The research paper presents a theoretical framework for constructing queue models, focusing on derive The Poisson distribution with parameter (), discussed relationship between Poisson distribution and the exponential distribution, the Memoryless property of the Exponential distribution, the Assumptions of the M/ M/ 1 model, the construction of the M/ M/1 model, And which included transition states diagram for a Markov chain) diagram of birth and death process of M/M/1 model ( containing a proposal to add the time interval (h) , The purpose of adding (h) is to maintain the accuracy of information continuity. This procedure is supposed to apply to research papers that include Markov state transition diagrams [1] [2] [3] [4] [5] and This contributed to understanding the construction of the models. The research paper included an experimental aspect (Simulation), where the simulation results were consistent with the result of the theoretical model. The model was also discussed in terms of practical application and reference was made to a number of research papers that included the application of the M/M/1 model the aim of studying the M/M/1 model in detail that it is considered the basis for understanding more advanced models such as M/M/C, M/G/1 and G/M/1.
Keywords
Poisson distributionExponential distributionBirth and Death processsimulation of the M/ M/1 model.
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