Ergodicity of a polling network

Ergodicity of a polling network

0.00 Avg rating0 Votes
Article ID: iaor19951128
Country: Netherlands
Volume: 50
Issue: 2
Start Page Number: 253
End Page Number: 262
Publication Date: Apr 1994
Journal: Stochastic Processes and Their Applications
Authors: ,
Keywords: polling systems
Abstract:

The polling network considered here consists of a finite collection of stations visited successively by a single server who is following a Markovian routing scheme. At every visit of a station a positive random number of the customers present at the start of the visit are served, whereupon the server takes a positive random time to walk to the station to be visited next. The network receives arrivals of customer groups at Poisson instants, and all customers wait until served, whereupon they depart from the network. Necessary and sufficient conditions are derived for the server to be able to cope with the traffic. For the proof a multidimensional imbedded Markov chain is studied.

Reviews

Required fields are marked *. Your email address will not be published.