Nonpreemptive Priority Queue Research Articles

Queueing analysis of nonpreemptive reservation priority discipline

Analysis is given to a nonpreemptive priority queueing system with P classes of messages where the class of message to be served next is the highest priority class waiting at the time of service start. (If this were the highest priority class waiting at the service completion epoch, we would have a classical nonpreemptive head-of-line priority queueing system.) We assume that the message service time distribution is identical for all classes. The mean message waiting time is obtained explicitly for each class, and numerically compared to the values in the corresponding head-of-line system. We have also proposed and evaluated a fairness measure to demonstrate the degree of discrimination. This model can be applied to the performance analysis of the prioritized token-ring scheme in local area computer networks when the propagation delay and bit latency are negligible compared to the frame transmission time.

A note on “analysis of a finite capacity nonpreemptive priority queue” by Kapadia, Kazmi and Mitchell

This note deals with the evaluation of blocking probabilities in a finite capacity multiseveer queue with non-preemptive priorities. Results obtained in Kapadia, Kazmi and Mitchell are simplified and extended.

Dynamic, Non-Preemptive Priority Queues with General, Linearly Increasing Priority Function

This paper considers a single server queueing system that services customers from P non-preemptive priority classes. We assume independent identically distributed exponential interarrival and general service times for each class of customer. We also assume that a customer's priority in the queue is determined not only by its class, but also by the length of time it has spent in the queue; the priority for each class can be a general linearly increasing priority function. Our development gives an expression for the expected waiting time of each customer class, and gives bounds on this expression. We demonstrate the calculation of the bounds by several numerical examples, and discuss the sensitivity of the bounds to priority function parameters and system utilization. We also show that, even under the most conservative assumptions, the bounds are remarkably tight. Furthermore, for the special case of an M/M/1 system with identical service time distributions, these bounds can be substantially improved if the ordinal ranking of expected waiting times is known a priori. The results of this research enable systems designers to anticipate and consequently to control system behavior for systems with general linearly increasing priority disciplines.

Delay Analysis of a Time Division Multiple Access (TDMA) Channel

The delay performance of a Time Division Multiple Access (TDMA) channel for transmitting data messages is considered. The channel is assumed to be fixed assigned to a station with unlimited buffer capacity and Poisson message arrivals. Each message gives rise to one or more packets for transmission into fixed-length time slots. The steady-state probability generating function of the queue size is derived. A formula for the expected message delay is given. The analysis is then generalized to a nonpreemptive priority queue discipline; expected message delay formulas are given for the priority classes.

A Priority Queue with Discounted Linear Costs

We consider a nonpreemptive priority queue with a finite number of priority classes, Poisson arrival processes, and general service time distributions. It is not required that the system be stable or even that the mean service times be finite. The economic framework is linear, consisting of a holding cost per unit time and fixed service reward for each customer class. Future costs and rewards are continuously discounted with a positive interest rate. Allowing general initial queue sizes, we develop an expression for the expected present value of rewards received minus costs incurred over an infinite horizon. From this we obtain the Laplace transform of the time-dependent expected queue length for each customer class.

Priority Assignment in a Network of Computers

This research is aimed at developing analytical tools for system modeling and analysis of real-time computer networks. We formulate an idealized mathematical model for a multiserver system with a finite length nonpreemptive priority queue.

Nonpreemptive Priority Queue with Binomial Input

In our queue model of nonpreemptive priority discipline, we assume that arrivals occur at discrete time points, follow binomial distribution, and have a discrete time service distribution. In the limit, it is shown that all the parameters of the resulting queue, with the above arrival and service pattern, agree with those derived already by various authors, except for different notations used for service and arrival rates. At the end of this paper, this discipline is compared with that of the “first-come-first-served” discipline and the effect of priorities on average waiting time is obtained.