We propose the formalism of the Dirac-Delta functions with polynomial argument to measure the probability of call completion (PCC) which plays an importance role in the development and assessment of the telecommunications. The measurement of the PCC is also translated as a rough estimate of the Quality-of-Service of providers of cellular communication. In order to test the model, the Dirac-Delta operator acts onto families of step-functions that would play the role of input functions. Thus, the I/O scheme is applied resulting in a nonlinear system of up to 12 parameters. In this manner, By assuming the case where the end users are performing handover under velocities less than 100 km/h, our simulations have determined a discrepancy between a known model and our approach which is of order of 7% due to the minor computational errors.