Loss and delay queue with state dependent rates under no passing restriction and discouragement

Abstract

In this investigation, the performance analysis for a loss and delay multi server queueing model with no passing, discouragement and additional servers has been made. Due to no-passing constraint, the customers can be categorised into two types: i) those who do not need service even waiting in the queue; ii) the customers having exponentially distributed service time. Furthermore, a customer is assumed to be discouraged looking into the length of the queue at the service station. Using birth death rate and corresponding product type solution, queue size distribution is established which is further employed to derive various performance indices namely expected waiting time, average number of customers in the system and the difference between the expected waiting time of both types of customers in the system. A numerical experiment for the comparison with analytic results is also facilitated.