c  Heldermann Verlag Economic Quality Control ISSN 0940-5151 Vol 21 (2006), No. 2, 291 – 299 Transient Analysis of a System with Queue Dependent Servers and Controllable Arrivals K. Udaya Chandrika 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. 1 Introduction Systems with the number of servers depending on the queue length may be observed in banks during the peak days of transactions every month, in tax offices for a period before the last date for submission of the returns or payments, at transport facilities during festival seasons and on many other places. Singh [2] has presented a paper on queue dependent servers and obtained the steady state characteristics for the system with homogeneous servers. Krishna Reddy, Nadarajan and Kandasamy [1] have analysed the Markovian general bulk service queueing system with vacation and additional servers. They have obtained steady state solutions using matrix geometric method. Srinivasa Rao and Shoba [3] have presented a paper on the M/M/1 interdependent queueing model with controllable arrival rates and obtained steady state results. In this paper transient and hence steady state results are derived for the queue with controllable arrival rates and variable number of channels. 2 Model Description It is assumed that the customers arrive individually at a service facility in accordance with a Poisson process having rate λ. The queue discipline is FIFO. The room capacity is restricted to N . The system starts operating with a regular channel having service rate Brought to you by | University of Iowa Libraries Authenticated Download Date | 5/30/15 7:58 PM