Optimal control of a deterministic multiclass queuing system for which several queues can be served simultaneously

We consider the optimal control problem of emptying a deterministic single server multiclass queuing system without arrivals. We assume that the server is able to serve several queues simultaneously, each at its own rate, independent of the number of queues being served. We show that the optimal seq...

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Bibliographic Details
Published in:Systems & control letters 2011-07, Vol.60 (7), p.524-529
Main Authors: Lefeber, Erjen, Lämmer, Stefan, Rooda, Jacobus E.
Format: Article
Language:English
Subjects:
[formula omitted]-rule
Applied sciences
Arrivals
Computer science
control theory
systems
Control systems
Control theory. Systems
Emptying
Exact sciences and technology
Mathematical programming
Multiclass queuing system
Operational research and scientific management
Operational research. Management science
Optimal control
Optimization
Quadratic programming
Queues
Queuing theory. Traffic theory
Servers
Simultaneous service
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Summary:We consider the optimal control problem of emptying a deterministic single server multiclass queuing system without arrivals. We assume that the server is able to serve several queues simultaneously, each at its own rate, independent of the number of queues being served. We show that the optimal sequence of modes is ordered by the rate of cost decrease. However, queues are not necessarily emptied. We propose a dynamic programming approach for solving the problem, which reduces the multi-parametric QP (mpQP) to a series of problems that can be solved readily.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2011.04.010