Open AccessAnalysis of retrial queue with heterogeneous servers and Markovian arrival process
Author(s) -
Мэй Лю
Publication year - 2020
Publication title -
informatika
Language(s) - English
Resource type - Journals
eISSN - 2617-6963
pISSN - 1816-0301
DOI - 10.37661/1816-0301-2020-17-1-29-38
Subject(s) - retrial queue , markovian arrival process , computer science , markov process , exponential distribution , markov chain , ergodicity , orbit (dynamics) , queue , server , real time computing , queueing theory , computer network , queueing system , mathematics , statistics , machine learning , engineering , aerospace engineering
Multi-server retrial queueing system with heterogeneous servers is analyzed. Requests arrive to the system according to the Markovian arrival process. Arriving primary requests and requests retrying from orbit occupy an available server with the highest service rate, if there is any available server. Otherwise, the requests move to the orbit having an infinite capacity. The total retrial rate infinitely increases when the number of requests in orbit increases. Service periods have exponential distribution. Behavior of the system is described by multi-dimensional continuous-time Markov chain which belongs to the class of asymptotically quasi-toeplitz Markov chains. This allows to derive simple and transparent ergodicity condition and compute the stationary probabilities distribution of chain states. Presented numerical results illustrate the dynamics of some system effectiveness indicators and the importance of considering of correlation in the requests arrival process.