Performance Analysis of Statistical Multiplexers with Finite Number of Input Links and a Train Arrival Process

In this paper, we present an exact discrete-time queuing analysis of a statistical multiplexer with a finite number of input links and whose arrival process is correlated and consists of a train of a fixed number of fixed-length packets. The functional equation describing this queuing model is manipulated and transformed into a mathematical tractable form. This allows us to apply the final value theorem to extract an exact expression for the steady-state probability generating functions (pgfs) of the queue length and packet arrivals. From the pgf of the queue length, several performance measures such as probabilities of buffer overflow, mean buffer occupancy and mean packet delay are derived. The transform approach used in the present analysis provides a general framework under which similar types of functional equations, arising in the performance analysis of statistical multiplexers, can be tackled. One of the salient characteristics of the analysis presented here is that it does not rely on matrix-geometric concepts such as spectral decomposition, probability generating matrix, and left and right eigenvectors Key-Words: ATM multiplexers, Performance analysis, Transform analysis, Train arrivals, Functional equations, Discrete-time queues.