Archive | 2019
A Coupling-Based Analysis of a Multiclass Retrial System with State-Dependent Retrial Rates
Abstract
We study a multiclass single-server retrial system with independent Poisson inputs and the state-dependent retrial rates. Meeting busy server, a new class-i customer joins orbit i. Orbit i is working as a FIFO-type queueing system, in which the top customer retries to occupy server. The retrial times are exponentially distributed with a rate depending on the current configuration of the binary states of all orbits, idle or non-idle. We present a new coupling-based proof of the necessary stability conditions of this retrial system, found earlier in the paper [17]. The key ingredient of the proof is a coupling of the processes of retrials with the corresponding independent Poisson processes. This result allows to apply classic property PASTA in the following performance analysis. A few numerical results verifying stability conditions of a 3-class system are included as well.