Sojourn time distributions in non-product queueing networks
Frontiers in queueing
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
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)
The Product Form for Sojourn Time Distributions in Cyclic Exponential Queues
Journal of the ACM (JACM)
On the correlation of sojourn times in open networks of exponential multiserver queues
Queueing Systems: Theory and Applications
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We investigate the joint distribution of successive sojourn times of a customer traversing a path in a Jackson network. It is shown in a general setting that sojourn times for a broad class of such paths exhibit positive dependence. This applies to paths which admit overtaking due to the network topology as well as due to the internal node structure. Our proofs utilize the concept of partition separated orders on multidimensional ordered spaces.