Queueing models with delayed state-dependent service times

In a state-dependent queueing model, the service rate is adjusted at both epochs of customer arrivals and departures. In certain situations, frequently changing service rates is neither economical nor practical. This paper studies an alternative queueing model in which the server changes its service rates, or service types, only at the beginning of service. The model is analyzed by using an embedded Markov chain technique. The probability generating functions for the steady-state queue length are determined for both queueing models with and without vacations. Two particular models are considered in detail. One is the delayed M/M/c queue and the other is the delayed M/Gi/1 queue with c service types. The performance measures such as the mean queue length and additional waiting time are calculated and compared with regular queues.