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Consider a closed queueing network with M service facilities and N circulating customers. Let <math>n_i</math> represent the number of customers present at the i-th facility, with <math>\sum_{i=1}^M n_i = N</math>. We assume that the service time for a customer at the i-th facility is given by an exponentially distributed random variable with mean <math>1/\mu_i</math> and that after completing service at the i-th facility a customer will proceed to the j-th facility with probability <math>p_{ij}</math>.
It follows from the [[
:<math>P(n_1,n_2,\cdots,n_M) = \frac{1}{G(N)}\prod_{i=1}^M \left( X_i \right)^{n_i}</math>
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