Clones: CLOsed queueing Networks Exact Sampling

Anne Bouillard 1, 2, 3 Ana Bušic 2, 3 Christelle Rovetta 2, 3
2 DYOGENE - Dynamics of Geometric Networks
CNRS - Centre National de la Recherche Scientifique : UMR8548, Inria Paris-Rocquencourt, DI-ENS - Département d'informatique de l'École normale supérieure
Abstract : 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
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Anne Bouillard, Ana Bušic, Christelle Rovetta. Clones: CLOsed queueing Networks Exact Sampling. ValueTools, Dec 2014, Bratislava, Slovakia. ⟨hal-01095314⟩

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