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Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times

Joseph Abate, Gagan L. Choudhury, Ward Whitt
1995 Operations Research  
In this paper, we focus on simple exponential approximations for steady-state tail probabilities in G/GI/1 queues based on large-time asymptotics.  ...  We relate the large-time asymptotics for the steady-state waiting time, sojourn time and workload.  ...  Table 3 compares exponential approximations for the tail probabilities of the steady-state workload and sojourn time with exact values computed using the algorithm in [11] .  ... 
doi:10.1287/opre.43.5.885 fatcat:bve2ogbh35fcrohpqeaobdzio4

Mean sojourn times in two-queue fork-join systems: bounds and approximations

Benjamin Kemper, Michel Mandjes
2011 OR spectrum  
The focus is on methods to quantify the mean value of the 'system's sojourn time' S: with S i denoting a job's sojourn time in queue i, S is defined as max{S 1 , S 2 }.  ...  This paper considers a fork-join system (or: parallel queue), which is a two-queue network in which any arrival generates jobs at both queues and the jobs synchronize before they leave the system.  ...  Acknowledgments The authors would like to thank the editor and the referees for their useful and valuable comments.  ... 
doi:10.1007/s00291-010-0235-y fatcat:dl3tdlqynbb23mnntfrzweicc4

Tail-robust scheduling via limited processor sharing

Jayakrishnan Nair, Adam Wierman, Bert Zwart
2010 Performance evaluation (Print)  
Specifically, we derive new asymptotics for the tail of the stationary sojourn time under Limited Processor Sharing (LPS) scheduling for both heavy-tailed and light-tailed job size distributions, and show  ...  From a rare events perspective, scheduling disciplines that work well under light (exponential) tailed workload distributions do not perform well under heavy (power) tailed workload distributions, and  ...  of the sojourn time tail in the LPS-c queue.  ... 
doi:10.1016/j.peva.2010.08.012 fatcat:bdo643amrfb3hfxszwniimamam

Tails in scheduling

Onno Boxma, Bert Zwart
2007 Performance Evaluation Review  
This paper gives an overview of recent research on the impact of scheduling on the tail behavior of the response time of a job.  ...  We cover preemptive and non-preemptive scheduling disciplines, consider light-tailed and heavy-tailed distributions, and discuss optimality properties.  ...  Queueing models with light-tailed service requirement distributions, like the exponential distribution and more generally phase-type distributions, typically also have light-tailed sojourn time distributions  ... 
doi:10.1145/1243401.1243406 fatcat:inuprakr7zabldmk4wv5r6rl2u

Beyond processor sharing

Samuli Aalto, Urtzi Ayesta, Sem Borst, Vishal Misra, Rudesindo Núñez-Queija
2007 Performance Evaluation Review  
Probability, Networks and Algorithms (PNA) Software Engineering (SEN) Modelling, Analysis and Simulation (MAS) Information Systems (INS)  ...  Listed below are the names of the clusters and in parentheses their acronyms.  ...  time asymptotics for heavy-tailed DPS queues described in Subsection 3.2.  ... 
doi:10.1145/1243401.1243409 fatcat:43m7eioivzb3li2vjmoclgj3p4

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

S. C. Borst, O. J. Boxma, R. Núñez-Queija
2002 Lecture Notes in Computer Science  
(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.  ...  (ii) The M/G/1 LCFS-NP queue For LCFS Non-Preemptive priority, the waiting time is equal to 0 with probability 1 − ρ, and with probability ρ it is equal to a busy period starting with a residual service  ... 
doi:10.1007/3-540-46029-2_1 fatcat:3pn3kd4wqrcdjk3alv4imelbzm

Heavy Traffic Analysis of Polling Systems in Tandem

Martin I. Reiman, Lawrence M. Wein
1999 Operations Research  
to compute the sojourn time distribution for a customer that arrives to find the network in a particular state.  ...  When setup times are zero (except perhaps at the first station) and additional "product-form" type assumptions are imposed, we find the steady-state sojourn time distribution for each customer type.  ...  The authors are grateful to Chalee Asavathiratham and Beril Toktay for performing the numerical computations reported in Section 4, and to the referees for their helpful comments.  ... 
doi:10.1287/opre.47.4.524 fatcat:fn5r27ogzbhw3e2lwx7n6qkkuu

Load balancing policies with server-side cancellation of replicas [article]

Rooji Jinan, Ajay Badita, Tejas Bodas, Parimal Parag
2020 arXiv   pre-print
Popular dispatching policies such as the join shortest queue (JSQ), join smallest work (JSW) and their power of two variants are used in load balancing systems where the instantaneous queue length or workload  ...  We focus on a criteria that is based on the waiting time experienced by a job or its replica and analyze several variants of this policy based on the assumption of asymptotic independence of queues.  ...  The workload distribution for the cavity queue under policy π(p, T 1 , T 2 ) has a closed form expression for exponentially distributed service time, and is provided in Corollary 10.  ... 
arXiv:2010.13575v1 fatcat:qrv7iwsnabbcbkyl2n42mz6zl4

