Investigation of the queuing system HIGI|GI|∞

Queuing system with high intensive recurrent input flow, infinite number of servers and arbitrary distributed service time is considered in the paper. Time periods т between consecutive input arrivals are defined by distribution function P{t < x} = A(Nx), where N is a great number (N ^ ж in theory). Service time is a random variable with distribution function B(x). The system was investigated under condition of unbound growth (N ^ ж) of input rate by the using of the asymptotical analysis and the dynamical screening methods. It was shown that stationary distribution of busy servers in condition when N is great enough can be approximated by normal distribution with mean NXb and variance (NXb + Мф), where b = j (1 - В(т)) dт is an /•да 2 1 322 average service time, P = j (1 - В(т)) d т , X = [ j (1 - A( z ))dz ] , к = X (a - a), a is mean and a is variance of the random variable with distribution function A(x).

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