Data networks
Journal of Computational and Applied Mathematics
Power series for stationary distributions of coupled processor models
SIAM Journal on Applied Mathematics
An interpolation approximation for queueing systems with Poisson input
Operations Research
An interpolation approximation for the mean workload in a GI/G/1 queue
Operations Research
Interpolation approximations of sojourn time distributions
Operations Research
Performance Analysis and Optimization with the Power-Series Algorithm
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
Enhanced Modeling and Solution of Layered Queueing Networks
IEEE Transactions on Software Engineering
Closed-form waiting time approximations for polling systems
Performance Evaluation
The distributional form of little's law and the fuhrmann-cooper decomposition
Operations Research Letters
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We consider an extension of the classical machine-repair model, also known as the computer-terminal model or time-sharing model. As opposed to the classical model, we assume that the machines, apart from receiving service from the repairman, supply service themselves to queues of products. The extended model can be viewed as a two-layered queueing network, of which the first layer consists of two separate queues of products. Each of these queues is served by its own machine. The marginal and joint queue length distributions of the first-layer queues are hard to analyse in an exact fashion. Therefore, we apply the power-series algorithm to this model to obtain the light-traffic behaviour of the queue lengths symbolically. This leads to two accurate approximations for the marginal mean queue length. The first approximation, based on the light-traffic behaviour, is in closed form. The second approximation is based on an interpolation between the light-traffic behaviour and heavy-traffic results for the mean queue length. The obtained approximations are shown to work well for arbitrary loaded systems. The proposed numerical algorithm and approximations may prove to be very useful for system design and optimisation purposes in application areas such as manufacturing, computer systems and telecommunications.