The Proof of a Folk Theorem on Queuing Delay with Applications to Routing in Networks
Journal of the ACM (JACM)
Balanced sequences and optimal routing
Journal of the ACM (JACM)
Multimodularity, Convexity, and Optimization Properties
Mathematics of Operations Research
Fraenkel's conjecture for six sequences
Discrete Mathematics
Optimal Load Balancing on Distributed Homogeneous Unreliable Processors
Operations Research
Routing Jobs to Servers with Deterministic Service Times
Mathematics of Operations Research
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We consider the problem of routing arriving jobs to parallel queues according to a deterministic periodic routing sequence. We introduce a combinatorial notion called the unbalance for such routing sequences. This unbalance is used to obtain an upper bound for the average waiting time of the routed jobs. The best upper bound for given (optimized) routing fractions is obtained when the unbalance is minimized. The problem of minimizing the unbalance is investigated and we show how to construct sequences with small unbalance.