A queueing approach for the analysis of finite bulk arrival production process with two-class arrivals and customer impatience

Abstract

The present paper explains the performance of a production process of finite capacity for two classes of customers who may exhibit impatience. The arrivals can be found in terms of batches and will be picked for service in FIFO mode. The production requests can come in two ways (i) on immediate demand, (ii) for future stock purposes. Taking this point, we have taken two-class customers with different arrival rates. Also assumed state-dependent service with which process has to be triggered to avoid congestion. A computer programme has been executed for the R-K method to solve the transient equations for transient probabilities with the given input values of arrival rates of two-class customer orders, service rates and system capacity. System performance indices have been computed and shown numerical illustrations to assess the influence input parameters on performance indices.

Keywords

• Batch arrival
• two-class customers
• customer impatience
• phase-wise service and multi-server facility
• Statistics & Probability
• Applied Mathematics