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.

翻译：本文定义了一类广泛的马尔可夫负载均衡网络，该网络由相同的单服务器无限缓冲区队列构成。这些网络可实现经典的并行服务器或工作窃取负载均衡策略，并且可能因拓扑约束等因素呈现非对称特性。即使忽略归一化常数，其不变测度通常也未知。我们提出了三种完美模拟算法，用于在平衡态下对目标量进行蒙特卡洛估计。由于状态空间是无限的，算法通过采用均匀路由的网络提供支配过程，并在保持与递增凸序相关的预序耦合下实现。该预序构成坐标置换意义下的序，严格弱于乘积序。在此背景下使用预序具有新颖性。第一种算法基于直接时间法，运用 Palm 理论与接受-拒绝方法。其运行时间几乎必然有限，但期望为无穷。另外两种算法采用过去支配耦合：一种通过向过去模拟支配过程直至其达到空状态来实现聚合；另一种适用于可交换策略，采用回退夹逼方法。这两种算法的运行时间具有某些指数矩。