Abstract
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(KM2), 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 http://www.di.ens.fr/~rovetta/Clones.
Highlights
Consider a closed network of K ./M/1/C queues with M customers in total
In the case of closed queueing networks the cardinality of the this paper, we focus on the algorithmic and implementation state space is exponential in the number of queues, which is issues
We present a sub-class of diagrams that can be represented even more compactly
Summary
Closed queueing networks are largely used in various application domains due to their modeling simplicity and productform stationary distribution in the unlimited capacity case [5]. This structure is no longer guaranteed when the queues queueing networks, that enables exact sampling from the stationary distribution without considering all initial conditions in the CFTP. The complexity of one-step transition of this new CFTP algorithm is O(KM ). Note that this is the same as the complexity of the computation of the normalizing constant in the product-form case using Buzen’s algorithm [4].
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