Network Performance Analysis of Packet Scheduling Algorithms

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 log H) in the path length H. This improves the results of the conventional method of adding per-node delay bounds scaling with O(H3).;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 Δ-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 theorem 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.