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Using Robust Queueing to Expose the Impact of Dependence in Single-Server Queues

Ward Whitt, Wei You
2018 Operations Research  
We propose a new functional robust queueing formulation for the steady-state workload that is exact for the steady-state mean in the M/GI/1 model and is asymptotically correct in both heavy traffic and  ...  Such dependence is common in networks of queues, where arrivals are departures from other queues or superpositions of such complicated processes, especially when there are multiple customer classes with  ...  Corollary 3 (Exact for M/GI/1).  ... 
doi:10.1287/opre.2017.1649 fatcat:wskpeaubjjaw5etfpf7rj7rbhu

Subexponential tail equivalence of the queue length distributions of BMAP/GI/1 queues with and without retrials [article]

Hiroyuki Masuyama
2014 arXiv   pre-print
The main contribution of this paper is to prove the subexponential tail equivalence of the stationary queue length distributions in the BMAP/GI/1 queues with and without retrials.  ...  The stochastic-decomposition-like result shows that the stationary queue length distribution in the BMAP/GI/1 retrial queue is decomposed into two parts: the stationary conditional queue length distribution  ...  Research of the author was supported in part by Grant-in-Aid for Young Scientists (B) of Japan Society for the Promotion of Science under Grant No. 24710165.  ... 
arXiv:1310.4608v3 fatcat:fwb3kcgj7jemvpgmapgurfouae

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Dimitris Bertsimas, Georgia Mourtzinou
2012 Queueing systems  
We derive a set of transient distributional laws that relate the number of customers in the system (queue) at time t, denoted by L(t) (Q(t)) and the system (waiting) time, S(t) (W(t)) of a customer that  ...  These transient distributional laws provide a complete set of equations that describe the dynamics of the system in the transient domain, provide insight on the influence of the initial conditions and  ...  case of M/GI/1 queueing system under FIFO.  ... 
doi:10.1023/a:1019100301115 fatcat:iepok4msdjfhlhflpbsrohriwu

On Transitory Queueing [article]

Harsha Honnappa, Rahul Jain, Amy R. Ward
2014 arXiv   pre-print
We introduce a framework and develop a theory of transitory queueing models.  ...  This may be useful in analysis of other non-stationary and non-ergodic queuing models.  ...  Subramanian for his help in proving a part of Theorem 10 and for many insightful conversations.  ... 
arXiv:1412.2321v1 fatcat:ex4u67vzjfgx3ptdketutp3pxe

A sufficient condition for the subexponential asymptotics of GI/G/1-type Markov chains with queueing applications [article]

Hiroyuki Masuyama
2014 arXiv   pre-print
In this paper, we demonstrate the application of our main result to the stationary queue length distribution in the standard BMAP/GI/1 queue.  ...  stationary queue length distribution.  ...  Acknowledgments Research of the author was supported in part by Grant-in-Aid for Young Scientists (B) of Japan Society for the Promotion of Science under Grant No. 24710165.  ... 
arXiv:1310.4590v3 fatcat:32aulscmjjhl5d5nzfn4hcxhcq

Modulated Branching Processes, Origins of Power Laws and Queueing Duality [article]

Predrag R. Jelenkovic, Jian Tan
2008 arXiv   pre-print
Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas.  ...  ubiquitous nature of power law distributions.  ...  Acknowledgements We are thankful to the anonymous reviewers for their helpful comments and, in particular, we are grateful to a reviewer who pointed to us reference [32] that led to Theorem 7.  ... 
arXiv:0709.4297v2 fatcat:evujk73stff6ja5dv7voikaz3u

A Robust Queueing Network Analyzer Based on Indices of Dispersion [article]

Ward Whitt, Wei You
2020 arXiv   pre-print
We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing.  ...  A robust queueing technique is used to generate approximations of the mean steady-state performance at each queue from the IDC of the total arrival flow and the service specification at that queue.  ...  The reference case is the classical M/GI/1 queue, for which we have c 2 Z (ρ) = 1 + c 2 s = I w (t) for all ρ, t, 0 < ρ < 1, t ≥ 0.  ... 
arXiv:2003.11174v1 fatcat:oalegvnndfhntpkzludyfndsta

The effect of local scheduling in load balancing designs

Ho-Lin Chen, Jason R. Marden, Adam Wierman
2008 Performance Evaluation Review  
In an M/GI/1 PS queue E[Ti] has the following simple form: E[Ti] = 1 µi − λi The mean response time under SRPT has a much more compli- mean response time of SRPT in an M/GI/1 queue as follows: cated form  ...  Thus, each Qi is a stationary M/GI/1 queue. Note that all incoming jobs are routed to one of the servers, i.e., there is no balking.  ... 
doi:10.1145/1453175.1453200 fatcat:7rdroumbo5he3mafvpksbblpja

