In this paper the authors derive an efficient computational procedure for the system in which fluid is produced by N1 on-off sources of type 1, N2 on-off sources of type 2 and transferred to a buffer which is serviced by a channel of constant capacity. This is a canonical model for multiservice ATM multiplexing, which is hard to analyze and also of wide interest. This paper’s approach to the computation of the buffer overflow probability, G(x)=Pr{buffer content>x}, departs from all prior approaches in that it transforms the computation of G(x) for a particular x into a recursive construction of an interpolating polynomial. For the particular case of two source types the interpolating polynomial is in two variables. The present main result is the derivation of recursive algorithms for computing the overflow probability G(x) and various other performance measures using their respective relations to two-dimensional interpolating polynomials. To make the computational procedure efficient the authors first derive a new system of equations for the coefficients in the spectral expansion formula for G(x) and then use specific properties of the new system for efficient recursive construction of the polynomials. They also develop an approximate method with low complexity and analyze its accuracy by numerical studies. The authors compute G(x) for different values of x, the mean buffer content and the coefficient of the dominant exponential term in the spectral expansion of G(x). The accuracy of the approximations is reasonable when the buffer utilization characterized by G(0) is more than 0.01.
