Analysis of a Two-server Queue with Consultation in Markovian Environment
T. Resmi *
Depertment of Mathematics, KKTM Govt. College, Pullut, Kerala, India.
*Author to whom correspondence should be addressed.
Abstract
Multi server queueing models with consultation by one well trained and experienced main server to the fellow servers play an important role in many modern service systems. In this paper, we analyze a two-server queueing model, where the main server provides consultation support in Markovian environment to the regular server. The main server serves customers directly but also extends consultation to the regular server with preemptive priority over its own customer service. The service of the customer at the main server will be interrupted due to higher-priority consultations. Both the number of interruptions at the main server and the number of consultations to the regular server are limited to finite upper bounds. The consultations are arised from M Markovian environmental factors which are related through a transition probability matrix F. The arrival process and consultation requirement are governed by two mutually independent Poisson processes. The service times at the main server and the regular server are modelled as mutually independent phase type distributions. The duration of the threshold clock is exponentially distributed whereas that of the super clock is a phase-type distributed parameter. The stability condition for the system is established and some performance measures are investigated through numerical analysis.
Keywords: Main server, regular server, consultation, interruption, Markovian environmental factors