Extreme values of queue lengths in M/G/1 and GI/M/1 systems
Mathematics of Operations Research
Conditioned limit theorem for the pair of waiting time and queue line processes
Queueing Systems: Theory and Applications
An interpolation approximation for the mean workload in a GI/G/1 queue
Operations Research
Application of the Diffusion Approximation to Queueing Networks I: Equilibrium Queue Distributions
Journal of the ACM (JACM)
Extreme and high-level sojourns of the single server queue in heavy traffic
Queueing Systems: Theory and Applications
Moderate deviations for queues in critical loading
Queueing Systems: Theory and Applications
Heavy-traffic extreme-value limits for queues
Operations Research Letters
| Hi-index | 0.98 |
This paper presents heavy traffic limit theorems for the extreme virtual waiting time of a customer in an open queueing network. In this paper, functional limit theorems are proved for extreme values of important probability characteristics of the open queueing network investigated as the maximum and minimum of the total virtual waiting time of a customer, and the maximum and minimum of the virtual waiting time of a customer. Also, the paper presents the previous related works for extreme values in queues and the virtual waiting time in heavy traffic.