A matrix-geometric solution for the multiserver nonpreemptive priority queueing model with mixed priorities.

This paper describes the analysis of multiserver queues with nonpreemptive mixed priorities. Such priority structures occur, for example, in initiator settings within the mainframe operating system MVS: job classes have to be assigned to initiators and their priorities may differ amongst the initiators. Results of the analysis provide insight in how average queue lengths in this priority system behave under different class loads. Bounds have to be defined in order to obtain a matrix-geometric solution and it is shown how this affects the average queue lengths. The results should eventually allow to derive guidelines with respect to initiator definitions.Model; Models;

Joint queue length distribution of multi-class, single-server queues with preemptive priorities

In this paper we analyze an MN/MN/1 queueing system with N customer classes and preemptive priorities between classes, by using matrix-analytic techniques. This leads to an exact method for the computation of the steady state joint queue length distribution. We also indicate how the method can be extended to models with multiple servers and other priority rules

Joint queue length distribution of multi-class, single-server queues with preemptive priorities

In this paper we analyze an MN/MN/1 queueing system with N customer classes and preemptive priorities between classes, by using matrix-analytic techniques. This leads to an exact method for the computation of the steady state joint queue length distribution. We also indicate how the method can be extended to models with multiple servers and other priority rules

Analysis of a multi-server queueing model of ABR

In this paper we present a queueing model for the performance analysis of Available Bit Rate (ABR) traffic in Asynchronous Transfer Mode (ATM) networks. We consider a multi-channel service station with two types of customers, denoted by high priority and low priority customers. In principle, high priority customers have preemptive priority over low priority customers, except on a fixed number of channels that are reserved for low priority traffic. The arrivals occur according to two independent Poisson processes, and service times are assumed to be exponentially distributed. Each high priority customer requires a single server, whereas low priority customers are served in processor sharing fashion. We derive the joint distribution of the numbers of customers (of both types) in the system in steady state. Numerical results illustrate the effect of high priority traffic on the service performance of low priority traffic

Joint queue length distribution of multi-class, single server queues with preemptive priorities

In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a multi-dimensional Markov process, where the coordinates keep track of the number of customers of each class in the system. Based on matrix-analytic techniques and probabilistic arguments we develop a recursive method for the exact determination of the equilibrium joint queue length distribution. The method is applied to a spare parts logistics problem to illustrate the effect of setting repair priorities on the performance of the system. We conclude by briefly indicating how the method can be extended to an $M/M/1$ queueing system with non-preemptive priorities between customer classes.Comment: 15 pages, 5 figures -- version 3 incorporates minor textual changes and fixes a few math typo

Analyzing multi-class, multi-server queueing systems with preemtive priorities

In this paper we consider a multi-class, multi-server queueing system with preemptive priorities. We distinguish two groups of priority classes that consist of multiple items, each having their own arrival and service rate. We assume Poisson arrival processes and exponentially distributed service times. We derive an approximate method to estimate the steady state probabilities with an approximation error that can be made as small as desired at the expense of some more numerical matrix iterations. Based on these probabilities, we can derive approximations for a wide range of relevant performance characteristics, such as the expected postponement time for each item class and the first and second moment of the number of items of a certain type in the system. We illustrate our method with some numerical examples. Comparison to simulation results shows that with a moderate number of matrix iterations (~20) we can estimate key performance measures, such as the mean and variance of the number of items in the system, with an error less than 1% in most cases