Clones: CLOsed queueing Networks Exact Sampling

Overview & Synopsis

We present Clones, a Matlab toolbox for exact sampling from the stationary distribution of a closed queueing net-work with finite capacities. This toolbox is based on re-cent results using a compact representation of sets of states that enables exact sampling from the stationary distribu-tion 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 al-gorithm to O(KM 2), 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 one-step transition complexity of the CFTP algorithm that is in O(KM). We provide a detailed description of our matrix-based implementation. The toolbox can be downloaded at