Discrete-time Queue with Batch Geometric Arrivals and State Dependent Retention of Reneging Customers

Yutae Lee

This paper considers a discrete-time queueing system with batch geometric arrivals and retention of reneging customers, in which retention probability depends on the number of customers in the system. The steady state probability distribution of the number of customers in the system is derived. Other performance measures such as mean number of customers in the system, blocking probability, abandon probability, and service completion probability are obtained. Numerical examples are also given.