Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Optimization of static traffic allocation policies
Theoretical Computer Science - Special issue on probabilistic modelling
Balanced sequences and optimal routing
Journal of the ACM (JACM)
Multimodularity, Convexity, and Optimization Properties
Mathematics of Operations Research
Optimal Load Balancing on Distributed Homogeneous Unreliable Processors
Operations Research
Optimal Routing Policies in Deterministic Queues in Tandem
WODES '02 Proceedings of the Sixth International Workshop on Discrete Event Systems (WODES'02)
NOTE ON THE CONVEXITY OF THE STATIONARY WAITING TIME AS A FUNCTION OF THE DENSITY
Probability in the Engineering and Informational Sciences
Discrete-Event Control of Stochastic Networks: Multimodularity and Regularity (Lecture Notes in Mathematics)
The price of forgetting in parallel and non-observable queues
Performance Evaluation
Open-loop control of stochastic fluid systems and applications
Operations Research Letters
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In this paper we investigate the problem of the effective computation of the optimal routing sequence in a queuing system made of two parallel queues with exponential service times. We first show that the optimal policy (minimizing the expected waiting time) is a Sturmian sequence and we establish several qualitative properties of this policy (monotonicity, continuity, convexity). Then, we propose an algorithm to compute the optimal routing sequence efficiently. We address the issues of time complexity as well as numerical stability of this algorithm. We then run an extensive set of experiments which show several interesting features of the optimal policy with apparent discontinuities and a fractal behavior and we provide several good approximations by using fast heuristics.