Customer Impatience in Multiserver Queues

In the modeling of many queuing systems, it is assumed that customers who arrive stay on till they receive service. In real life, this does not always happen. Arriving customer may decide against joining the system. In queuing parlance, this is known as balking. In this paper, we shall assume that customers may balk if service is not instantly available. Even if a customer joins the system, the customer may withdraw and leave without completely receiving service. This is known as reneging. In this paper, we consider a multiserver Markovian queuing system where customers may balk as well as renege. In addition to the traditional performance measures, some freshly designed ones have also been presented. The relevance of this work stems from the fact that not withstanding related analysis of similar customer behavior already available in literature, explicit closed form expressions are still not available for M/M/k model. In this paper, we present the same. A numerical problem with design aspects has also been presented to demonstrate results derived.