Abstract
Consider a queueing system with a single server, where customer arrivals follow a Markovian arrival process and service times follow a phase-type distribution. The main server has the capability to recruit an additional server when the number of customers in the system exceeds a certain threshold, denoted as L. Both servers provide normal service to customers, and optional service is provided upon request. The main server takes multiple vacations, with the durations following an exponential distribution with rate parameter η, until there is at least one customer in the system. This system can be represented as a Markov chain process, and its steady state can be analyzed using matrix analytic methods. Performance measures such as the average number of customers, waiting time, and system throughput can be evaluated using the steady state probabilities. Numerical and graphical representations can be established to visualize the system’s behavior. By studying this system, we can gain insights into its efficiency, identify areas for improvement, and make informed decisions to enhance overall performance.
Recommended Citation
Ayyappan, G. and Sankeetha, S.
(2024).
(R2077) Enhancing Queue Management: Dynamic Server Allocation and Optional Services in Stochastic Modeling,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 21,
Iss.
1, Article 2.
Available at:
https://digitalcommons.pvamu.edu/aam/vol21/iss1/2