Modified Bessel series solution of the single server queueing model with feedback

Abstract

In multi-access systems, scheduling mechanism often requires a proper feedback policy. In this paper, the direct and simple transient solution technique for the state of the system in a single server/processor Markovian queueing model with feedback is presented using the modified Bessel function of the second kind. This technique appears to economise in algebra. The expression for a time-dependent measure of effectiveness such as an expected number of the customers in the system is also derived. We demonstrate how fast the state probabilities tend to their equilibrium limits when it exists. The sensitivity of the state of the system and expected number of the customers in the system has been also analysed and the results are depicted in the tables and graphs.