Product form in networks of queues with batch arrivals and batch services
Queueing Systems: Theory and Applications
Push and pull production systems: issues and comparisons
Operations Research
On the arrival theorem for queueing networks operating under a just-in-time protocol
Performance Evaluation
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
A Characterization of Product-Form Queuing Networks
Journal of the ACM (JACM)
Queueing Systems: Theory and Applications
ON TRUNCATION PROPERTIES OF FINITE-BUFFER QUEUES AND QUEUEING NETWORKS
Probability in the Engineering and Informational Sciences
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In this paper, we introduce a new class of queueing networks called arrival first networks. We characterise its transition rates and derive the relationship between arrival rules, linear partial balance equations, and product form stationary distributions. This model is motivated by production systems operating under a kanban protocol. In contrast with the conventional departure first networks, where a transition is initiated by service completion of items at the originating nodes that are subsequently routed to the destination nodes (push system), in an arrival first network a transition is initiated by the destination nodes of the items and subsequently those items are processed at and removed from the originating nodes (pull system). These are similar to the push and pull systems in manufacturing systems.Our characterisation provides necessary and sufficient conditions for the network to possess linear traffic equations, and sufficient conditions for the network to have a product form stationary distribution. We apply our results to networks operating under a kanban mechanism and characterise the rate at which items are pulled as well as the routing and blocking protocols that give rise to a product form stationary distribution.