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Abstract

Generally, it is very common in our daily life to meet up with queuing systems. This study examines the concept of encouraged arrival in M/M (a,b)/1/Multiple Working Vacations queuing model that follows the General Bulk Service Rule. The considered queuing model consists of three states namely idle, working vacation and regular busy period. The single server available in the system usually goes on vacation whenever the system is idle, that is, when it is empty. This model deals with multiple working vacations of the server which are exponentially distributed and the concept of encouraged arrival of the customers is examined particularly in the regular busy period. Specifically, the term encouraged arrival is a recent addition to the queue with the existing customers following Poisson distribution and are served in batches. The main objective of the study is to calculate the mean queue length (Lq) and various other performance measures of the discussed queuing model. Moreover, a real life application of the studied model has been implemented in a case study and the expected queue length has been discussed.

Keywords

Encouraged arrival, Expected queue length, General bulk service rule, Multiple working vacations, Queuing model

Subject Area

Mathematics

Article Type

Article

First Page

1621

Last Page

1629

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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