An approximation to the response time for shortest queue routing
SIGMETRICS '89 Proceedings of the 1989 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
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Algorithmic approach to bounding the mean response time of a minimum expected delay routing system
SIGMETRICS '92/PERFORMANCE '92 Proceedings of the 1992 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Bounds for Two Server Fork-Join Queueing Systems
Bounds for Two Server Fork-Join Queueing Systems
Theory, Volume 1, Queueing Systems
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Bounding of performance measures for a threshold-based queueing system with hysteresis
SIGMETRICS '97 Proceedings of the 1997 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Mean value technique for closed fork-join networks
SIGMETRICS '99 Proceedings of the 1999 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Bound Computation of Dependability and Performance Measures
IEEE Transactions on Computers
A Hybrid Solution of Fork/Join Synchronization in Parallel Queues
IEEE Transactions on Parallel and Distributed Systems
Optimizing systems by work schedules: (a stochastic approach)
WOSP '02 Proceedings of the 3rd international workshop on Software and performance
Computing Performance Bounds of Fork-Join Parallel Programs Under a Multiprocessing Environment
IEEE Transactions on Parallel and Distributed Systems
Response Time Analysis of Parallel Computer and Storage Systems
IEEE Transactions on Parallel and Distributed Systems
An Eclectic Survey of Bounding Methods for Markov Chain Models
MASCOTS '95 Proceedings of the 3rd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems
An Algorithmic Approach to Stochastic Bounds
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
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Probability in the Engineering and Informational Sciences
Bounding stationary results of Tandem networks with MAP input and PH service time distributions
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
Analysis of join-the-shortest-queue routing for web server farms
Performance Evaluation
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Dynamic routing of real-time jobs among parallel EDF queues: A performance study
Computers and Electrical Engineering
Stochastic bounds for randomized load balancing
ACM SIGMETRICS Performance Evaluation Review
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Balancing loads in a multi-server system can have a significant impact on performance. In this paper, we model such a system as a heterogeneous multi-server queueing system. We study the behavior of such a system operating under the minimum expected delay (MED) routing policy, i.e., an arriving customer is assigned to the queue which has the minimal expected value of unfinished work. This routing discipline can be viewed as a generalization of the join-the-shortest queue (SQ) discipline for homogeneous servers. There is no closed-form solution for this class of queueing problem. In this paper, we provide a methodology to compute upper and lower bounds on the mean response time of the system. This methodology allows one to tradeoff the tightness of the bounds and computational cost. Applications and numerical examples are presented which show how to use this methodology for deriving performance measures and also illustrating that the excellent accuracy of the computational algorithm which is achievable with modest computational cost.