The Cycle Time Distribution of Exponential Cyclic Queues
Journal of the ACM (JACM)
The Time for a Round Trip in a Cycle of Exponential Queues
Journal of the ACM (JACM)
Some Extensions to Multiclass Queueing Network Analysis
Proceedings of the Third International Symposium on Modelling and Performance Evaluation of Computer Systems: Performance of Computer Systems
The Distribution of Queueing Network States at Input and Output Instants
Proceedings of the Third International Symposium on Modelling and Performance Evaluation of Computer Systems: Performance of Computer Systems
Mean Value Analysis fo Queueing Networks - A New Look at an Old Problem
Proceedings of the Third International Symposium on Modelling and Performance Evaluation of Computer Systems: Performance of Computer Systems
Approximating passage time distributions in queueing models by Bayesian expansion
Performance Evaluation
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Prediction of detailed characteristics of the time delays experienced by customers in queueing networks is of great importance in various modelling and performance evaluation activities: operations research, computer systems and communication networks. Their statistical properties have been investigated predominantly by simulation techniques with the exception of mean value analyses for which Little's Law is applied. Theoretical studies of the probability distributions of time delays tend to be based on their Laplace transforms, which are of limited use, can be inverted analytically only in very simple cases and present substantial computation problems for numerical inversion. An exact derivation is presented for the distribution of cycle times in so called tree-like queueing networks. The analysis is performed for a network structure which is such that it is not necessary to mark a special customer, so avoiding expansion of the state space. Cycle time distribution is derived initially in the form of its Laplace Transform, from which its moments follow. A recurrence relation for a uniformly convergent discrete representation of the distribution then follows by a similar argument. Finally, the numerical results obtained for some simple test networks are presented and compared with those corresponding to an approximate method, hence indicating the accuracy of the latter.