Waiting and sojourn times in a multi-server queue with mixed priorities

Authors:
Sergey Zeltyn;Zohar Feldman;Segev Wasserkrug
Affiliations:
IBM Haifa Research Lab, Haifa University, Haifa, Israel 31905;IBM Haifa Research Lab, Haifa University, Haifa, Israel 31905;IBM Haifa Research Lab, Haifa University, Haifa, Israel 31905
Venue:
Queueing Systems: Theory and Applications
Year:
2009

Citing 10
Cited 1

On a preemptive Markovian queue with multiple servers and two priority classes

Mathematics of Operations Research
Priority Queues with Feedback

Journal of the ACM (JACM)
Threshold-based interventions to optimize performance in preemptive priority queues

Queueing Systems: Theory and Applications
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects

Manufacturing & Service Operations Management
An Exact Solution for the State Probabilities of the Multi-Class, Multi-Server Queue with Preemptive Priorities

Queueing Systems: Theory and Applications
Multi-Server Queueing Systems with Multiple Priority Classes

Queueing Systems: Theory and Applications
Closed form solutions for mapping general distributions to quasi-minimal PH distributions

Performance Evaluation - Modelling techniques and tools for computer performance evaluation
A Unified Framework for Numerically Inverting Laplace Transforms

INFORMS Journal on Computing
Staffing of Time-Varying Queues to Achieve Time-Stable Performance

Management Science
Approximations for Markovian multi-class queues with preemptive priorities

Operations Research Letters

Expected Tardiness Computations in Multiclass Priority M/M/c Queues

INFORMS Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider a multi-server queue with K priority classes. In this system, customers of the P highest priorities (PK) can preempt customers with lower priorities, ejecting them from service and sending them back into the queue. Service times are assumed exponential with the same mean for all classes.The Laplace---Stieltjes transforms of waiting times are calculated explicitly and the Laplace---Stieltjes transforms of sojourn times are provided in an implicit form via a system of functional equations. In both cases, moments of any order can be easily calculated. Specifically, we provide formulae for the steady state means and the second moments of waiting times for all priority classes. We also study some approximations of sojourn-time distributions via their moments. In a practical part of our paper, we discuss the use of mixed priorities for different types of Service Level Agreements, including an example based on a real scheduling problem of IT support teams.