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This paper presents an efficient and fairly accurate approximation method for a loss system having two types of calls and three types of server groups. In this model, two types of calls arrive at the individual server group for each call type. If an arriving call fmds all the servers of a corresponding group busy, the call overflows to a common server group. If the overflowed call again fmds all the common servers busy, the call is lost. This model is constructed around a telephone based ticket reservation system, as well as around integrated services digital net. works which will be introduced in the near future. By approximating the overflow process using an interrupted Poisson process (lPP), the main problem is reduced to solving a queueing model with a common server group having two independent lPP inputs with different mean service times. The proposed method makes it possible to compute loss probabilities in a far shorter time as compared with the exact method employing the lumping method. The accuracy of the results is shown to be sufficiently good for practical use carrying out numerical experiments.

AN APPROXIMATION OF A LOSS SYSTEM WITH TWO HETEROGENEOUS TYPES OF CALLS