A unified view of product-form approximation techniques for general closed queueing networks
Performance Evaluation
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Computers and Operations Research
Calculating equilibrium probabilities for &lgr;(n)/Ck/1/N queues
PERFORMANCE '80 Proceedings of the 1980 international symposium on Computer performance modelling, measurement and evaluation
An Approximate Analytical Method for General Queueing Networks
IEEE Transactions on Software Engineering
Solution of queuing problems by a recursive technique
IBM Journal of Research and Development
A spare parts model with cold-standby redundancy on system level
Computers and Operations Research
A multi-class closed queueing maintenance network model with a parts inventory system
Computers and Operations Research
OR FORUM---Little's Law as Viewed on Its 50th Anniversary
Operations Research
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We consider a maintenance network where a set of bases is supported by a replacement parts inventory system and a centrally located repair depot. The ordering policy for the parts is the (S, Q) inventory policy. We extended the previous results to the network, where processing times at each node follow a two-phase Coxian distribution. The proposed network was modeled as a multi-class closed queueing network with a synchronization station. To make the analysis of the network computationally tractable, we developed a two-phase approximation method. In the first phase of the method, the proposed network was analyzed with the previous algorithm based on a product-form approximation. In the second phase, a sub-network was again analyzed with the procedure of a product-form approximation method such that the state space of the sub-network was reduced. In the analysis of a sub-network, a recursive method was also used to solve balance equations by exploiting the special structure of the Markov chain. The new algorithm provided a good estimation of the performance measures of interest. In addition to being accurate, the new algorithm is simple and converges rapidly.