A semidefinite optimization approach to the steady-state analysis of queueing systems
Queueing Systems: Theory and Applications
On Markov---Krein characterization of the mean waiting time in M/G/K and other queueing systems
Queueing Systems: Theory and Applications
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We derive an upper bound on the tail distribution of the transient waiting time for the GI/GI/1 queue from a formulation of semidefinite programming (SDP). Our upper bounds are expressed in closed forms using the first two moments of the service time and the interarrival time. The upper bounds on the tail distributions are integrated to obtain the upper bounds on the corresponding expectations. We also extend the formulation of the SDP, using the higher moments of the service time and the interarrival time, and calculate upper bounds and lower bounds numerically.