Study of a two types of general heterogeneous service queueing system in a single server with optional repeated service and feedback queue

Yıl 2024, Erken Görünüm, 1 - 28

Snigdha Mahanta Nitin Kumar Gautam Choudhury

https://doi.org/10.15672/hujms.1312795

Öz

This paper addresses a model on a single server queue and two service representatives. After a customer is served, he/she has the three options: opting for receive the same service again (re-service), joining as a new customer for another regular service (feedback), or leaving the service system altogether. To ensure the queueing system is Markovian, we introduce an additional variable (supplementary variable) and using this approach, we derive the explicit distribution of queue size at random and departure epochs. Additionally, we determine the distribution of response time, inter-departure time, and busy period. By using the embedded Markov chain technique we have also derived the queue size distribution at departure epoch. We have also presented the cost analysis of the model with some numerical examples. The numerical illustration validates our findings and provides valuable insights into the queuing system.

Anahtar Kelimeler

Bernoulli feedback, busy period, queueing system, re-service

Destekleyen Kurum

NA

Proje Numarası

NA

Teşekkür

NA

Kaynakça

• [1] L. Abolnikov and A. Dukhovny, Markov chains with transition delta-matrix: ergodicity conditions, invariant probability measures and applications, Int. J. Stoch. Anal. 4, 333–355, 1991. [2] R.F. Anabosi and K.C. Madan, A single server queue with two types of service, Bernoulli schedule server vacations and a single vacation policy, Pakistan J. Statist. 19 (3), 331–342, 2003. [3] A. Begum and G. Choudhury, Analysis of an M/(G1 G2)/1 queue with Bernoulli vacation and server breakdown, Int. J. Appl. Comput. Math. 9 (9), 1–32, 2023. [4] P.J. Burke, Delays in single-server queues with batch input, Oper. Res. 23(4), 830– 833, 1975.