The M/Ma.b/C interdependent queueing model with controllable arrival rates

Abstract

In this paper we introduce an M/Ma.b/C interdependent queueing model with controllable arrival rates. The steady state solutions and the system characteristics are derived and analysed for this model. It is observed that the mean dependence rate between the arrival and service processes can reduce the congestion in queues and delays in transmission. This is the most general model which includes most of the earlier models as particular cases for specific or limiting values of the parameters. The tabulation values help to control the queue length with the suitable selection of the parameters. The graphical figures help us to select the optimal values of the parameters to control the queue length. As an illustration, if the faster arrival rates are increasing, then the service rate should also be increased so that the queue length is empty.