrium where such tradeoff is optimized all connections hold strictly positive amounts of variable bandwidth and bufer.