Some of the applications in modern data networks are delay sensitive (e.g., video and voice). An end-to-end delay analysis is needed to estimate the required network resources of delay sensitive applications. The schedulers used in the network can impact the resulting delays to the applications. When multiple applications are multiplexed in a switch, a scheduler is used to determine the precedence of the arrivals from different applications. Computing the end-to-end delay and queue sizes in a network of schedulers is difficult and the existing solutions are limited to some special cases (e.g., specific type of traffic). The theory of Network Calculus employs the min-plus algebra to obtain performance bounds. Given an upper bound on the traffic arrival in any time interval and a lower bound on the available service (called the service curve) at a network element, upper bounds on the delay and queue size of the traffic in that network element can be obtained. An equivalent end-to-end service curve of a tandem of queues is the min-plus convolution of the service curves of all nodes along the path. A probabilistic end-to-end delay bound using network service curve scales with O(H logH) in the path length H. This improves the results of the conventional method of adding per-node delay bounds scaling with O(H^3). We have used and advanced Network Calculus for end-to-end delay analysis in a network of schedulers. We formulate a service curve description for a large class of schedulers which we call Delta-schedulers. We show that with this service curve, tight single node delay and backlog bounds can be achieved. In an end-to-end scenario, we formulate a new convolution theoii rem which considerably improves the end-to-end probabilistic delay bounds. We specify our probabilistic end-to-end delay and backlog bounds for exponentially bounded burstniess (EBB) traffic arrivals. We show that the end-to-end delay varies considerably by the type of schedulers along the path. Using these bounds, we also show that a if the number of flows increases, the queues inside a network can be analyzed in isolation and regardless of the network effect.

Some of the applications in modern data networks are delay sensitive (e.g., video and voice). An end-to-end delay analysis is needed to estimate the required network resources of delay sensitive applications. The schedulers used in the network can impact the resulting delays to the applications. When multiple applications are multiplexed in a switch, a scheduler is used to determine the precedence of the arrivals from different applications. Computing the end-to-end delay and queue sizes in a network of schedulers is difficult and the existing solutions are limited to some special cases (e.g., specific type of traffic). The theory of Network Calculus employs the min-plus algebra to obtain performance bounds. Given an upper bound on the traffic arrival in any time interval and a lower bound on the available service (called the service curve) at a network element, upper bounds on the delay and queue size of the traffic in that network element can be obtained. An equivalent end-to-end service curve of a tandem of queues is the min-plus convolution of the service curves of all nodes along the path. A probabilistic end-to-end delay bound using network service curve scales with O(H logH) in the path length H. This improves the results of the conventional method of adding per-node delay bounds scaling with O(H^3). We have used and advanced Network Calculus for end-to-end delay analysis in a network of schedulers. We formulate a service curve description for a large class of schedulers which we call Delta-schedulers. We show that with this service curve, tight single node delay and backlog bounds can be achieved. In an end-to-end scenario, we formulate a new convolution theoii rem which considerably improves the end-to-end probabilistic delay bounds. We specify our probabilistic end-to-end delay and backlog bounds for exponentially bounded burstniess (EBB) traffic arrivals. We show that the end-to-end delay varies considerably by the type of schedulers along the path. Using these bounds, we also show that a if the number of flows increases, the queues inside a network can be analyzed in isolation and regardless of the network effect.

In this thesis, we study different Internet pricing schemes and how they can be applied to a multiple ISP environment. We first take a look at the current Internet architecture. Then the different classes that make up the Internet hierarchy are discussed. We also take a look at peering among Internet Service Providers (ISPs) and when it is a good idea for an ISP to consider peering. Moreover, advantages and disadvantages of peering are discussed along with speculations of the evolution of the Internet peering ecosystem. We then consider different pricing schemes that have been proposed and study the factors that make up a good pricing plan. Finally, we apply some game theoretical concepts to discuss how different ISPs could interact together. We choose a pricing model based on a Stackelberg game that takes into consideration the effect of the traffic variation among different customers in a multiple ISP environment. It allows customers to specify their desired QoS in terms of maximum allowable end-to-end delay. Customers only pay for the portion of traffic that meet this delay bound. Moreover, we show the effectiveness of adopting this model through a comparison with a model that does not take traffic variation into account. We also develop a naïve case and compare it to our more sophisticated approach.

In this thesis, we study different Internet pricing schemes and how they can be applied to a multiple ISP environment. We first take a look at the current Internet architecture. Then the different classes that make up the Internet hierarchy are discussed. We also take a look at peering among Internet Service Providers (ISPs) and when it is a good idea for an ISP to consider peering. Moreover, advantages and disadvantages of peering are discussed along with speculations of the evolution of the Internet peering ecosystem. We then consider different pricing schemes that have been proposed and study the factors that make up a good pricing plan. Finally, we apply some game theoretical concepts to discuss how different ISPs could interact together. We choose a pricing model based on a Stackelberg game that takes into consideration the effect of the traffic variation among different customers in a multiple ISP environment. It allows customers to specify their desired QoS in terms of maximum allowable end-to-end delay. Customers only pay for the portion of traffic that meet this delay bound. Moreover, we show the effectiveness of adopting this model through a comparison with a model that does not take traffic variation into account. We also develop a naïve case and compare it to our more sophisticated approach.