Analysis of a Consultation-Based Three-Server Queue under Interruption Constraints
T. Resmi *
Department of Mathematics, KKTM Govt. College, Pullut, Kerala, India.
*Author to whom correspondence should be addressed.
Abstract
This paper analyzes a queueing model with three servers, comprising one main server and two regular servers. The main server not only serves its own customers but also provides consultation to the regular servers whenever assistance is requested, with consultation requests receiving preemptive priority over customer service. As a result, the service of customers at the main server experiences interruptions due to consultation activities. The arrival of customers and the generation of consultation requests are assumed to follow independent Poisson processes. The number of interruptions is limited by a finite upper bound. The service times at the regular servers are assumed to be independent and identically distributed random variables following a phase-type distribution, whereas the service time at the main server follows another phase-type distribution. The stochastic model corresponding to the system is formulated, and the implicit stability condition is established. Some important performance measures are derived and numerically analyzed to examine the influence of various system parameters on system behavior. Overall, the numerical experiments demonstrate that both increased customer arrivals and increased consultation activity adversely affect system performance by elevating congestion levels, customer accumulation, interruption frequency, and traffic intensity, highlighting the significant impact of consultation-related interruptions on system behavior.
Keywords: Main server, regular servers, consultation queue, service interruption, three-server queue, pre-emptive priority, phase-type distribution, Poisson arrival, stability condition, performance measures, traffic intensity