A Multi-Server Markovian Queueing Model With Primary And Secondary Services

Abstract

We study a multi-server queueing model in which arrivals occur according to a Markovian arrival process. An arriving customer either (a) is lost due to all main servers being busy; or (b) enters into service with one of the main servers and leaves the system (as a satisfied primary customer); (c) enters into service with one of the main servers, gets service in self-service mode, and being impatient to get a final service with one of the main servers, may leave the system (as a dissatisfied secondary customer); or (d) enters into service with one of the main servers, gets service in self-service mode, becomes successful in getting a final service from one of the main servers, and departs (as a satisfied secondary customer). This queueing model is studied in steady state and some selected performance measures are derived.