Discrete time queueing networks with product form steady state. Availability and performance analysis in an integrated model

Christian Malchin (1) , Hans Daduna (1)

1 University of Hamburg

For a discrete time network of generalized Bernoulli servers with unreliable nodes we derive the steady state probabilities for the joint queue length vector for all nodes and the availability status of the network. This allows us to assess the performance behavior and the reliability, resp. availability, of the network in an integrated model. Because our result exhibits a product form for the steady state distribution it opens the path to fast algorithmic evaluation of the desired performance and reliability indices.

Keywords: Networks of discrete time queues; Unreliable nodes; Availability; Time reversed process; Product form theorem; Geometrical nodes; 60K25; 90B22; 68M20

Domains: Networking and Internet Architecture [cs.NI]

Christian Malchin, Hans Daduna. Discrete time queueing networks with product form steady state. Availability and performance analysis in an integrated model. Queueing Systems, 2010, 65 (4), pp.385-421. ⟨10.1007/s11134-010-9181-2⟩. ⟨hal-00715653⟩