On servers in series with losses in descrete time

We study a $m$-phase queueing system without buffers, operating in discrete time. The input flow is Bernoulli with parameter $a$. Service times in server $i$ have geometric distribution with parameter $b_i$. A customer, trying to enter a server at an instant, when it is busy, is lost. There have been obtained system of equilibrium equations and recurrence relations for its coefficients which enable us to formulate the algorithm to build the system. Recurrence formulas for computation of the empty system probability and some other performance characteristics of the system, are determined. The problem of optimal allocation of the servers is studied numerically.