Transient Analysis of a System with Queue Dependent Servers and Controllable Arrivals

Abstract A finite capacity Markovian queueing system with a number of heterogeneous channels depending on the system size is considered. The system consists of one regular channel and a maximum of c additional channels. When all the channels are in operation, the arrival rate is controlled depending on the queue length in order to minimize the waiting time of the customers. Expressing the Laplace transforms of the system of governing equations in matrix form and using the properties of symmetric tridiagonal matrices, the transient and steady state probabilities are derived. Some numerical results are presented.