A Service Abstraction with Applications to Network

In this paper, we define a general service abstraction for a network element. The service abstraction is defined in terms of a “service mapping,” which is a montotone operator that maps an arrival process to a lower bound on the corresponding departure process. We consider service mappings which are shift invariant, which includes the previously studied service curve model defined in terms of convolution in the “min-plus” algebra. For a network element with a shift invariant service mapping, we obtain bounds on the maximum delay, maximum backlog, and a traffic envelope for the departure process, assuming that the arrival process to the network element conforms to a traffic envelope. These bounds have a unified graphical interpretation and reduce to previously known bounds in the case of a service curve model. Next, we apply the service mapping abstraction to a First-In First-Out (FIFO) multiplexer whose arrival processes conform to traffic envelopes. The corresponding service mapping is non-linear in the min-plus algebra. We note that the quality of service bounds reduce to previously known tight bounds. We then consider a tandem configuration of FIFO multiplexers. Analysis of the tandem network with the service mapping abstraction yields achievable upper bounds on end-to-end delay which are smaller than those that can be obtained with previously proposed methods.