Mathematical Model Description and Statistical Analyse on Residual Waiting Time in K-Phase Erlang Queueing

S. Geetha, B. Rameshkumar, S. Murugesan


Generally, our peoples are avoided by waiting the queue length (time) at any situation because they expect to get an immediate service. But it’s not possible once due to on condition that the parameters. Queuing methodology is helpful to rectify the problem and it’s made a design of the system and it may realize the system performance level. Consider the bulk arrival queueing system. Initially the arriving customer has completed the service unfortunately that customer need for the service at the same station but not receiving an immediate service. Thus the customer last the time. So, in this paper we discussed the mathematical modeling (alternate) of minimizing the waiting time of replacement queueing system. We have proposed in two stages: first we derive the service time setup Lq and Wq of steady state condition in non Markovian process. Second, using alpha- cut methods to construct the pair of Multi Integer Nonlinear program and analyze the system performance level. Here, our proposed method is discussed about fuzzy environment at the same time queue parameters are considered as triangular fuzzy numbers. Finally, the collected data’s are analyzed the prediction of residual waiting time with the help of time series (descriptive) algorithm. A numerical example is included.


Erlang Distribution, Arima Model, Time Series, Residual Regression, Prediction, Fuzz Logic


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