Deterministic Network Calculus

7 Multiple Flows Crossing One Server

A network is generally composed of several flows and servers. Each server can be shared by several flows, with each flow crossing a sequence of servers. In Chapter 5, we presented the model of one server crossed by a single flow, and in Chapter 6, we presented the model of one flow crossing a sequence of servers. In this chapter, we focus on the model of one server crossed by several flows.

The network calculus theory is based on the computation of performances of one flow crossing one server. The main argument of the previous chapter is that a sequence of servers can be modeled as a server whose service curve is the (min,plus) convolution of the service curves of the servers of that sequence.

In this chapter, we address the complementary problem: if one server is crossed by several flows, our goal is to compute the individual guarantee for each flow, or more precisely, a service curve for each individual flow. We will call this type of service curve a residual service curve. The other denominations found in the literature are left-over service curves and individual service curves.

Different characteristics of the server must be known before computing residual service curves:

• – the global service offered by the server, which will be given by a service curve. The result will depend on the type of service curve;
• – the arrival curve of each flow crossing the server;
• – the service policy, which tells at each time what flow will be served.