What are the conditions on d1 and d2 for the end-to-end delay bounds to be satisfied ?

A network consists of two nodes in tandem. There are n₁ flows of type 1 and n2 flows of type 2. Flows of type i have arrival curve α_i(t) = r_it + b_i, i = 1, 2. All flows go through nodes 1 then 2. Every node is made of a shaper followed by an EDF scheduler. At both nodes, the shaping curve for flows of type i is some σ_i and the delay budget for flows of type i is di. Every flow of type i should have a end-to-end delay bounded by Di. Our problem is to find good values of d₁ and d₂.

1. We assume that σ_i = α_i. What are the conditions on d₁ and d₂ for the end-to-end delay bounds to be satisfied ? What is the set of (n1, n2) that are schedulable ?

2. Same question if we set σ_i = λ_ri