Jñānābha‎ > ‎Special Issue 2018‎ > ‎

Jñānābha‎ Special Issue (2018), 45-53

FINITE BUFFER QUEUEING SYSTEM WITH ACCESSIBLE AND NON-ACCESSIBLE BATCHES AND SINGLE VACATION

By
Seema Agarwal1 and Madhu Jain2
1Department of Mathematics, I.B.S., Dr B. R. Ambedkar University, Agra-282002
2Department of Mathematics, IIT Roorkee, Roorkee-247667(India)
1dr.seema1982@gmail.com, 2 madhufma@iitr.ac.in
(Received : November 24, 2017 ; Revised: August 22, 2018; Final form: September 07, 2018)

Abstract

In this paper, we introduce a finite buffer queueing model with single vacation in which the customers are served in batches. The service is provided according to a bulk service rule in which at least ‘a’ customers are needed to start a service with maximum serving capacity ‘b’ customers. The inter-arrival time and service time are assumed to be exponentially and arbitrarily distributed. The server takes a vacation as soon as the queue length falls below ‘a’ at the completion of service. For analysis purpose we have used supplementary variable technique. Some performance measures such as mean idle period and mean busy period are obtained.

 

Keywords and phrases: Bulk queue, Accessible and non-accessible batches, Singlevacation,  Finite buffer, Supplementary variable, Queue size.

2010 Mathematics Subject Classification: 90B22.

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