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Abstract
Queueing theory is one of the most diverified fields of applied sciences that is widely used in a variety of areas including operations research , management science, computer science , telecommunication, production systems , and many others. Queuing system phenomenon is becoming more and more prevalent in increasing , congested and urbanized societies.Much effort has been denoted to the study the problem of state dependent queues in the finite and infinite waiting space to find transient probabilities and some measures of effectiveness for the queue.