Non-preemptive Priority Service Discipline Research Articles

A Framework for Packet Delay Analysis of Point-to-Multipoint Underlay Cognitive Radio Networks

This paper presents a queueing analytical framework for the performance evaluation of the secondary user (SU) packet transmission with service differentiation in a point-to-multipoint underlay cognitive radio network. The transmit power of the SU transmitter is subject to the joint outage constraint imposed by the primary user receivers (PU-Rxs) and the SU maximum transmit power limit. The analysis considers a queueing model for secondary traffic with multiple classes, and different types of arrival and service processes under a non-preemptive priority service discipline. The SU quality of service (QoS) is characterized by a packet timeout threshold and target bit error rate. Given these settings, analytical expressions of the packet timeout probability and average transmission time are derived for opportunistic and multicast scheduling. Moreover, expressions of the average packet waiting time in the queue and the total time in the system for each class of traffic are obtained. Numerical examples are provided to illustrate the secondary network performance with respect to various parameters such as number of PU-Rxs and SU receivers, SU packet arrival process, QoS requirements, and the impact of interference from the primary network to the secondary network.

Deterministic performance bounds in a window‐based token ring network supporting two priorities

Abstract A window‐based token ring protocol supporting two priority traffic streams is proposed. This protocol uses the window timers to limit the packet transmissions of a token holding station. The packets arriving during a window period are always transmitted before those arriving during subsequent window periods. Nonpreemptive priority service discipline is used to serve high priority packets. A call admission control policy based on delay bound is then employed to guarantee QoS such as the packet delay, delay jitter, and the packet loss‐free requirement for both priority traffic streams. Under such window‐based token ring operation and call admission control, network‐wide fairness can be achieved and the network output traffic characteristics become predictable. With these properties, we would expect that the window‐based token protocol is more appropriate for real‐time communications.

An Iterative Algorithm for a Multiple Finite-source Queueing Model with Dynamic Priority Scheduling

A multiple finite source queueing model with a single server and dynamic, non-preemptive priority service discipline is studied in this paper. The times the customers spend at the corresponding sources are exponentially distributed. The service times of the customers can follow exponential, Erlang or hyperexponential probability density function. By using results published earlier and an extension of mean value analysis, an iterative algorithm was developed to obtain approximate values of the mean waiting times in queues for the priority classes. The mean number of waiting customers and the server utilization of each class are obtained using the result of this algorithm and Little's formula. The algorithm is preferable to the earlier method, because it does not increase in complexity as the number of customer classes increases.

An Iterative Algorithm for a Multiple Finite-source Queueing Model with Dynamic Priority Scheduling

A multiple finite source queueing model with a single server and dynamic, non-preemptive priority service discipline is studied in this paper. The times the customers spend at the corresponding sources are exponentially distributed. The service times of the customers can follow exponential, Erlang or hyperexponential probability density function. By using results published earlier and an extension of mean value analysis, an iterative algorithm was developed to obtain approximate values of the mean waiting times in queues for the priority classes. The mean number of waiting customers and the server utilization of each class are obtained using the result of this algorithm and Little's formula. The algorithm is preferable to the earlier method, because it does not increase in complexity as the number of customer classes increases.

Diffusion approximations for queues with server vacations

This paper studies the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, modified by having the server take random vacations. In the first model, there is a vacation each time the queue becomes empty, as occurs for high-priority customers with a non-preemptive priority service discipline. Approximations for both the transient and steady-state behavior are developed for the case of relatively long vacations by proving a heavy-traffic limit theorem. If the vacation times increase appropriately as the traffic intensity increases, the workload and queue-length processes converge in distribution to Brownian motion with a negative drift, modified to have a random jump up whenever it hits the origin. In the second model, vacations are generated exogenously. In this case, if both the vacation times and the times between vacations increase appropriately as the traffic intensity increases, then the limit process is reflecting Brownian motion, modified by the addition of an exogenous jump process. The steady-state distributions of these two limiting jump-diffusion processes have decomposition properties previously established for vacation queueing models, i.e., in each case the steady-state distribution is the convolution of two distributions, one of which is the exponential steady-state distribution of the reflecting Brownian motion obtained as the heavy-traffic limit without vacations.

Diffusion approximations for queues with server vacations

This paper studies the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, modified by having the server take random vacations. In the first model, there is a vacation each time the queue becomes empty, as occurs for high-priority customers with a non-preemptive priority service discipline. Approximations for both the transient and steady-state behavior are developed for the case of relatively long vacations by proving a heavy-traffic limit theorem. If the vacation times increase appropriately as the traffic intensity increases, the workload and queue-length processes converge in distribution to Brownian motion with a negative drift, modified to have a random jump up whenever it hits the origin. In the second model, vacations are generated exogenously. In this case, if both the vacation times and the times between vacations increase appropriately as the traffic intensity increases, then the limit process is reflecting Brownian motion, modified by the addition of an exogenous jump process. The steady-state distributions of these two limiting jump-diffusion processes have decomposition properties previously established for vacation queueing models, i.e., in each case the steady-state distribution is the convolution of two distributions, one of which is the exponential steady-state distribution of the reflecting Brownian motion obtained as the heavy-traffic limit without vacations.

Multiple finite source queueing model with dynamic priority scheduling

This article involves the study of a multiple finite source queueing model with a single server and dynamic, nonpreemptive priority service discipline. The input to the queue is comprised of customers from multiple finite sources. The time which the customers spend at the corresponding sources are exponentially distributed. The service times of the customers can follow exponential, Erlang, or hyperexponential probability density function, with the same mean regardless of the class. Using an extension of mean value analysis, a recursive algorithm is developed to obtain approximate values of the mean waiting time in queues for each priority class. The mean number of waiting customers and the server utilization of each priority class can be obtained using the result of this recursive algorithm and Little's formula. Numerical examples are presented to illustrate the methodology. The algorithm developed in this article is validated using simulation.

An algorithmic approach for a special class of Markov chains

In this paper, we develop an algorithmic method for the evaluation of the steady state probability vector of a special class of finite state Markov chains. For the class of Markov chains considered here, it is assumed that the matrix associated with the set of linear equations for the steady state probabilities possess a special structure, such that it can be rearranged and decomposed as a sum of two matrices, one lower triangular with nonzero diagonal elements, and the other an upper triangular matrix with only very few nonzero columns. Almost all Markov chain models of queueing systems with finite source and/or finite capacity and first-come-first-served or head of the line nonpreemptive priority service discipline belongs to this special class.

Optimal Control of an M/G/1 Priority Queue Via N-Control

SYNOPTIC ABSTRACTIn this paper we consider an M/G/1 queue with non-preemptive priority service discipline and N-control policy (of Heyman, Yadin and Naor). The Laplace-Stieltjes transforms of the waiting times are derived using properties of level crossings of regenerative processes and delayed busy cycles. The mean waiting times, the mean cost rate, and the optimal policy are also derived. Use of these results is illustrated through two numerical examples.