Optimal multi-layered congestion based pricing schemes for enhanced QoS

Pricing is an effective tool to control congestion and achieve quality of service (QoS) provisioning for multiple differentiated levels of service. In this paper, we consider the problem of pricing for congestion control in the case of a network of nodes with multiple queues and multiple grades of service. We present a closed-loop multi-layered pricing scheme and propose an algorithm for finding the optimal state dependent price levels for individual queues, at each node. This is different from most adaptive pricing schemes in the literature that do not obtain a closed-loop state dependent pricing policy. The method that we propose finds optimal price levels that are functions of the queue lengths at individual queues. Further, we also propose a variant of the above scheme that assigns prices to incoming packets at each node according to a weighted average queue length at that node. This is done to reduce frequent price variations and is in the spirit of the random early detection (RED) mechanism used in TCP/IP networks. We observe in our numerical results a considerable improvement in performance using both of our schemes over that of a recently proposed related scheme in terms of both throughput and delay performance. In particular, our first scheme exhibits a throughput improvement in the range of 67-82% among all routes over the above scheme. (C) 2011 Elsevier B.V. All rights reserved.