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In this section we introduce the mathematical formalism of the M/M/c queue and summarize the main results. For the complete discussion of the problem, the reader should refer to \cite{allen1978queueing}. \\  The number of customers in the system is a discrete random variable that evolves according to a \textit{continuous time Markov chain}, with the following transition probabilities:  \begin{itemize}  \item probability $p_{up}$ thatthe  in the time interval $\Delta t$ the number of customers in the system increases by one unit is $p_{up} = \lambda \Delta t$; \item probability $p_{down}$ that in the time interval $\Delta t$ the number of customers in the system decreases by one unit is $p_{down} = \mu \Delta t$ if there is a single customer in the system. If there are more customers, the probability $p_{down}$ increases, since there are several serves available, so that $p_{down} = 2 \mu \Delta t$ if there are two customers, $p_{down} = 3 \mu \Delta t$ if the number of customers in the system is three and so on. However, if the number of customers in the system equals the number of servers, the system is saturated and a queue is formed.  \end{itemize}  The state space diagram for this chain is as below: