Power series for stationary distributions of coupled processor models
SIAM Journal on Applied Mathematics
Dynamic scheduling of a multiclass make-to-stock queue
Operations Research
On a preemptive Markovian queue with multiple servers and two priority classes
Mathematics of Operations Research
Dynamic scheduling in multiclass queueing networks: Stability under discrete-review policies
Queueing Systems: Theory and Applications
On Markovian Multi-Class, Multi-Server Queueing
Queueing Systems: Theory and Applications
Dynamic Scheduling of a Two-Class Queue with Setups
Operations Research
Optimal Inventory Modeling of Systems: Multi-Echelon Techniques (INTL SERIES IN OPERATIONS RESEARCH & MANAGEMENT SCIENCE)
Multi-Server Queueing Systems with Multiple Priority Classes
Queueing Systems: Theory and Applications
How many servers are best in a dual-priority M/PH/k system?
Performance Evaluation
Stationary delays for a two-class priority queue with impatient customers
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Waiting and sojourn times in a multi-server queue with mixed priorities
Queueing Systems: Theory and Applications
The impact of buffer finiteness on the loss rate in a priority queueing system
EPEW'06 Proceedings of the Third European conference on Formal Methods and Stochastic Models for Performance Evaluation
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We consider a multi-class, multi-server queueing system with preemptive priorities. We distinguish two groups of priority classes that consist of multiple customer types, each having their own arrival and service rate. We assume Poisson arrival processes and exponentially distributed service times. We derive an exact method to estimate the steady state probabilities. Because we need iterations to calculate the steady state probabilities, the only error arises from choosing a finite number of matrix iterations. Based on these probabilities, we can derive approximations for a wide range of relevant performance characteristics, such as the moments of the number of customers of a certain type in the system en the expected postponement time for each customer class. We illustrate our method with some numerical examples. Numerical results show that in most cases we need only a moderate number of matrix iterations (~20) to obtain an error less than 1% when estimating key performance characteristics.