(R2142) Queueing System with Batched Services, Server-Controlled Re-Service, Set-Up Time and Multiple Vacation

Authors

• S. Karpagam, Institute of Science and Technology, India
• N. Aarthy, Institute of Science and Technology, India
• B. Somasundaram, Institute of Science and Technology, India

Abstract

To analyze a bulk queueing system with server-controlled admission for reservice, low-batch service, multiple vacation and set-up time. The study explores how the server dynamically adjusts between low-batch and bulk services based on the queue size. After completing a bulk service, the departing batch may request reservice with a certain probability. However, accepting the request is not mandatory, and the server admits it with some probability. Whenever the queue becomes empty, whether after reservicing, completing service with no reservice request, or ending the low-batch service, the server enters a random-length vacation. If the queue still has less than ‘a’ customers after the vacation, the server goes on another vacation. This will continue until at least ‘a’ customers are waiting. Once the vacation is over, if there are at least ‘a’ customers, the server requires set-up time to restart service. The probability-generating function (PGF) is derived using the SVT and LST techniques to obtain the steady-state solution. Key performance metrics of the queueing model are analyzed for various server states by leveraging the properties of the probability-generating function. The proposed model provides insights into server behavior, facilitating the reduction of queue length, waiting time, busy period, and TAC while enhancing idle time in a bulk queueing system.

Recommended Citation

Karpagam, S.; Aarthy, N.; and Somasundaram, B. (2026). (R2142) Queueing System with Batched Services, Server-Controlled Re-Service, Set-Up Time and Multiple Vacation, Applications and Applied Mathematics: An International Journal (AAM), Vol. 21, Iss. 1, Article 4.
Available at: https://digitalcommons.pvamu.edu/aam/vol21/iss1/4