Abstract

This paper model the phenomenon of waiting in lines and predict Expected queue length and waiting time in queue of kth customer arrive at any time x based on Cumulative Approach Analytical Technique CAAT to inform customers on the system state at the time of estimation Using Modeling Technique developed and cumulative Arrival and service data collected up to time x functions approximately fit Cumulative arrival and service data distribution trend lines values were formulated and required queue values along a continuum within these discrete values were estimated and estimate Expected waiting time in the queue of kth customer arrive at any time x in case Queuing systems consist of one stations with no customer classes FIFO service protocols unlimited sizes of waiting room two number of Identical or independent servers and two types of Identical or independent service are studied Finally the author concludes that based on Cumulative Arrival and service data distribution trend lines curve fitting equations and A Cumulative Approach Modeling Technique CAMT we can easily predict Expected queue length and waiting time in FCFS queuing system queue line of j th customer arrive at the time of estimation Moreover the application of this model is feasible to drive equations and analyze phenomenon of waiting in lines and also this model offers better queuing systems analysis result which can be used to simulate a queuing system s performance and allows the determination of Customer appointments and effective arrival pattern management and hence service quality improvement trend lines curve fitting equations of