+.. _cfg=smpi/IB-penalty-factors:
+
+Infiniband model
+^^^^^^^^^^^^^^^^
+
+InfiniBand network behavior can be modeled through 3 parameters
+``smpi/IB-penalty-factors:"βe;βs;γs"``, as explained in `this PhD
+thesis
+<http://mescal.imag.fr/membres/jean-marc.vincent/index.html/PhD/Vienne.pdf>`_ (in French)
+or more concisely in `this paper <https://hal.inria.fr/hal-00953618/document>`_,
+even if that paper does only describe models for myrinet and ethernet.
+You can see in Fig 2 some results for Infiniband, for example. This model
+may be outdated by now for modern infiniband, anyway, so a new
+validation would be good.
+
+The three paramaters are defined as follows:
+
+- βs: penalty factor for outgoing messages, computed by running a simple send to
+ two nodes and checking slowdown compared to a single send to one node,
+ dividing by 2
+- βe: penalty factor for ingoing messages, same computation method but with one
+ node receiving several messages
+- γr: slowdown factor when communication buffer memory is saturated. It needs a
+ more complicated pattern to run in order to be computed (5.3 in the thesis,
+ page 107), and formula in the end is γr = time(c)/(3×βe×time(ref)), where
+ time(ref) is the time of a single comm with no contention).
+
+Once these values are computed, a penalty is assessed for each message (this is
+the part implemented in the simulator) as shown page 106 of the thesis. Here is
+a simple translation of this text. First, some notations:
+
+- ∆e(e) which corresponds to the incoming degree of node e, that is to say the number of communications having as destination node e.
+- ∆s (s) which corresponds to the degree outgoing from node s, that is to say the number of communications sent by node s.
+- Φ (e) which corresponds to the number of communications destined for the node e but coming from a different node.
+- Ω (s, e) which corresponds to the number of messages coming from node s to node e. If node e only receives communications from different nodes then Φ (e) = ∆e (e). On the other hand if, for example, there are three messages coming from node s and going from node e then Φ (e) 6 = ∆e (e) and Ω (s, e) = 3
+
+To determine the penalty for a communication, two values need to be calculated. First, the penalty caused by the conflict in transmission, noted ps.
+
+
+- if ∆s (i) = 1 then ps = 1.
+- if ∆s (i) ≥ 2 and ∆e (i) ≥ 3 then ps = ∆s (i) × βs × γr
+- else, ps = ∆s (i) × βs
+
+
+Then, the penalty caused by the conflict in reception (noted pe) should be computed as follows:
+
+- if ∆e (i) = 1 then pe = 1
+- else, pe = Φ (e) × βe × Ω (s, e)
+
+Finally, the penalty associated with the communication is:
+p = max (ps ∈ s, pe)
+
