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Explicit M/G/1 waiting-time distributions for a class of long-tail service-time distributions

Joseph Abate, Ward Whitt
1999 Operations Research Letters  
Cohen recently obtained an explicit expression for the M/G/1 steady-state waiting-time distribution for a class of service-time distributions with power tails.  ...  Our result here also extends our own earlier explicit expression for the M/G/1 steady-state waiting-time distribution when the service-time distribution is an exponential mixture of inverse Gaussian distributions  ...  However, recently, Boxma and Cohen [7] obtained an explicit expression for the M/G/1 waiting-time distribution for a class of long-tail service-time distributions.  ... 
doi:10.1016/s0167-6377(99)00014-0 fatcat:dq3cj3w7p5bkniwwhq3qs3gkge

Some parametrized dynamic priority policies for 2-class M/G/1 queues: completeness and applications [article]

Manu K. Gupta, N. Hemachandra, J. Venkateswaran
2018 arXiv   pre-print
2-class M/G/1 queue.  ...  Next, we re-derive the celebrated c/ρ rule for 2-class M/G/1 queues by an elegant argument and also simplify a complex joint pricing and scheduling problem for a wider class of scheduling policies.  ...  There is a one-to-one nonlinear transformation for the mean waiting time vector of HOL-PJ and extended DDP, and hence HOL-PJ is complete for 2-class M/G/1 queues.  ... 
arXiv:1804.03564v1 fatcat:zv6xocwobfdovehtsedlko2hpm

The rate of convergence to stationarity for M/G/1 models with admission controls via coupling [article]

Martin Kolb, Wolfgang Stadje, Achim Wübker
2012 arXiv   pre-print
We study the workload processes of two restricted M/G/1 queueing systems: in Model 1 any service requirement that would exceed a certain capacity threshold is truncated; in Model 2 new arrivals do not  ...  enter the system if they have to wait more than a fixed threshold time in line.  ...  Introduction In this paper we consider the long-run behavior of the workload processes V t of the two most important M/G/1 queueing systems with admission restrictions.  ... 
arXiv:1201.0532v1 fatcat:yjj5poi2cvbs5llfxzfqh7ekna

Second Order Asymptotic Properties for the Tail Probability of the Number of Customers in the M/G/1 Retrial Queue [article]

Bin Liu, Yiqiang Q. Zhao
2019 arXiv   pre-print
In this paper, we study tail asymptotic properties for the number of the customers in the M/G/1 retrial queueing system.  ...  The main contribution of this paper is the second order asymptotic analysis for the M/G/1 retrial queue.  ...  Acknowledgments The authors would like to thank three anonymous reviewers and the handling editor for their valuable comments and suggestions, which improved the quality of this paper significantly.  ... 
arXiv:1801.09607v2 fatcat:62m6wo34wfdkhe5f4bqbr537by

Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue

Sing-Kong Cheung, Hans van den Berg, Richard J. Boucherie
2006 Queueing systems  
This paper studies the M/G/1 processor-sharing (PS) queue, in particular the sojourn time distribution conditioned on the initial job size.  ...  Keywords M/G/1 PS • Conditional sojourn time • Moments • Insensitive bounds • Instantaneous sojourn time • Euler's number triangle • Moment ordering • Permanent customers  ...  Acknowledgments The authors would like to thank the referees for offering valuable and constructive comments on an earlier version of this paper.  ... 
doi:10.1007/s11134-006-7583-y fatcat:iegj62siwnb6ffubnhwlt6733a

On the transition from heavy traffic to heavy tails for the M/G/1 queue: The regularly varying case

Mariana Olvera-Cravioto, Jose Blanchet, Peter Glynn
2011 The Annals of Applied Probability  
Two of the most popular approximations for the distribution of the steady-state waiting time, W_∞, of the M/G/1 queue are the so-called heavy-traffic approximation and heavy-tailed asymptotic, respectively  ...  , while the heavy tailed asymptotic describes power law decay in the tail of the distribution of W_∞ for a fixed traffic intensity.  ...  Let (W n (ρ) : n ≥ 0) be the waiting time sequence for an M/G/1 FIFO queue that is fed by a Poisson arrival process having arrival rate λ = ρ/EV 1 and independent iid processing times (V n : n ≥ 0).  ... 
doi:10.1214/10-aap707 fatcat:qziwliqzo5gffijt2rjjnx36gu

High-Priority Expected Waiting Times in the Delayed Accumulating Priority Queue with Applications to Health Care KPIs [article]

