Proceedings of the workshop held at the Mathematical Sciences Institute Cornell University on Mathematical theory of queueing systems
The evaluation of normalizing constants in closed queueing networks
Operations Research
The Cycle Time Distribution of Exponential Cyclic Queues
Journal of the ACM (JACM)
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
The Distribution of Queuing Network States at Input and Output Instants
Journal of the ACM (JACM)
The Time for a Round Trip in a Cycle of Exponential Queues
Journal of the ACM (JACM)
The Product Form for Sojourn Time Distributions in Cyclic Exponential Queues
Journal of the ACM (JACM)
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
The Time-To-Empty For Tandem Jackson Networks
Probability in the Engineering and Informational Sciences
Cycle times in single server cyclic Jackson networks
Operations Research Letters
An invariance property of sojourn times in cyclic networks
Operations Research Letters
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We present an extension of the arrival theorem for the output process from a node in closed Markovian networks which we use to obtain simple representations and explicit expressions for the throughput, the distribution of the cycle time, and the joint distribution of interoutput times from a node in single class closed networks with exponential servers. Our approach uses tools from Palm calculus to obtain a recursion on the number of customers in the system. The analysis relies on a non-overtake condition and thus many of the results obtained here apply only to cyclic, single server networks. One of the surprising conclusions of our analysis is that the interoutput times that comprise the cycle time of a customer are (finitely) exchangeable, i.e., that their joint distribution is invariant under permutations.