Modulated Branching Processes, Origins of Power Laws, and Queueing Duality

Predrag R. Jelenković, Jian Tan
2010 Mathematics of Operations Research  
In socio-economic areas, in addition to income distributions, the fluctuations in stock prices have also been observed to be characterized by power laws [27, 47] .  ...  Furthermore, in the course of our analysis, we observe a duality between the reflected multiplicative processes and queueing theory.  ...  This equivalence is established using classical results on M/GI/1 queue.  ... 
doi:10.1287/moor.1100.0464 fatcat:phbo2blffbhhradq4hbj4vqkpi

Page 4037 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
The first model considered is an M*/GI/1/k queue with batch Poisson arrivals and buffer size 1 < k < oo. The equilibrium distri- bution depends on the service distribution only through its mean.  ...  Serfozo (1-GAIT-I; Atlanta, GA) 94g:60172 60K25 60G70 McCormick, William P. (1-GA-S; Athens, GA); Park, You Sung (1-GA-S; Athens, GA) Approximating the distribution of the maximum queue length for M/M_  ... 

The price of forgetting in parallel and non-observable queues

J. Anselmi, B. Gaujal
2011 Performance evaluation (Print)  
the coecient of variation of the service time distributions.  ...  Finally, we put our results in the context of game theory revisiting the Price of Anarchy (PoA) of parallel queues: It can be decomposed into the product of the PoA achieved by a probabilistic broker (  ...  Therefore, the PoF is the ratio between the response times of a M/GI/1 and of a Γ/GI/1 having the same mean arrival rate and service time distribution.  ... 
doi:10.1016/j.peva.2011.07.023 fatcat:5areqalrhfeibdf3vytx44tdxa

Queueing-theoretic approaches for dynamic scheduling: A survey

Daria Terekhov, Douglas G. Down, J. Christopher Beck
2014 Surveys in Operations Research and Management Science  
of queueing approaches.  ...  Scheduling Queueing A survey of dynamic scheduling in manufacturing systems (Ouelhadj and Petrovic, 2009) Queueing theory in manufacturing: A survey (Govil and Fu, 1999) Scheduling and control of flexible  ...  One of the most important results is that the waiting time in an M/GI/1 queue with vacations follows the distribution of the sum of two independent components: the waiting time in an M/GI/1 queue without  ... 
doi:10.1016/j.sorms.2014.09.001 fatcat:q3qodawkwnawneatlnzm4depcm

On First Come, First Served Queues with Two Classes of Impatient Customers [article]

Ivo Adan, Brett Hathaway, Vidyadhar G. Kulkarni
2018 arXiv   pre-print
Analyzing these systems using a queue length process proves intractable as it would require us to keep track of the class of each customer at each position in queue.  ...  of customers waiting in queue.  ...  Iravani and Balcıoglu [17] use the level-crossing technique proposed in Brill and Posner [8] and Brill and Posner [9] to study two M /GI/1 settings.  ... 
arXiv:1710.03798v2 fatcat:5sa2plmkynaalbydfoasq2huyy

Geo/Geo/1/N Queue with In-Immune and Immune Service Killing Discipline

Madhu Jain Madhu Jain
2012 journal of King Abdulaziz University Engineering Sciences  
The stationary probability distribution and other performance measures are derived in terms of the generating functions.  ...  from any where in the queue, otherwise get lost.  ...  M/GI/1 queues have been studied by Zhu and Zhang [9] , in which both positive and negative arrivals require a service.  ... 
doi:10.4197/eng.23-1.6 fatcat:ezap7sp5lfgqbbsoi4trdtdezy

Simple and explicit bounds for multi-server queues with 1/(1 - ρ) (and sometimes better) scaling [article]

David A. Goldberg, Yuan Li
2022 arXiv   pre-print
Our main results are bounds for the tail of the steady-state queue length and the steady-state probability of delay.  ...  The strength of our bounds (e.g. in the form of tail decay rate) is a function of how many moments of the inter-arrival and service distributions are assumed finite.  ...  We note that 1 2 E[(Sµ S ) 2 ] ρ 1−ρ closely resembles the steady-state expected number in queue in an M/GI/1 queue with inter-arrival times having the same distribution as A, and service times having  ... 
arXiv:1706.04628v2 fatcat:yterx725qberjgkgqen3f6zxdy
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