This paper presents analytically explicit results for the distribution of the number of customers served during a busy period vegas golden knights background for special cases of the M/G/1 queues when initiated with m customers.The functional equation for the Laplace transform of the number of customers served during a busy period is widely known, but several researchers state that, in general, it is not easy to invert it except for some simple cases such as M/M/1 and M/D/1 queues.Using the Lagrange inversion theorem, we give an elegant solution to this equation.We obtain the distribution of the number of customers served during a busy period for various service-time distributions such as exponential, deterministic, Erlang-k, gamma, chi-square, inverse Gaussian, generalized Erlang, matrix exponential, hyperexponential, uniform, Coxian, phase-type, Markov-modulated Poisson process, and interrupted Poisson weleda skin food 75ml best price process.Further, we also provide computational results using our method.
The derivations are very fast and robust due to the lucidity of the expressions.