Volume 41, No. 02, Month MARCH, Year 2019, Pages 363 - 374

Optimum cost analysis of batch service retrial queuing system with server failure, threshold and multiple vacations

Niranjan S. P., Chandrasekaran V. M, Indhira K.

Abstract Download PDF

The aim of this paper is to analyze the queuing model entitled to cost optimization in bulk arrival and a batch service retrial queuing system with threshold, server failure, non-disruptive service, and multiple vacations. When bulk arrival of customers find the server is busy, then all customers will join in the orbit. On the other hand, if the server is free, then batch service will be provided according to the general bulk service rule. Batch size varies from a minimum of one and a maximum of ‘b’ number of customers. Customers in the orbit seek service one by one through constant retrial policy whenever the server is in idle state. The server may encounter failure during service. If the server fails, then ‘renewal of service station’ will be considered with probability . If there is no server failure with probability in the service completion or after the renewal process and if the orbit is empty, the server then leaves for multiple vacations. The server stays on vacation until the orbit size reaches the value N. For this proposed queuing model, a probability generating function of the orbit size will be obtained by using the supplementary variable technique and various performance measures will be presented with suitable numerical illustrations. A real time application is also discussed for this system. Additionally, a cost effective model is developed for this queuing model.


bulk arrival, batch service, constant retrial policy, server failure, threshold, renewal time


Published by : Prince of Songkla University
Contributions welcome at :