Discrete-time renewal input multiple vacation queue with accessible and non-accessible batches

• Published in: Opsearch 2011-12, Vol.48 (4), p.335-354
• Main Authors: Goswami, Veena, Laxmi, P. Vijaya
• Format: Article
• Language: English
• Subjects: Business and Management; Customer services; Customers; Management; Markov analysis; Mathematical analysis; Mathematics; Operations research; Operations Research/Decision Theory; Queues; Queuing; Random variables; Sensitivity analysis; Servers; Steady state; Studies; Tables (data); Theoretical Article; Thresholds; Vacations
• ISSN: 0030-3887; 0975-0320
• DOI: 10.1007/s12597-011-0055-0

This paper analyzes a discrete-time finite buffer single server accessible and non-accessible batch service queue with multiple vacations. The inter-arrival times of customers are arbitrarily distributed. The service times and vacation times are both geometrically distributed. The server starts service in batches of maximum size b with a minimum threshold value a , otherwise it goes for vacation. There is a provision to include the late arriving customers in the ongoing service batch if the size of the batch being served is less than a threshold value d   ( a  ≤  d  ≤  b ) and the service times are not affected by such inclusions. Using the supplementary variable and the embedded Markov chain techniques, we obtain the steady state probabilities at pre-arrival and arbitrary epochs. Some performance measures, waiting time distribution in the queue, and special cases of the model have also been discussed. Finally, sensitivity analysis is carried out in the form of table and graphs.