PRODUCT-FORM MARKOVIAN QUEUEING SYSTEMS WITH MULTIPLE RESOURCES. Issue 1 (January 2021)

• Record Type: Journal Article
• Authors: Naumov, Valeriy; Samouylov, Konstantin
• Is Part Of: Probability in the engineering and informational sciences. Volume 35:Issue 1(2021)
• Page Start: 180
• Page End: 188
• Publication Date: 2021-01
• Subjects: loss system, -- Markovian models, -- multiple resources, -- random resource requirements; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S026996481900024X
• Languages: English
• ISSNs: 0269-9648

Abstract

Abstract : In the paper, we study general Markovian models of loss systems with random resource requirements, in which customers at arrival occupy random quantities of various resources and release them at departure. Customers may request negative quantities of resources, but total amount of resources allocated to customers should be nonnegative and cannot exceed predefined maximum levels. Allocating a negative volume of a resource to a customer leads to a temporary increase in its volume in the system. We derive necessary and sufficient conditions for the product-form of the stationary probability distribution of the Markov jump process describing the system.