Application–Based Statistical Approach for Identifying Appropriate Queuing Model

Queuing theory is a mathematical study of queues or waiting lines. It is used to model many systems in different fields in our life, whether simple or complex systems. The key idea in queuing theory of a mathematical model is to improve performance and productivity of the applications. Queuing models are constructed in order to compute the performance measures for the applications and to predict the waiting times and queue lengths. This thesis is depended on previous papers of queuing theory for varies application which analyze the behavior of these applications and shows how to calculate the entire queuing statistic determined by measures of variability (mean, variance and coefficient of variance) for variety of queuing systems in order to define the appropriate queuing model. Computer simulation is an easy powerful tool to estimate approximately the proper queuing model and evaluate the performance measures for the applications. This thesis presents a new simulation model for defining the appropriate models for the applications and identifying the variables parameters that affect their performance measures. It depends on values of mean, variance and coefficient of the real applications, comparing them to the values for characteristics of the queuing model, then according to the comparison the appropriate queuing model is approximately identified.The simulation model will measure the effectiveness performance of queuing models A/B/1 where A is inter arrival distribution, B is the service time distributions of the type Exponential, Erlang, Deterministic and Hyper-exponential. The effectiveness performance of queuing model are: *L : The expected number of arrivals in the system. *Lq : The expected number of arrivals in the queue. *W : The expected time required a customer to spend in the system. *Wq : The expected time required a customer to spend in Queue. *U : the server utilization