An analysis of bulk service queueing models and application of single service queueing systems in bank sectors

Abstract

Queuing theory is a branch of applied mathematics which deals with the mathematical study of waiting lines. It is applicable in business, commerce, industry, healthcare, public service and engineering etc. The study of queues deals with quantifying the phenomenon of waiting lines using representative measures of performance, such as average queue length, average waiting time in queue and average facility utilization. The motivation for bulk service queueing models arises from manufacturing environments with batch service work stations. For example machines for computer components and chip productions. In this research work, an analysis has been carried out on a bulk service M/M(a,b)/(2,1) and M/M(a,d,b)/(2,1) queueing models with servers different vacation policies in which atleast one server is available for service in the system always and M/M(a,b)/1 also discussed in detail. In all these models, it is assumed that the arrival follows Poisson distribution with newlineparameter and#955;gt0 and service is done in a batch which is exponentially distributed with parameter and#956;. The analysis also has been carried for non- identical servers with different service rate for M/M(a,b)/(2,1) queueing model. In which, the fast server is always available in the system and the slow server is allowed to take vacation whenever the queue length is less than a . The successive service times and#956;1 and and#956;2 are assumed to be mutually independent and exponentially distributed where and#956;1gtand#956;2. newline