Predictable revenue under processor sharing

This paper considers the case of a single service provider employing processor sharing discipline and serving randomly arriving users with random service requirements. The operator is assumed to charge a user based on the service rate allocated. The pricing mechanisms considered in this paper are the fixed rate pricing, Vickrey-Clarke-Groves (VCG) auctions, and congestion-based pricing (or the Lagrange shadow prices). Under such a model, we explicitly calculate the mean revenue of the operator and the mrean payments made by the users by exploiting the property of insensitivity associated with processor sharing. We also consider the effect of imposing a minimum rate requirement of a user on the revenue (a Quality of Service constraint). This paper presents our results and draws insights on the structure of the mean user payments and on the relation between the mean operator revenue and the zeroth, first, and the second moment of the total number of users present in the system under the three pricing mechanisms.