State dependent arrival in bulk retrial queueing system with immediate Bernoulli feedback, multiple vacations and threshold

Abstract

The objective of this paper is to analyse state dependent arrival in bulk retrial queueing system with immediate Bernoulli feedback, multiple vacations, threshold and constant retrial policy. Primary customers are arriving into the system in bulk with different arrival rates λa and λb. If arriving customers find the server is busy then the entire batch will join to orbit. Customer from orbit request service one by one with constant retrial rate γ. On the other hand if an arrival of customers finds the server is idle then customers will be served in batches according to general bulk service rule. After service completion, customers may request service again with probability δ as feedback or leave from the system with probability 1 − δ. In the service completion epoch, if the orbit size is zero then the server leaves for multiple vacations. The server continues the vacation until the orbit size reaches the value ‘N’ (N > b). At the vacation completion, if the orbit size is ‘N’ then the server becomes ready to provide service for customers from the main pool or from the orbit. For the designed queueing model, probability generating function of the queue size at an arbitrary time will be obtained by using supplementary variable technique. Various performance measures will be derived with suitable numerical illustrations.