Blair Bilodeau, David A. Stanford
2022 arXiv   pre-print
respect to both classes' waiting time distributions.  ...  We provide the first analytical expressions for the expected waiting time of high-priority customers in the delayed APQ by exploiting a classical conservation law for work-conserving queues.  ...  Doug Down for his insights regarding the geometric tail decay rate of the M/D/1 queue length, and to Elisheva Schwarz-Zur for pointing out that the statement of Theorem 1 was incomplete in a preliminary  ... 
arXiv:2001.06054v4 fatcat:ai3qozoxknepnk2ogmubajofr4

Heavy Tails: The Effect of the Service Discipline [chapter]

S. C. Borst, O. J. Boxma, R. Núñez-Queija
2002 Lecture Notes in Computer Science  
In the remainder of this section, we present an overview of the tail asymptotics of the waiting-time and sojourn time distributions in the M/G/1 queue for six key service disciplines: (i) The M/G/1 FCFS  ...  (ii) The M/G/1 PS queue Theorem 2 indicates that, contrary to the FCFS case, the sojourn time tail in the M/G/1 PS queue is just as heavy as the service time tail.  ... 
doi:10.1007/3-540-46029-2_1 fatcat:3pn3kd4wqrcdjk3alv4imelbzm

Page 2842 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
Cohen recently obtained an explicit expression for the M/G/1 steady-state waiting-time distri- bution for a class of service-time distributions with power tails.  ...  Tobias Rydén (S-LUND-CM; Lund) 2000d:60142 60K25 90B22 Abate, Joseph; Whitt, Ward (1-ATT3-SH; Florham Park, NJ) Explicit M/G/1 waiting-time distributions for a class of long-tail service-time distributions  ... 

Waiting-time tail probabilities in queues with long-tail service-time distributions

Joseph Abate, Gagan L. Choudhury, Ward Whitt
1994 Queueing systems  
We also derive multi-term asymptotic expansions for the waiting-time tail probabilities in the M/G/1 queue.  ...  We investigate the steady-state waiting-time tail probabilities P(W > x) when the service-time distribution has a long-tail distribution, i.e., when the service-time distribution fails to have a finite  ...  Gaver for helpful comments.  ... 
doi:10.1007/bf01158960 fatcat:b2db4gxx5fcutcoj5cqfvxijvy

The impact of the service discipline on delay asymptotics

S.C. Borst, O.J. Boxma, R. Núñez-Queija, A.P. Zwart
2003 Performance evaluation (Print)  
distributions for M/G/1-type queues with regularly varying service requirement distribution(s): (i) an analytical one, which relies on Tauberian theorems relating the tail behavior of a probability distribution  ...  This paper surveys the M/G/1 queue with regularly varying service requirement distribution.  ...  The waiting-time tail in the M/G/1 FCFS queue is 'one degree heavier' than the service requirement tail, in the regularly varying case.  ... 
doi:10.1016/s0166-5316(03)00071-3 fatcat:nuto7ak3unc4bgc2q6uqbxdwva

Asymptotic behaviour of the tandem queueing system with identical service times at both queues

O. J. Boxma, Q. Deng
2000 Mathematical Methods of Operations Research  
For this tandem queue, we relate the tail behavior of the sojourn time distribution and the workload distribution at the second queue to that of the (residual) service time distribution.  ...  Consider a tandem queue consisting of two single-server queues in series, with a Poisson arrival process at the rst queue and arbitrarily distributed service times, which f o r a n y customer are identical  ...  Sigman for interesting discussions.  ... 
doi:10.1007/s186-000-8317-z fatcat:rr436ev2jvg4ncl5dohaoosroe

Page 5956 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
Summary: “This paper considers an M/G/1 queue with Poisson rate 2 > 0 and service time distribution G(t) which is supposed to For the web version of Mathematical Reviews, see http: //www.ams.org/mathscinet  ...  Some results for the single-arrival M/G/1 queue with single server vacation and bulk-arrival M*/G/1 queue, but with no server vacation, can be derived directly using the results obtained in this paper.  ... 

Page 9175 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
Summary: “The M*/G/1 queueing system as well as several of its variants have long ago been studied by considering the em- bedded discrete-time Markov chain at service completion epochs.  ...  Summary: “We study M*/G/1 nonpreemptive, and preemptive- resume priority queues with/without vacations under the random order of service (ROS) discipline within each class.  ... 

Estimating queue length distributions for queues with random arrivals

Daniel S. Myers, Mary K. Vernon
2012 Performance Evaluation Review  
DERIVATION Consider an M/G/1 queue with average service time x, Poisson arrival rate λ, and a squared coefficient of variation of service time c 2 x .  ...  Finally, the approximation is accurate for a wide range of light-tailed service time distributions with high and low coefficients of variation.  ...  DERIVATION Consider an M/G/1 queue with average service time x, Poisson arrival rate λ, and a squared coefficient of variation of service time c 2 x .  ... 
doi:10.1145/2425248.2425268 fatcat:kppon3yw75hv5fq3r6j7trktvy
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