Clones: CLOsed queueing Networks Exact Sampling

We present Clones, a Matlab toolbox for exact sampling from the stationary distribution of a closed queueing network with finite capacities. This toolbox is based on recent results using a compact representation of sets of states that enables exact sampling from the stationary distribution without considering all initial conditions in the coupling from the past (CFTP) scheme. This representation reduces the complexity of the one-step transition in the CFTP algorithm to O(KM), where K is the number of queues and M the total number of customers; while the cardinality of the state space is exponential in the number of queues. In this paper, we focus on the algorithmic and implementation issues. We propose a new representation, that leads to onestep transition complexity of the CFTP algorithm that is in O(KM). We provide a detailed description of our matrixbased implementation. The toolbox can be downloaded at http://www.di.ens.fr/~rovetta/Clones.