Finite-Buffer M/G/1 Queues with Time and Space Priorities

Many communication systems have finite buffers and service delay-sensitive and loss-sensitive types of traffic simultaneously. To meet the diverse QoS requirements of these heterogeneous types of traffic, it is desirable to offer delay-sensitive traffic time priority over loss-sensitive traffic, and loss-sensitive traffic space priority over delay-sensitive traffic. To analyze the performance of such systems, we study a finite-buffer M/G/1 priority queueing model where nonpreemptive time priority is given to delay-sensitive traffic and push-out space priority is given to loss-sensitive traffic. Compared to the previous study on finite-buffer M/M/1 priority queues with time and space priority, where service times are identical and exponentially distributed for both types of traffic, in our model we assume that service times are different and are generally distributed for different types of traffic. As a result, our model is more suitable for the performance analysis of communication systems accommodating multiple types of traffic with different service-time distributions. For the proposed queueing model, we derive the queue-length distributions, loss probabilities, and mean waiting times of both types of traffic, as well as the push-out probability of delay-sensitive traffic. With numerical examples, we also explore how the performance measures are affected by system parameters such as the buffer size, and the arrival rates and mean service times of both types of traffic for different service-time distributions.