  We define a wide class of Markovian load balancing networks of identical
single-server infinite-buffer queues. These networks may implement classic
parallel server or work stealing load balancing policies, and may be
asymmetric, for instance due to topological constraints. The invariant laws are
usually not known even up to normalizing constant. We provide three perfect
simulation algorithms enabling Monte Carlo estimation of quantities of interest
in equilibrium. The state space is infinite, and the algorithms use a
dominating process provided by the network with uniform routing, in a coupling
preserving a preorder which is related to the increasing convex order. It
constitutes an order up to permutation of the coordinates, strictly weaker than
the product order. The use of a preorder is novel in this context. The first
algorithm is in direct time and uses Palm theory and acceptance rejection. Its
duration is finite, a.s., but has infinite expectation. The two other
algorithms use dominated coupling from the past; one achieves coalescence by
simulating the dominating process into the past until it reaches the empty
state, the other, valid for exchangeable policies, is a back-off sandwiching
method. Their durations have some exponential moments.
