Abstract
This paper deals with a batch arrival that customers arrive to the system according to a compound Poisson process. The customer’s behavior is incorporated according to which loss with a certain probability and the server begins to provide a service only when a queue size minimum say ‘a’ and maximum service capacity is ‘b’. Once the server completes the service, the unsatisfied customers may get the same service under Bernoulli schedule is termed as instantaneous Bernoulli feedback. The occurrence of negative customer cause the server to fail and removes a group of customers or an amount of work if present upon its arrival. As soon as the failure instant, the service channel send to the two delays of verification, the first verification delay starts before the repair process and the second verification delay begins after the repair process. We use the generating function method to derive the stationary queue size distribution. Some important performance measures such as different states of the system and the expected length of the queue explicitly. Some important special cases and numerical examples are determined.
Highlights
Bulk arrival and batch service queueing system are quite common in many real life situations such as the arrival of aircraft passengers, elevators, manufacturing systems, communication network, giant wheel, tourism etc
Performance Measures If the system is in a steady-state condition, we have found Vq(1), Hq(1), Dq(1) and Rq(1) be the probabilities that the server is in vacation, busy, two delays of verification and repair state respectively
Numerical Results This section deals with the numerical illustration of the proposed queueing model through variations in the parameters using MATLAB to examine the performance measures of the system
Summary
Bulk arrival and batch service queueing system are quite common in many real life situations such as the arrival of aircraft passengers, elevators, manufacturing systems, communication network, giant wheel, tourism etc. Haridass and Arumuganathan (2008) analyzed a batch arrival, bulk service queue with the random breakdown and single vacation. Ayyappan and Shyamala (2013) studied the batch arrival queueing model with vacation and balking. Retrial queue with two stage service under Bernoulli vacation schedule and random failure was greatly discussed by Rajadurai et al (2018). Two different types of the service model subject to the server breakdown and delay time to repair were studied by Choudhury and Tadj (2009). If an arriving batch of customers find the server being busy, feedback service, vacation, two delays of verification, repair or idle period, the. The server may take a Bernoulli vacation with probability θ and wait for the batch of customers with complementary probability 1 − θ.
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