Analytically simple solution to discrete-time queue with catastrophes, balking and state-dependent service

A queuing system with catastrophes, balking and state-dependent service has gained importance in the recent past due to its applications in various fields like communication system, health care system, production system and computer science. Keeping this in mind, the current paper analyses Geo/Geo/1 queuing system with catastrophes, balking and state-dependent service. Whenever a catastrophe occurs at the system, all customers are forced to leave the system immediately. Two different service rates, depending on the critical value of number of customers in the system (denoted by r), have been used. If a customer on arrival finds other customers in the system, it either decides to enter the system or balks with a constant probability. The expression for steady state probability vector of system size for two models i.e. Late Arrival System with Delayed Access (LAS-DA) and Early Arrival System (EAS) has been found via rate element R using matrix geometric technique. The expressions for probability generating function of number of customers in the system and some performance measures have also been derived. A numerical study has been performed to show the effect of various values of parameters on performance measures. A cost function has also been presented and impact of varying values of various parameters on it has been studied. The model has also been solved for two particular cases of r i.e. when r = 1 and when r = 2. The study reveals that the optimum value of r is 1. Hence, it can be concluded that fast service rate should be given when the number of customers in the system are 2 or more for both the models. The comparative study of two models reveals that LAS-DA model is better than EAS model. The study also exhibits that when the concept of balking and state dependent service are added to Geo/Geo/1 with catastrophe model then there is increase in cost in both the models (LAS-DA and EAS).