In this study, we analyze a finite-buffer M/G/1 queueing model with randomized pushout space priority and nonpreemptive time priority. Space and time priority queueing models have been extensively studied to analyze the performance of communication systems serving different types of traffic simultaneously: one type is sensitive to packet delay, and the other is sensitive to packet loss. However, these models have limitations. Some models assume that packet transmission times follow exponential distributions, which is not always realistic. Other models use general distributions for packet transmission times, but their space priority rules are too rigid, making it difficult to fine-tune service performance for different types of traffic. Our proposed model addresses these limitations and is more suitable for analyzing communication systems that handle different types of traffic with general packet length distributions. For the proposed queueing model, we first derive the distribution of the number of packets in the system when the transmission of each packet is completed, and we then obtain packet loss probabilities and the expected number of packets for each type of traffic. We also present a numerical example to explore the effect of a system parameter, the pushout probability, on system performance for different packet transmission time distributions.

Recently, M/G/1 priority queues with a finite buffer for high-priority customers and an infinite buffer for low-priority customers have applied to the analysis of communication systems with two heterogeneous traffics : delay-sensitive traffic and loss-sensitive traffic. However, these studies are limited to M/G/1 priority queues with finite and infinite buffers under a work-conserving priority discipline such as the nonpreemptive or preemptive resume priority discipline. In many situations, if a service is preempted, then the preempted service should be completely repeated when the server is available for it. This study extends the previous studies to M/G/1 priority queues with finite and infinite buffers under the preemptive repeat-different and preemptive repeat-identical priority disciplines. We derive the loss probability of high-priority customers and the waiting time distributions of high- and low-priority customers. In order to do this, we utilize the delay cycle analysis of finite-buffer M/G/1/K queues, which has been recently developed for the analysis of M/G/1 priority queues with finite and infinite buffers, and combine it with the analysis of the service time structure of a low-priority customer for the preemptive-repeat and preemptive-identical priority disciplines. We also present numerical examples to explore the impact of the size of the finite buffer and the arrival rates and service distributions of both classes on the system performance for various preemptive priority disciplines.

Priority disciplines are an important scheme for service systems to differentiate their services for different classes of customers. (N, n)-preemptive priority disciplines enable system engineers to fine-tune the performances of different classes of customers arriving to the system. Due to this virtue of controllability, (N, n)-preemptive priority queueing models can be applied to various types of systems in which the service performances of different classes of customers need to be adjusted for a complex objective. In this paper, we extend the existing (N, n)-preemptive resume and (N, n)-preemptive repeat-identical priority queueing models to the (N, n)-preemptive repeat-different priority queueing model. We derive the queue-length distributions in the M/G/1 queueing model with two classes of customers, under the (N, n)-preemptive repeat-different priority discipline. In order to derive the queue-length distributions, we employ an analysis of the effective service time of a low-priority customer, a delay cycle analysis, and a joint transformation method. We then derive the first and second moments of the queue lengths of high- and low-priority customers. We also present a numerical example for the first and second moments of the queue length of high- and low-priority customers. Through doing this, we show that, under the (N, n)-preemptive repeat-different priority discipline, the first and second moments of customers with high priority are bounded by some upper bounds, regardless of the service characteristics of customers with low priority. This property may help system engineers design such service systems that guarantee the mean and variance of delay for primary users under a certain bounds, when preempted services have to be restarted with another service time resampled from the same service time distribution.

We propose a new priority discipline called the strict T-preemptive priority discipline, and derive the waiting time distributions of each class in the strict T-preemptive priority M/G/1 queue. Using this queueing analysis, we evaluate the performance of an opportunistic spectrum access in cognitive radio networks, where a communication channel is divided into time slots, a licensed primary user is assigned to one channel, and multiple unlicensed secondary users may opportunistically exploit time slots unused by the primary user. We also present a numerical example of the analysis of the opportunistic spectrum access where the arrival rates and service times distributions of each users are identical.