Polling Systems with Positive and Negative Customers

We study Polling Systems (POLS) with both positive and negative customers, a direction not yet pursued in the literature on POLS. We analyze the Gated, Exhaustive and Globally-Gated service regimes and derive expressions for the Probability Generating Functions (PGFs) of the system’s states and for the Laplace-Stieltjes Transforms of the waiting times. Since the transforms depend on an unknown PGF of a key variable, we bring into use Interpolation Theory, never before exploited in the analyses of POLS, and obtain (approximated) explicit results for the PGFs and means of the variables involved. Numerical examples are presented, demonstrating the use of the solution procedure.