Abstract –We develop a model with priority classes where users allocate traffic into classes dynamically after estimating the error vector for the classes. We propose a decentralized scheme for user adaptation and study its dynamics. We analyze the user behavior and find the condition for the equilibrium to exist.

Index Terms – Congestion Control, Pricing, Priority Service, Dynamic Traffic allocation

INTRODUCTION

Today’s Internet is enough to support services such as web browsing and e-mail, but it is not sufficient for new real-time services such as voice and video which require a more predictable quality of service (QoS) model. One proposed means to address this issue is to classify Internet traffic into priority classes. In an environment with a great diversity of users and applications, it is particularly challenging to tightly constrain user attributes and user requirements. This motivates shifting the burden of rate allocation from the network to the end systems. So we develop a service model where the user decides the allocation in different priority classes. User’s incentive to use different priority classes is the service quality it achieves, which also defines his utility based on the demand and the quality of the class. The ISP’s incentive for providing different priority classes would be to increase its revenue.

Networks offering this service model needs a mechanism to serve the traffic of priority classes; otherwise all users declare their traffic as high priority and the above priority model degenerates to a best-effort service. We make the following assumptions regarding priority assignment, pricing, and charging.

We assume that users assign packets to priority classes and that the priority of a packet does not change as it travels through the network.

There are different ways of charging the packets. Pricing due to the bandwidth consumed, pricing based on current demand or pricing packets for the service quality provided. In this paper, price per unit packet is a function of the priority class to which it belongs. Thus the packets are charged for the bandwidth consumed and the service provided.

We consider a static pricing scheme where the prices associated with the different priority classes are fixed and do not change as the traffic load in the network changes.

In this model users receive the feedback of error rate(quality) of every priority class from the network which they use to predict future quality of every priority class and accordingly to adapt to new transmission rates. We propose a mechanism for users to respond to the error rate information which is motivated by the assumption that they are trying to maximize their individual utilities.

In this paper, we deal with a finite user population and study the dynamics of the network corresponding to our model of user behaviour

PROBLEM FORMULATION

We develop a model with priority services where users get the information about the classes every instant which they use to dynamically update their allocation. We consider a discrete time model of a link which is divided into N priority classes and shared by R users. In each time slot n, user r updates its allocation vector drn to maximize its net benefit.

The unit price of bandwidth in a priority class i is a function of i.

User r derives its utility in time slot n from the demand at time n and the error vector estimated at time n. User’s total utility is the sum of user’s utilities in each priority class.

The only information available to a user when choosing its transmission rate in time slot n is the history of error rate vectors e(n-1), e(n-2)..and so on and the history of its own action. This suggests the following natural framework for user adaptation. Each user r forms its own estimate of error vector at time slot n based on the information available to it. It then optimizes its transmission rate based on this estimate. In other words, user r chooses drn(i) to maximize Ur(dr(i),e(i))-ui* dr(i). We propose a simple model of N priority classes where users form expectations of the error rate and use this to analyze the system.