Pricing schemes in processor sharing systems

In this paper we study charging schemes for bandwidth or server usage under the processor sharing discipline. Specifically, we analyze post-payment and pre-payment (or payment on arrival) schemes in three charging frameworks: fixed-rate charging, Vickrey–Clarke–Groves based charging, and congestion based charging for users with logarithmic utilities. We show that in the absence of QoS constraints, the network operator can earn unbounded profits and thus there is a need to devise schemes where users are only charged if they are given a minimum rate. We obtain explicit characterizations for mean user payments and the operator’s mean revenue for these frameworks. We also analyze charge volatility via the second moments of the above implementations of arrival-based payments and post-payments. The volatility reflects the confidence in mean revenue for the operator and expected charges for a user. We present conditions under which a pre-payment mechanism is preferable over a post-payment mechanism. We also show that the same analysis can be applied to a scenario with admission control where each entering user is guaranteed a minimum service rate.