Analysis of a Two-server Queue with Consultation by Main Server
T. Resmi *
Department of Mathematics, KKTM Govt. College, Pullut, Kerala, India.
*Author to whom correspondence should be addressed.
Abstract
Multi-server queueing systems with consultation arise in many practical service environments. In such systems, an experienced main server provides assistance to other servers when required. These models are particularly relevant for analyzing the performance of complex and interdependent service operations. This paper investigates a two-server queueing system consisting a main server and a regular server, where the main server provides consultation to the regular server while simultaneously serving its own customers under a preemptive priority discipline. Consequently, the service process at the main server is subject to interruptions triggered by consultation requests. The external arrival process and the consultation request process are modeled as mutually independent Poisson processes. Service times at both the main server and the regular server are assumed to be independent and exponentially distributed. Under these assumptions, the underlying stochastic process is formulated and the stability condition for the system is derived. Key performance measures are obtained and evaluated numerically to illustrate the impact of system parameters.
Keywords: Main server, regular server, consultation, interruption