A sequence of multitype agents and a sequence of multitype goods are matched first come first served, subject to a bipartite compatibility graph.  I will survey work on this model, in particular the following two papers:

(1) Theory: Ivo Adan, Ana Busic, Jean Mairesse and Gideon Weiss, “Reversibility and further properties of FCFS infinite bipartite matching,” Mathematics of Operations Research 43(2): 598-621, (2018),

(2) Application: Ivo Adan, Marko Boon and Gideon Weiss, “Design heuristic for parallel many server systems,”  European Journal of Operational Research 273(1): 259-277, (2019),

and suggest some future research.