Analysis of a queue with two priority classes and feedback controls

Tien V. Do,Hung T. Tran,Laszlo Pap

doi:10.1007/s40595-013-0005-2

Abstract

In this paper, a queueing system with two priority classes of customers is investigated. In the queueing system, customers of high priority can preempt the service of customers of low priority. Customers can wait in buffers of finite size. A congestion control mechanism is proposed to model various practical problems. The steady-state probabilities are computed with the help of the framework of quasi-birth–death processes using the theory of generalized invariant subspace. Performance measures of interest are also derived and demonstrated by numerical results.

Highlights

The preemptive queue with two priority classes has been treated in earlier works [10,11,13] because it can be used for the performance evaluation of practical systems
The system works under the preemptive discipline, i.e. an admitted high-priority customer immediately gets service upon his arrival either by getting an idle service unit or by occupying service unit being used by low-priority customers
The proposed queue can be used to model Differentiated Service Architecture [14] in IP networks. We show that this queue can be analyzed within the framework of Quasi Birth and Death (QBD) processes [4,5,7,8]

Summary

Introduction

The preemptive queue with two priority classes has been treated in earlier works [10,11,13] because it can be used for the performance evaluation of practical systems. Customers of two classes (high and low priority) arrive into the system. Each high-priority customer requires a single service unit. The system works under the preemptive discipline, i.e. an admitted high-priority customer immediately gets service upon his arrival either by getting an idle service unit or by occupying service unit being used by low-priority customers. The service capacity for low-priority customers depends on the number of high-priority customers in the system. If the number of low-priority customers is above the second control threshold, each arriving batch of low-priority customers will be discarded with a certain probability. The proposed queue can be used to model Differentiated Service Architecture [14] in IP networks. 3. The paper ends with some conclusions in Sect.

A system model and performance analysis

Batch loss probability

Customer loss probability

System time distribution

Numerical results

Conclusion