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)  
distribution, and (ii) what is the effect of various well-known scheduling disciplines on the tail behavior of the waiting-time and/or sojourn-time distribution?  ...  After introducing the model and reviewing the main results for various basic disciplines in Section 2, we discuss four different methods for obtaining the tail behavior of waiting-time and/or sojourn-time  ...  (ii) The M/G/1 PS queue. Theorem 2.2 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 requirement tail.  ... 
doi:10.1016/s0166-5316(03)00071-3 fatcat:nuto7ak3unc4bgc2q6uqbxdwva

Large deviations of sojourn times in processor sharing queues

Michel Mandjes, Bert Zwart
2006 Queueing systems  
C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a PNA Probability, Networks and Algorithms Probability, Networks and Algorithms Large deviations of sojourn times in processor sharing queues  ...  The present paper departs from the exponentiality assumptions required in (1.1): we analyze sojourn-time asymptotics in the GI/G/1 PS queue, for a broad class of lighttailed service-time distributions.  ...  Let, as before, W denote the workload at time 0. The likelihood ratio is composed from contributions of the items (i), (ii), and (iii) above.  ... 
doi:10.1007/s11134-006-5567-6 fatcat:bpfbk2bb4fed5pywc46fuks4bi

A large-deviations analysis of the GI/GI/1 SRPT queue

Misja Nuyens, Bert Zwart
2006 Queueing systems  
We consider a GIIGI II queue with the shortest remaining processing time discipline (SRPT) and light-tailed service times.  ...  Our interest is focused on the tail behavior of the sojourn-time distribution. We obtain a general expression for its large-deviations decay rate.  ...  Acknowledgments We would like to thank Marko Boon for helping us out with the numerics in Section 6.1, and Ton Dieker and Michel Mandjes for several useful comments.  ... 
doi:10.1007/s11134-006-8767-1 fatcat:s2ohkd54hzfw5a7gl4tcciklry

ASIdE: Using Autocorrelation-Based Size Estimation for Scheduling Bursty Workloads

Ningfang Mi, Giuliano Casale, Evgenia Smirni
2012 IEEE Transactions on Network and Service Management  
Extensive experiments show that (1) ASIdE achieves good service time estimates from the temporal dependence structure of the workload to implicitly approximate the behavior of SJF; and (2) ASIdE successfully  ...  Temporal dependence in workloads creates peak congestion that can make service unavailable and reduce system performance.  ...  ACKNOWLEDGMENTS We would like to thank Feng Yan for his assistance with the Microsoft trace.  ... 
doi:10.1109/tnsm.2012.041712.100073 fatcat:e2vz7atk45axdjwdripxj3ghre

Sojourn time asymptotics in processor-sharing queues

Sem Borst, Rudesindo Núñez-Queija, Bert Zwart
2006 Queueing systems  
In contrast to the simple geometric queue length distribution, the sojourn time lacks such a nice closed-form characterization, even for exponential service requirements.  ...  The state-of-the-art with regard to sojourn time asymptotics in PS queues with light-tailed service requirements is also briefly described.  ...  In particular, the above result implies that if B 1 is exponentially distributed, then the sojourn time has an exponentially bounded tail as well.  ... 
doi:10.1007/s11134-006-7585-9 fatcat:fugrba5pvvho5meoepsx2mhn7a

Time-Stable Performance in Parallel Queues With Non-Homogeneous and Multi-Class Workloads

Soongeol Kwon, Natarajan Gautam
2016 IEEE/ACM Transactions on Networking  
Based on time-stability, our suggested approach can provide performance bounds and guarantees for time-varying and transient system.  ...  We assume that the underlying environment is such that at all times the load from each class is very high and a large number of servers are necessary which, for example, is fairly common in many data centers  ...  The authors thank the associate editor and five reviewers for their comments that resulted in significant improvement of the content and presentation of this work.  ... 
doi:10.1109/tnet.2015.2406280 fatcat:br4cnlnil5btzf5hyfaecubxgy

Sojourn time asymptotics in Processor Sharing queues with varying service rate

Regina Egorova, Michel Mandjes, Bert Zwart
2007 Queueing systems  
This paper addresses the sojourn time asymptotics for a GI/GI/· queue operating under the Processor Sharing (PS) discipline with stochastically varying service rate.  ...  Our focus is on the logarithmic estimates of the tail of sojourn-time distribution, under the assumption that the jobsize distribution has a light tail.  ...  Concluding remarks We have considered a PS queue with fluctuating service rate and light-tailed service times and established logarithmic tail asymptotics for the sojourn time in a Processor Sharing queue  ... 
doi:10.1007/s11134-007-9026-9 fatcat:uxsl2idbyrc7taanrruod3htje
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