On Markov–Krein characterization of the mean waiting time in M/G/K and other queueing systems

  title={On Markov–Krein characterization of the mean waiting time in M/G/K and other queueing systems},
  author={Varun Gupta and Takayuki Osogami},
  journal={Queueing Systems},
We propose a new research direction to reinvigorate research into better understanding of the M/G/K and other queueing systems—via obtaining tight bounds on the mean waiting time as functions of the moments of the service distribution. Analogous to the classical Markov–Krein theorem, we conjecture that the bounds on the mean waiting time are achieved by service distributions corresponding to the upper/lower principal representations of the moment sequence. We present analytical, numerical, and… 
Extremal GI/GI/1 queues given two moments: exploiting Tchebycheff systems
Tight upper bounds for the mean and higher moments of the steady-state waiting time in the GI / GI /1 queue are studied given the first two Moments of the interarrival-time and service-time distributions.
  • Yan Chen, W. Whitt
  • Mathematics
    Probability in the Engineering and Informational Sciences
  • 2022
This work designs extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability and illustrates the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval ofvalues for the mean waiting times.
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We study the upper bound of the transient mean waiting time in the classical GI/GI/ 1 queue over candidate interarrival-time distributions with finite support, given the first two moments of the
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In order to understand queueing performance given only partial information about the model, we propose determining the set of all possible values given that limited information. We illustrate this
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Recent Papers on Bounds for Queues
This is an overview of my papers on bounds for queues, emphasizing recent work with Yan Chen.
Robust capacity planning for accident and emergency services
A robust-optimization based approximation for the patient waiting times in an A&E and a simulation optimization heuristic to solve this capacity planning problem are proposed.
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On Markov-Krein Characterization of Mean Sojourn Time in Queueing Systems
We present a new analytical tool for three queueing systems which have defied exact analysis so far: (i) the classical M/G/k multi-server system, (ii) queueing systems with fluctuating arrival and
Comparison conjectures about the M/G/ s queue
A Light-Traffic Theorem for Multi-Server Queues
It is shown that as the traffic goes to zero, the probability of delay depends only on the mean of the service-time distributions and that the delay when positive converges in distribution to the minimum of c independent equilibrium-excess service-times is zero.
Approximations for the M/G/m Queue
A simple approximation for the queue length distribution of the M/G/m queue with finite waiting room is proposed and some numerical results indicate that the proposed approximation is rather accurate.
Steady-state analysis of a multiserver queue in the Halfin-Whitt regime
This work characterize the limiting scaled stationary queue length distribution in terms of the stationary distribution of an explicitly constructed Markov chain, and obtains an explicit expression for the critical exponent for the moment generating function of a limiting stationary queuelength.
The steady-state solution of the M/K2/m queue
  • P. Hokstad
  • Mathematics
    Advances in Applied Probability
  • 1980
The many-server queue with service time having rational Laplace transform of order 2 is considered. An expression for the asymptotic queue-length distribution is obtained. A relatively simple formula
On the inapproximability of M/G/K: why two moments of job size distribution are not enough
The M/G/K queueing system is one of the oldest models for multiserver systems and has been the topic of performance papers for almost half a century. However, even now, only coarse approximations
The effect of variability in the GI/G/s queue
  • W. Whitt
  • Mathematics
    Journal of Applied Probability
  • 1980
In 1969 H. and D. Stoyan showed that the stationary waiting-time distribution in a GI/G/1 queue increases in the ordering determined by the expected value of all non-decreasing convex functions when
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An upper bound on the tail distribution of the transient waiting time for the GI/GI/1 queue is derived from a formulation of semidefinite programming (SDP) using the first two moments of the service time and the interarrival time.