A Probabilistic Approach to Mass Serving System

Clients are coming randomly and are served immediately if there is a free serving station in the system, and if all the stations are occupied, they enter the queue. After being served they leave the system. There are many serving systems depending on: the process which describes arrival; serving mechanisms; length of queue; a) 0 - system with cancellation, b) k – system with a finite queue, c) ? - system with an infinite queue. This paper will describe in detail a system with one serving station, where the requisition flow is a Poisson process under the assumption that serving time at a serving station has exponential distribution.