Exponential bounds with applications to call admission
Journal of the ACM (JACM)
Mathematics of Operations Research
Mathematics of Operations Research
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Optimal Inequalities in Probability Theory: A Convex Optimization Approach
SIAM Journal on Optimization
A semidefinite optimization approach to the steady-state analysis of queueing systems
Queueing Systems: Theory and Applications
System Modeling and Analysis: Foundations of System Performance Evaluation
System Modeling and Analysis: Foundations of System Performance Evaluation
Simple bounds for a transient queue
DSN '11 Proceedings of the 2011 IEEE/IFIP 41st International Conference on Dependable Systems&Networks
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We derive upper bounds on the tail distribution of the transient waiting time in the GI/GI/1 queue, given a truncated sequence of the moments of the service time and that of the interarrival time. Our upper bound is given as the objective value of the optimal solution to a semidefinite program (SDP) and can be calculated numerically by solving the SDP. We also derive the upper bounds in closed form for the case when only the first two moments of the service time and those of the interarrival time are given. The upper bounds in closed form are constructed by formulating the dual problem associated with the SDP. Specifically, we obtain the objective value of a feasible solution of the dual problem in closed from, which turns out to be the upper bound that we derive. In addition, we study bounds on the maximum waiting time in the first busy period.